Table of Contents - learninglinkshub.org.au · Web viewMathematics has a very precise vocabulary and the language of mathematics in a broader sense requires specific instruction

Addition & Subtraction Facts Intervention Handbook

Table of ContentsTable of Contents..........................................................................................1

Introduction....................................................................................................3

Assumptions of this Intervention............................................................3

Progression through this Intervention...................................................3

Intervention Principles................................................................................5

Glossary...........................................................................................................6

Manipulatives: Physical & Virtual............................................................7Unit 1: Counting Numerals........................................................................9

Unit 2: Place Value.....................................................................................12

Unit 3: Counting Patterns........................................................................21

Unit 4: Counting Concepts.......................................................................24

Unit 5: Addition Facts +0.........................................................................28


Unit 7: Addition Facts +10......................................................................36


Unit 9: Using Known Facts to Solve for Unknown (Missing Addends)........................................................................................................44

Unit 10: Addition Facts + 9.....................................................................46

Unit 11: Addition Facts - Doubles..........................................................50

Unit 12: Addition Facts - Almost Doubles (Associative Property)..........................................................................................................................53

Unit 13: Addition Facts - Adding to 10................................................57

Unit 14: Remaining Addition Facts.......................................................60

Unit 15: Subtraction Facts with 0 & 1..................................................63

Unit 16: Subtraction Facts with 10.......................................................70

Unit 17: Subtraction Facts with 2..........................................................72

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Unit 18: Subtraction Facts with 9..........................................................75

Unit 19: Subtract with Doubles..............................................................78

Unit 20: Subtraction Facts from 10......................................................81

Unit 21: Remaining Subtraction Facts.................................................84

Where to now?.............................................................................................89

Second Pathway: Tandem Addition & Subtraction Facts.............91

Fact Family 1: Zero....................................................................................92

Fact Family 2: One.....................................................................................94

Fact Family 3: Ten......................................................................................97

Fact Family 4: Two.....................................................................................98

Fact Family 5: Nine....................................................................................99

Fact Family 6: Doubles...........................................................................100

Fact Family 7: Making & Subtracting from 10................................102

Fact Family 8: Almost Doubles............................................................103

Fact Family 9: Remaining Facts...........................................................104

Session Planning Form A........................................................................107

Session Planning Form B........................................................................108

Resource Summary..................................................................................110

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IntroductionAddition and Subtraction are the first two operations to be understood by students, in preparation for multiplication and division. Addition is about combining or “adding” amounts or numbers together to find a total or sum. Subtraction is the inverse or opposite operation involving separating or “subtracting” amounts or numbers to find the difference. To maximise the learning time and connections between these operations we will introduce them in close proximity. We will begin the intervention intervention by introducing a group of core addition facts, then solving for an unknown number (which is the introduction to subtraction) and then link to subtraction facts as the addition facts are known and understood. We will be working with smaller numbers initially to build fluency and support students in retrieving known maths facts to solve or work out new maths facts. Hence, much attention is placed on “knowing” core facts and the time required for students to become fluent here will differ for each student.

Assumptions of this InterventionThis intervention is intended for students who have experienced at least 1-2 years of schooling and is suitable for all subsequent years of schooling. Although the early concepts (e.g., counting, subitising, numeral identification) within this intervention are suitable for younger children, we recommend a much longer period working with these concepts if they are being introduced for the first time. They are included in this intervention to ensure a strong understanding of the foundation skills in mathematics before we connect these to the operations. Our intervention leaves no stone unturned; we ensure these pre-requisite skills are fully understood before expecting students to use these in calculations.

Progression through this InterventionThe first half of this handbook provides a sequence for introducing core addition facts, introducing missing addends (or solving for unknown values) before progressing to subtraction facts. The cycle for teaching subtraction facts is very similar to

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addition facts, with a strong focus on using the known addition facts to retrieve the related subtraction facts.

This first pathway is suggested for:

students in lower primary grades; students who require extensive revision of a single

concept before progressing; and students who do not have a conceptual understanding of

addition means counting on and subtraction means counting back.

The second half of this handbook provides an alternate sequence where addition and subtraction facts are introduced in tandem, as a set of related facts (e.g., working with 0, 10, doubles …). This pathway promotes learning a single addition fact and then focussing on retrieval of this fact to solve multiple facts going forward. It is more strongly strategy based.

This second pathway is suggested for:

students who understand addition means counting on and subtraction means counting back, but cannot recall the answers;

students from mid primary who are expected to be working with multiple digits in all four operations; and

students who respond well to the first three facts *

This final point is the greatest caveat here. Unless you are introducing addition for the first time for a student, the second pathway will yield stronger connections between the numeral facts and reduces the time needed to introduce these. Extended time is then available for spaced interleaved retrieval practice, strengthening the students’ capacity to recall addition facts to solve subtraction facts. However, if you begin with the second pathway and your student is experiencing significant difficulty swapping between the operations after the first three numeral groups are introduced (0, 1, 10) simply return to the first pathway to focus on addition before introducing subtraction and solidifying the connections between these.

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Intervention PrinciplesAs with all Learning Links interventions there are several research-informed principles which underlie the development and delivery of the intervention.

Pre-test to identify where gaps are presento One Minute Basic Maths Facts Test identifies whether

addition is age appropriate, otherwise all students begin with addition.

o Learning Links Numeracy Screener identifies the competencies related to counting forwards and backwards, identifying and writing numerals, subitising common numbers and place value awareness.

Retrieval Practice: Review previously learnt materials in all sessions

o Each session begins (and can end with) brief retrieval practice of previously learnt materials. Weekly session recording forms allow you to prepare for this, the inclusions are listed at the beginning of each Unit outline and there are extensive decks available with all required numerals and facts.

Explicit teaching of new topics with a focus on Make – Say - Record

o Physical and virtual manipulatives are the starting point for all concepts, Make with Materials – Say Aloud - Record with Writing is a common instructional thread throughout. You’ll be reminded of this regularly with the image below:

o Each Unit outline begins with a clear set of outcomes.

Consider cognitive load when introducing conceptso Be mindful of selecting materials and links to real

world examples that are enough to engage students, but not too much to distract from the learning.

Persist until mastered o This aspect is key, continue with I do, We do, You do

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required, provide oral and written practice opportunities – keep going and don’t move on until ready. Weekly retrieval practice will inform when progression can occur.

Apply to worded problems throughouto As computational competence is beginning to be

observed, apply to worded problems – these shouldn’t be too complex, but always with a focus on the strategy being learned.

Record Progresso Keep track of concepts understood so that retrieval is

possible and easy each week – use discretion as to recording progress together with the student, it is motivating when success is occurring.

Continue to review previous topics in subsequent weeks (spaced interleaved retrieval practice)

o A repeated item for a very important reason, you’ll be covering lots of content (hopefully) with students, the focus of this intervention isn’t on rote memorisation of all addition and subtraction facts, but retrieval of relevant known facts when required to generate new relationships and facts.

GlossaryMathematics has a very precise vocabulary and the language of mathematics in a broader sense requires specific instruction. Where possible, try to include specific language in your instruction, focus on one word initially to introduce a concept and then interchange the language during retrieval practice activities to ensure the concept is more widely understood.

Addend: Numbers being combined in an addition questionAssociative Property: We can regroup or re-associate addends in a problem without affecting the sumCommutative Property: When adding whole numbers, the order of addends can change without affecting the sumDifference: Answer to a subtraction problemDigit: There are 10 digits in mathematics, 0-1-2-3-4-5-6-7-8-9 which form the numerals in our number system to represent the numbers required

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Minuend: Number being changed in a subtraction problem (the number being subtracted from)Number: Describes the total or count (quantity) that is represented by numerals – it is an idea or concept until it is labelled or recorded with a numeralNumeral: Describes the name (label) or symbol (written) we use to describe a numberPlace Value: Describes the worth (value) of a digit, based on its position (place) in the numeral. It describes the kind of counting numeral in the whole numeral: units-tens-hundred-thousands … We can only combine numerals with the same value.Subtrahend: Number being taken away from a minuend (the number being subtracted)Sum: Answer to an addition questionUnits: Correct terminology to describe a single units / numeral – often referred to as “ones”, however as “one” is also the label for a numeral we recommend using the label units to describe a single numeral

Please reach out if additional terms are required within this intervention handbook or if you identify a word incorrectly used throughout – specificity of language is important but very hard to maintain 100% accuracy with, please help us ensure this handbook is as accurate as possible. Thanks!

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When you see this sign throughout the handbook it means “Important Note - Please Read Me!”


Manipulatives: Physical & VirtualTo model place value for students (and all of the activities throughout the intervention using the Make-Record-Say methodology), you’ll need to begin by selecting your concrete materials or manipulatives.

There are many manipulatives available to represent place value in our number system. We will be using blocks, similar to MAB or Base 10 for all of our representations throughout the intervention. MAB blocks are the only materials which provide proportional units, tens and hundreds representations with uniform size and shape. Others are included for your reference.

MAB blocksAlso known as Base 10 Materials or Dienes Blocks. These are 3D cubes, with proportional measurements – 1cm3 (1x1x1) to represent units, 10cm3 (10x1x1) to represent tens and 100cm3

(10x10x10) to represent hundreds. They are available as wooden blocks with no colour, coloured plastic blocks in 3D representations. When working online they are also available as 2D digital manipulatives on web-based interventions or tablet apps. They are available as magnetic 2D representations 1cm2

(1x1) to represent units, 10cm2 (10x1) to represent tens and 100cm2 (10x10) to represent hundreds.

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If you have access to no other materials, printing 2D representations of MAB blocks are the most uniform and consistent way to support understanding of place value.

There are other alternatives to represent place value if MAB alternatives are simply not possible.

Wooden Sticks Also known as paddle pop sticks purchased from the discount shop can be used singularly to represent units, bundled as a group of 10 with glue or a rubber band to represent 10 and then 10 of these bundles glued or banded together to represent one hundred. They will still model place value, although the units begin very large (similar size to a ten in MAB materials used at school).

Wooden CubesRegular cubes also from the discount shop can also be glued together as a cheaper alternative to MAB blocks. This can address the issue of the initial size of the units block.

Interlocking BlocksThese are available from education suppliers can be used to model place value in the early stages of mathematics learning and have additional uses throughout all mathematics learning. It is not possible to have one colour for units, tens or hundreds using these interlocking blocks (unless you’ve bought large amounts) but there is a consistent size to these.

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AbacusAn abacus uses beads (9 in each place value position) to represent and count numerals. Although these have been used for centuries as a counting tool, be aware there is no dimensional difference between the units and the tens, only their place. These may be better used later in a child’s mathematics learning journey once they have fully understood that the value of 70 is very distinct to the value of 7.

Cuisenaire Rods These are definitely making a comeback as a maths manipulative; they demonstrate the value of counting numerals 1-10 well. In a set of Cuisenaire rods units and tens are well represented and very similar to MAB blocks, however there is not an equivalent hundred block (or capacity to make this).

Other CountersRegular counters of any size can be used to represent place value on a place value chart once the student understands and can apply knowledge of the magnitude of numerals in place value.

All images obtained from eBay listings.

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Unit 1: Counting Numerals Our number system is based on 10 (known as deci), there are only 10 digits (0-1-2-3-4-5-6-7-8-9) which form all of the numerals used to represent numbers. We will begin with a review of these 10 digits, in terms of identification, writing and understanding.

Pre-testThis will already have been covered in the initial screening process. If in doubt, quickly complete these tasks.

1. On a lined piece of paper, ask the student to write these 10 digits (say aloud and in random order) 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 (can extend 10-20 to ascertain if appropriate spacing between multiple digits is occurring)

2. Present flashcards, or use Digit PPT, or simply point to the digits on the written page if well formed, ask student to say the numerals (can extend 10-20 in preparation for counting demonstration.

3. Count as far as you can go

If any digits are not formed clearly when writing or are not instantly recognised or made with materials. STOP HERE! Review digit formation 0-9, with materials and flashcards introducing 2-3 numerals at a time. They are the foundation for all

mathematics learning as they are the only 10 symbols needed in the entire number system and without this conscious attention is needed to recognise the numerals.

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Digit FormationTwinkl and other resource sites have many rhymes and resources available to revise numeral formation. Please be mindful of cognitive load when selecting rhymes for numeral formation as extraneous details can detract from the learning process. Below are simplified, directional cues. Add dotted thirds paper, grass and sky paper and any additional tools to ensure digit formation is automatic, requiring no conscious processing.

0 Start at the top, go around to your left like we’re writing a capital O 0

1 Start at the top and go straight down to the bottom of the line 1

2Start a little lower to the left, like you’re drawing a heart and at the bottom of the line move straight across to the right

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Starts like a 2, but halfway round we come into the left then go back out to make another curve 3

4Start at the top and go down at a little angle, halfway down come across like you’re drawing a triangle and lift your pencil. Now draw a shorter straight line down, like a small 1

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Start at the top right and draw a straight line across, then down and around in a curve like the bottom of number 3 5

6Start at the top and head down like number 4, but rounded and keep going to the bottom of the line and come up halfway with the curve line and join it up

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Start at the top left and draw a straight line across, then down on an angle right to the 8bottom of the line 7

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8Start at the top and write and then come back and around to close the whole number up 8

9Start at the top right and draw rounded line across, around and up, like an a then go right down to the bottom of number 3

9Counting IntroductionWe recommend starting to count numerals from 0 – zero/nothing – and continue to 9 before starting again with 10, 11, 12 … 19 and 20, 21, 22, 23 … 29 and so forth. This supports the rhythm/pattern of counting or saying the numerals, bridging from 9 to the next decade and later in mathematics learning understanding the concept of integers, or negative numbers (0 is the anchor number before the counting patterns resume as negative numbers -1, -2, -3 …) The transition in counting from 9 to 10 (or the next decade) is an essential skill to support students working with larger numerals. The rehearsal of counting beginning with 0 and anchoring the transition from 9 to the next decade with a new line reinforces this concept. The counting grid for this intervention has been designed in this way (see below).

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The two sets of patterns to pay most attention to are the teens and the decades. You’ll notice these are in different colours on the counting grid. Explicit instruction in place value is the most effective way to deal with the names or labels for these numerals being unpredictable and not as closely related to their value. All other patterns in counting are very regular and predictable, the numerals 10-11-12-13-14-15-16-17-18-19 and 10-20-30-40-50-60-70-80-90-100 have unique labels that are different to the rest of the predictable labels and can often be a stumbling block for many students.

Even if students are counting forwards with relative ease, the demonstration of the place value composition and the associated label can be quickly completed and ensures the correct knowledge when trading is introduced later in the

intervention.

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Unit 2: Place Value By the end of this unit, students will be able to make – write - say:0 1 2 3 4 5 6 7 8 9

10 20 30 40 50 60 70 80 90100

10 11 12 13 14 15 16 17 18 19 20 Numerals 0 – 100 (and beyond)0 1 2 3 4 5 6 7 8 910 11 12 13 14 15 16 17 18 1920 21 22 23 24 25 26 27 28 2930 31 32 33 34 35 36 37 38 3940 41 42 43 44 45 46 47 48 4950 51 52 53 54 55 56 57 58 5960 61 62 63 65 65 66 67 68 6970 71 72 73 74 75 76 77 78 7980 81 82 83 84 85 86 87 88 8990 91 92 93 94 95 96 97 98 99100 101 102 103 104 105 106 107 108 109110 111 112 113 114 115 116 117 118 119120 121 122 123 124 125 126 127 128 129…

Equipment Required Counting Grid Manipulatives (physical or virtual) Numerals (flashcards or virtual display file) Writing materials (books & pencils or virtual whiteboards) Place Value supports (optional)

Demonstration Script IntroductionSay, “Every numeral has a place and the worth (or value or quantity) of that numeral depends on where it is (or its position or place in a numeral). These places (or positions) are called (or labelled): units, tens, hundreds, thousands, ten thousands …”

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If you’re working with older students, you may wish to also show the Decimal Place Value PPT for reference and familiarity – one pattern of numbers helps to know others.

We recommend using the label “units” instead of “ones” when referring to place value as “one” is a label for a numeral. You’ll also notice bracketed terms in the explanations of terms or later in the handbook the scripts for instruction. These brackets

are the supplementary words to include in your language in subsequent sessions once initial understanding is observed.

Begin with the numerals 0-9 to quickly develop familiarity with the materials before introducing the teens and beyond. Ensure you provide students with opportunities to Make – Say – Record at all times.

Making Numerals – Introduction to Place Value (0-10)Say, “This is the numeral 0, its name is zero and we write it like this 0 (model) – this numeral represents no items when we’re counting. There are no blocks on the table, there is nothing on the table, there are zero blocks on the table” (place 0 numeral card on the table, show 0 virtually or write 0 on a magnetic board, piece of paper, book.)

Say, “This is the numeral 1, its name is one and we write it like this 1 (model) – this numeral represents one item when we’re counting. There is one block on the table” (place 1 numeral

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0


card on the table, show 1 virtually or write 0 on a magnetic board, piece of paper, book).

Say, “This is the numeral 2, its name is two and we write it like this 2 (model) – this numeral represents two items when we’re counting. There are two blocks on the table” (place 2 numeral card on the table, show 2 virtually or write 2 on a magnetic board, piece of paper, book).

Continue this brief demonstration through to 10 and the table or virtual whiteboard will look like this.

You’ll notice that all of the diagrams here have the blocks increasing vertically in a line – this is purposeful, to model the number is getting closer to 10 block but is less than that currently.

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1

2

111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111

222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222


Making Numerals – Introducing 10 BlockOnce you have reached an understanding of 10 (Make – Record – Say) you can now talk about the teens, there are now two digits to be working with and the value of the numeral is now changing because its place is beginning to change.

Once you reach 10 by counting 10 individual units blocks, it is time to introduce the 10 block. Bring the 10 block directly next to the stack of 10 units blocks and say “This 10 block is the same as the 10 units blocks you’ve just counted (check, confirm, have student agree). Only one digit (0-9) can be in any place, once we reach the numeral 10 we have two numerals and will use these 10 block to represent these numerals. When we write the numeral 10 the 1 represents the 10 block and the 0 means there are no units in the number (model with cards and writing)”

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Change the block representation initially to look like this below and then move the 10 down to underneath the 0 to physically represent the counting chart.

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Swap the 10 units blocks for

a 10 block

The move the 10 block

underneath the 0 to replicate


To reinforce this concept (if further assistance is required), you could use a place value layout on the table. Say, “10 units blocks don’t fit on our place value chart, because we’ve now moved into the next place in our number system – tens. On this mat 10 units blocks physically cannot be placed here as they don’t fit, 10 tens blocks cannot be placed here as they don’t fit.” If you’re using different materials, you can simply create a board to match the materials you’re using.

Making Numerals – DecadesThe teens and the decades are the only groups of numbers we need to pay some special attention to. Your table or electronic whiteboard will already have a 10 block set up (if not get this ready)

Say, “Here are 2 tens (model 20). We call this numeral twenty, it is made up of 2 tens and no (zero) units and we write it like this 20 (model) – this numeral

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represents twenty items when we’re counting.” Clear the blocks, place the numeral 20 on the table or virtually and say “Make 20”

Say, “Here are 3 tens (model 30). We call this numeral thirty, it is made up of 3 tens and no (zero) units and we write it like this 30 (model) – this numeral represents thirty items when we’re counting.” Clear the blocks, place the numeral 30 on the table or virtually and say “Make 30”

Continue until you reach 100, making – writing and saying the decades. Adding a new 10 block each time in the pattern. Once you reach 100, model how to trade (swap, exchange) the 100 block as we now have 3 digits. The desk or virtual layout will change from ten 10 blocks to one 100 block.

Say, “These are the decades – 0 10 20 30 40 50 60 70 80 90 100 and are the first numerals in each pattern (or line or group) when we’re counting. We are counting up by equal groups of 21© Learning Links


10, we don’t say 3 tens, we say its correct name of thirty – but it is important we know it is made of up 3 tens. This information will help you later in adding, subtracting, multiplying and dividing big numbers!” (show on counting grid)

Say, “Knowing the decades, or first number in a counting pattern means you can count almost every number to 100. The counting pattern 0 – 1- 2- 3- 4- 5- 6- 7- 8- 9 repeats throughout almost all of the remaining numbers.”Read to or with the student (from the counting grid) “20 – 21 – 22 … 40 – 41 – 42 … 90 – 91 – 92 – 93.”

Making Numerals – TeensOnce your student has reached an understanding of numerals 0 to 10 (Make – Record – Say) and then the decades (10-100) you can now talk about the teens. By this stage the students will be familiar with two digits from their review of decades and that the value of the numeral changes because its place is beginning to change.

Say, “There is another group of numbers, like the decades which we need to pay special attention to. They have names (or labels) that don’t easily show the place value of the numerals, just as twenty, thirty, forty …. We’ll be looking at the numbers after 10 or the teens.”

Say, “This is the numeral 11, it is made of one 10 and one units (make this with blocks) – ten and one more, its name is eleven and we write it like this 11 (model).”

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Clear the table, place the 11 numeral card on the table, show 11 virtually or write 11 on a magnetic board, piece of paper, book) and say “Make 11”.

Say, “This is the numeral 12, it is made of one 10 and two units (make this with blocks) – ten and two more, its name is twelve and we write it like this 12 (model).” Clear the table, place the 12 numeral card on the table, show 12 virtually or write 12 on a magnetic board, piece of paper, book) and say “Make 12”.

Continue for the remainder of the teens – this can occur quickly if the pattern is understood or more slowly and repeatedly if the concept is taking time to be fully understood. Teens occur very quickly in our counting patterns, if conscious processes are needed to remember that 13 comes after 12 or that 15 is made up of 10 and 5 more, the computations you’re working on with the student are not accessible.

To conclude, say, “These are the teens –10 11 12 13 14 15 16 17 18 19 and are the set of numerals after 10 that have been given special (unique, their own) names (or labels) when we’re counting.”

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Making Numerals – Place Value to 100 and BeyondSpending time ensuring 0-20 and the decades are well understood provides a solid foundation to introduce all numerals to 100 and beyond, as the concept of place value is beginning to be understood.

Begin with a modelled demonstration to ensure the concept is underway and then continue to include make-write-say activities for numerals 0-100 and then move to 0-1000 in retrieval practice tasks throughout the duration of the intervention. Please note that anything beyond 0-1000 is challenging in relation to manipulatives, stay with smaller numerals initially. Aim to progress to “making” the numerals by placing numeral cards in the positions on the place value chart to represent there would be, for example, 8 hundreds blocks, in that position.

Modelling activities for place value to 100 and beyond should include:

Adult makes numeral with blocks – student writes and says numeral

Adult says numeral – student makes and writes numeral Adult writes numeral – student makes and says numeral Ensure that you include numerals with 0 acting as a place

holder in larger numerals (e.g., 605 means 6 hundreds, zero tens and five units – the zero is important)

You can supplement this with colouring activities, similar to those found in textbooks or pre-colour/shade these

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representations for more traditional school-based work in relation to reading numerals. This is a paper and labour-intensive activity but may be required for your student.

Making or Identifying Larger or Smaller Numbers?Questions in commercial textbooks or assessments of place value include variations of:

Make the largest/smallest number possible with these 3+ digitsWhich number is smaller/larger?

These questions require students to know the concept that the value of numerals depend on their place within the larger numeral and then demonstrate this by ordering the numerals in ascending (smallest) or descending (largest) order. It is not a specific skill as such to master and as such has not been included within the activities in this handbook. However, the language of “Which of these two numerals is worth more / less? Represents the largest / smallest number or amount?” can be included during demonstrations.

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Unit 3: Counting Patterns The first units may require 1-2 sessions to confirm with certainty that your student can count to 100 and beyond confidently, represent numerals with manipulatives to reflect place value and write and say these numerals. This learning curve may have been far steeper for your students and has taken several sessions, this is time well spent.

Counting Patterns is a necessary extension or next step to ensure students can apply their knowledge of the number system to add and subtract. At its core addition is simply counting forwards and subtraction is counting backwards – some of our students will need a little bit more rehearsal to be fluent with these counting patterns. This has been established as a units in the handbook, however, there is little demonstration required – it is more a units of retrieval practice

By the end of this unit, students will be able to: Count forwards & backwards by 1s (from 0

then random numbers) Use language of “next number” and “number

before” Count forwards and backwards by 10s (from 0 then

random numbers) Use language “ten more” and “10 less”

Equipment Required Counting Grid Numeral Patterns ALL (presentation deck, need count

forwards & backwards slides, next number, number before)

Please Note: If manipulatives are required, review Units 1 again to ensure the concept of numerals and their place within 0-100 is more fully understood.

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The presentation decks for this intervention are slide decks with all of the required patterns in order in one file (hence ‘ALL’ at the end of each filename). To use these decks at each stage of the intervention you’ll need to select the slides you

need (either as printed flashcards or virtually).

Virtually this is quickly achieved by making a copy of the file, delete the slides your student isn’t ready for yet and then move the slides around in random order (change the view to contact sheet and then simply move the slides). In this way you’ll have several files with the presentation decks to suit a students’ needs.

The slide deck begins in order.

Then you simply swap them around for random presentation.

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This random format can then be shared virtually in slide show mode or can be printed for worksheets by selecting your slides and then entering the Print window. Here you can print the maximum number of slides to a page (e.g., 16). If you wish for more than this to be included on a page, print this page to a PDF file where you can repeat the shrinking process (print 1-4 pages to a single page). Only one presentation deck is available with all of the files so that you can easily customise the materials for the students. It is simply a matter of selecting the slides you need, randomising these and then reducing the slide size by increasing the number of slides printed to a single page to suit the student.

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Demonstration Script Say, “Now you know your numerals and how to make, write and say these confidently we will practice counting forwards and backwards so you can use these numbers to quickly add and subtract.”

The remainder of this units is not a demonstration script as such but includes strategies to support students who find the counting patterns more effortful. The goal for each of these is to respond with little hesitation and confidence, without the aid of manipulatives or the counting grid. These may be required initially, and if they are take your time to master one counting pattern before adding any further.

Activities for counting patterns should include:

Count forwards (from 0 then from any numeral) Count backwards (from 10, then from 20, then from any

numeral) What is the next number? What is the number before? Count forwards by 10 (from 0 then from any numeral) Count backwards by 10 (from 50, then from 100, then

from any numeral) What number is 10 after? What number is 10 before?

Additional counting patterns to support addition and subtraction in later units of this handbook include:

Count forwards by 2’s with even numbers (from 2, then from any numeral)

Count forwards by 2’s with odd numbers (from 1, then from any numeral)

What is the next odd number? What is the next even number?

Most sessions should begin with some counting practice and these patterns can be included in the retrieval tasks. Where they are a requirement for the addition or subtraction facts it is also included as part of the demonstration script for review.

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There are multiple opportunities to review this, but early introduction will support its mastery sooner.

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Unit 4: Counting ConceptsThroughout the first four units of Addition and Subtraction Facts, several key concepts related to counting are assumed. They are listed here for your reference and to assist in identifying where students may still be requiring additional support. This unit will focus on subitising, progressing from single unit blocks to blocks which represent 2 – 9 and relies on an understanding of these earlier concepts.

Stable OrderThis is the repeated pattern of counting – the counting words or numeral labels we use (0-9). Students experience challenges with the teen numbers and moving to the next decade from 9 as this pattern is less common.

One-to-One CorrespondenceEach counting object in a group must be counted but counted only once. This is a very early concept in numeracy and difficulties here need to be addressed prior to any combining of numerals.

CardinalityThe last number in a count represents how many or the total of that group. Difficulties here present when students count a group of counters and then count again if asked “how many?”, as they are not identifying the final number in the count is the total items.

ConservationThe count or total of a group of objects is unchanged if the objects are close together or spread apart. Similar to subitising in the sense that subitising resources often stretch objects apart far or close to reinforce recognition.

Order IrrelevanceCounting objects can begin from anywhere (left to right, top to bottom …), providing each item is counted only once and the last item counted represents the total.

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AbstractionAny item can be counted in a group and the total is the same, objects can be different sizes and each item still only represents one item.

SubitisingInstantly recognise a small group of numerals without the need to count those items individually. Subitising is a mathematics concept addressed at length in the first year of school (and often before) as it is strongly correlated with future success in mathematics (see Daniel Ansari’s work). Subitising Resources available for subitising in the early years will include visual recognition of objects, dots, symbols for numerals 1 to often 12. There are unlimited downloadable files available online for this. Your approach here will be influenced by the materials you’re using, age of the student.Units blocks have been used to date to represent the numerals in the units place during place value demonstrations. A small extension of the 10 block has also been introduced. The next step for students is to recognise three units blocks as 3 instantly and know what 3 means without needing to count 1-2-3. This supports 3 + 2 (start at 3 and count 2 more without needing to count 3 first).

We are going to refine this and only concentrate on subitising numerals and materials used widely in mathematics.

There is value in subitising Cuisenaire Rods or connected blocks or other segmented blocks to model the value of numerals 0-10

There is value in subitising numerals 1-6 in the dot pattern for dice as dice are used as a quick tool in review activities.

There is value in subitising symbols for card patterns 1-10 or 12 as these are used for review activities and rely on the instant recognition

By the end of this unit, students will be able to: Instantly recognise dot patterns on die Instantly recognise 2-9 blocks for counting Instantly recognise patterns on traditional

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Equipment Required Manipulatives (connected blocks, Cuisenaire Rods, Math U

See Blocks) Decks of Cards Dice Subitising cards

Demonstration Script

Say, “Here is 2 (place 2 units blocks on table).”

Say, “It is still worth 2 if I place it here (physically move on the table) or here (physically move again)?”

Say, “How many are here?” (point to total on table)Say, “How many are under my hand now?” (cover object). If incorrect, prompt with “Have I taken any away? Have I added any? Is it the same? – reinforce with I have not changed this, I have only covered this – it is the same, how many?

If using Cuisenaire Rods or Math U See Blocks or creating a set of other blocks, add this.

Say, “This is also 2 (show with the materials you’re using)”

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Say, “Are they the same?” (yes to confirm)Say, “When we use this 2 block we need 2”

Repeat for all numerals 1-9. 10 is not required as it has been used extensively up until now. Include reference to 0 – there are no blocks to represent this because it means nothing but is still a numeral we use in counting and holds value when there’s nothing in that place.

Language to support comparing numerals and recognising the magnitude of numerals (when multiple representations are on the table) can include:

Which one is worth more? Which one is worth less? Which one represents a larger amount? Which one represents a smaller amount? Which one represents a bigger total? Which one represents a smaller total?

Activities to consolidate this include:

Card Games: Memory, Concentration, Fish Find My Block: Placing blocks on the table (units and

collated) and asking, “find #” What colour is the # block? (if appropriate)

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The goal here is for students to see the 3 block you’ll be using (if you have a set of equipment with single and collated blocks) and instantly recognise this as 3. This is best if the collated blocks are one colour as there’s another memory cue during instruction for the remainder of the intervention. Some blocks for purchase also have the unit markings on them, providing an additional cue.

Try not to write the numerals on the blocks – this doesn’t aid memory of the connections needed in relation to the size (length) of numerals as it becomes a reading exercise.

Some students may only require one lesson for this demonstration, others will need the identification activities to be spaces (1-3, add 4 & 5, add 6 & 7 and finally 8 & 9). Your discretion is required to determine the pacing of this.

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Unit 5: Addition Facts +0 Retrieval Practice

Counting (identified patterns for review) Make – Say – Record Numerals What number (subitising, one-to-one

correspondence)

By the end of this unit, students will be able to: Add 0 to numerals, regardless of order (full set

shown below)

0 + 0

0 + 1

0 + 2

0 + 3

0 + 4

0 + 5

0 + 6

0 + 7

0 + 8

0 + 9

0 + 10

1 + 0

2 + 0

3 + 0

4 + 0

5 + 0

6 + 0

7 + 0

8 + 0

9 + 0

10 + 0

Equipment Required Manipulatives Addition Facts Grid Writing Materials Digit and Numeral Deck (add zero) Numeral Patterns ALL (add zero) Addition Facts ALL Deck (+0) Worded Presentations Deck Addition (+0)

You’ll notice the orientation of the materials change in the diagrams going forward. This is deliberate. When introducing place value, vertical orientations are used to visually represent three vertical columns the numerals will be written in. As we

move to computations, we turn the block horizontally, so that addition is represented as blocks getting longer and subtraction is represented as missing numerals.

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The demonstration scripts for the facts will be presented with the multiple language choices to include after initial teaching.

Say, “We have 2 (place corresponding block on table)”

Say, “Then we add nothing / get nothing / add zero / plus zero (do nothing on the table!)”Say, “How many do we have now?”

Complete this in reverse order throughout demonstration to introduce the concept of the commutative property (the order doesn’t matter when adding whole real numerals).

Say, “We have nothing or zero (do nothing on a blank table)”Say, “Then we add 2 / get # / plus #” (place corresponding block on table)

Say, “How many do we have now?”Once oral answers are correct add writing, initially modelled, then student writes. Both vertical and horizontal forms should be included in the demonstration. Both orders should be written.

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This is repetitive, it is supposed to be – it is designed to build confidence for students – one piece of “math” is really 4 and can be written in 8 different ways.

Continue with demonstrations for all of the addition facts below.0 + 0

0 + 1

0 + 2

0 + 3

0 + 4

0 + 5

0 + 6

0 + 7

0 + 8

0 + 9

0 + 10

1 + 0

2 + 0

3 + 0

4 + 0

5 + 0

6 + 0

7 + 0

8 + 0

9 + 0

10 + 0

Key MessageWhen we add zero to any numeral the sum is the same numeral.

Worded PresentationsSimply interchange names, items and numerals to provide adequate practice with worded presentations of the addition fact. Below is a sample of specific prompts for +0 (subsequent sections include more variety)

1. The door opened once but wouldn’t open again. How many times did the door open?

2. I ate # grapes before dinner. My dad wouldn’t let me have any more. How many grapes did I eat?

3. Brianna collected # points at school last week. This week is school holidays, and no points can be collected. How many points does Brianna have?

4. Christian ate # potatoes. He asked for more, but there were none left. How many potatoes did he eat?

5. It didn’t rain yesterday. Today it is raining. For how many days has it rained?

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RecordingColour, tick, add stamps to the +0 facts on the Addition Facts Grid when you’re comfortable this is appropriate.

ExtensionIf you’re completing this intervention in order, with the goal of consolidating learning for a student and are progressing through these earlier stages quickly, take the opportunity to extend the numbers to reinforce the concept. When we add zero to any number the number stays the same works for numbers above 10 as it does for the numbers 0-10 used in the demonstration above. Include bigger numbers (54, 82, 133) and crazy numbers (thousands) if appropriate for your student to explicitly connect the learning of very foundational concepts to the numbers they are likely to be seeing in their classroom work to demonstrate this learning is applicable and helpful to them at any stage of learning or age.

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Counting forwards by 1s Make – Say - Record Numerals What number (subitising, one-to-one

correspondence) Next number? +0


shown below)

1 + 0

1 + 1

1 + 2

1 + 3

1 + 4

1 + 5

1 + 6

1 + 7

1 + 8

1 + 9

1 + 10

0 + 1

2 + 1

3 + 1

4 + 1

5 + 1

6 + 1

7 + 1

8 + 1

9 + 1

10 + 1

Equipment Required Manipulatives Addition Facts Grid Writing Materials Digit and Numeral Deck Numeral Patterns ALL (Next Number?) Addition Facts ALL Deck (+1) Worded Presentations Deck Addition (5 examples in unit,

but deck can be randomised)

Demonstration Script Begin with the blocks set up 0-9.

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Say “Point to #. Now point to the numeral that is 1 more / 1 more than / the next number / add one / plus one.”Say, “If you add one to #, what do you have? / how many are there? / what is the total? / what is the sum?”Say, “Let’s check by adding one units block to # (add one units block on top of # to confirm the next number is the same as the model)

Repeat with any numeral 1-10 until student is confidently identifying the next number before working on a clear desk space and introducing writing. There are PPT materials prepared with next number review opportunities.

Say, “We have 3 (place the 3 block on table) and add one (add one units block to the 3). How many do we have?”

Prompts to support instant recognition that +1 is the next counting numeral include:

Number after # Next number after # # (say slowly to prompt student to continue counting and

say next numeral)

Discourage any attempt to count the first number, cover if required.

Ensure you consistently demonstrate the concepts using the model:

You’ll notice that there are several language choices embedded within the demonstration script.

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Select 1 for the initial introduction and then begin to insert varied language choices to improve transference.

Commutative PropertyThis is an incredibly powerful maths property to support the links between known facts to new facts. It underscores the power of focusing on addition facts first and building a strong connection between the three numerals involved in addition facts.

Key MessageWe can change the order of whole numerals when adding without changing the answer.

Demonstration Script Say, “Make 4 and add 1, what is the answer?” (responses should be fluent at this stage, if not return to earlier activities)

Say, “Make 1 and add 4, is this the same? is the answer the same?”

Write these associated algorithms vertically and horizontally in both orders.

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Continue demonstrations with all addition facts below:1 + 0

1 + 1

1 + 2

1 + 3

1 + 4

1 + 5

1 + 6

1 + 7

1 + 8

1 + 9

1 + 10

0 + 1

2 + 1

3 + 1

4 + 1

5 + 1

6 + 1

7 + 1

8 + 1

9 + 1

10 + 1

Key MessageWhen we add one to any numeral it is the next counting numeral.

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Worded PresentationsSimply interchange names, items and numerals to provide adequate practice with worded presentations of the addition fact. The list below can be modified to include +1 presentations.

1. There are # bears in my room and I find # outside. How many altogether?

2. I have # red pencils and # yellow pencils. There are # pencils altogether.

3. # apples are green and # are red. How many in all?4. Max sharpened # pencils before recess and # after

recess. How many pencils did he sharpen today?5. Trish is # years old. How old will she be in # years?


ExtensionIf you’re completing this intervention in order, with the goal of consolidating learning for a student and are progressing 45© Learning Links


through these earlier stages quickly, take the opportunity to extend the numbers to reinforce the concept. When we add one to any number it is the next counting number stays the same works for numbers above 10 as it does for the numbers 0-10 used in the demonstration above. Include bigger numbers (54, 82, 133) and crazy numbers (thousands) if appropriate for your student to explicitly connect the learning of very foundational concepts to the numbers they are likely to be seeing in their classroom work to demonstrate this learning is applicable and helpful to them at any stage of learning or age.


Make – Record – Say Numerals Counting forwards by 10s +0 +1

By the end of this unit, students will be able to: Count forwards by 10s Add 10 to numerals, regardless of order (full

set shown below)

10 + 0

10 + 1

10 + 2

10 + 3

10 + 4

10 + 5

10 + 6

10 + 7

10 + 8

10 + 9

10+ 10

0 + 10

1 + 10

2 + 10

3 + 10

4 + 10

5 + 10

6 + 10

7 + 10

8 + 10

9 + 10

Equipment Required Manipulatives Addition Facts Grid Writing Materials Digit and Numeral Deck Numeral Patterns ALL (teens) Addition Facts ALL Deck (+10) Worded Presentations Deck Addition (5 examples in unit,


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Demonstration Script Begin by confirming counting by 10’s pattern is confidently recalled. This unit then follows the same process as Add 1 and Add 2 (see diagram below) using the Make – Say – Record process. Use the addition facts listed above for demonstration.

Continue demonstrations with all addition facts:10 + 0

10 + 1

10 + 2

10 + 3

10 + 4

10 + 5

10 + 6

10 + 7

10 + 8

10 + 9

10+ 10

0 + 10

1 + 10

2 + 10

3 + 10

4 + 10

5 + 10

6 + 10

7 + 10

8 + 10

9 + 10

Key MessageWhen we add ten to any numeral it is the tens that change by just one more ten.

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Worded PresentationsSimply interchange names, items and numerals to provide adequate practice with worded presentations of the addition fact.

1. The boy has # cars. He gets # more for his birthday. How many cars does he have now?

2. # cars were in the car park when we arrived with our car. How many cars are there now?

3. Ava has # birds. She also has # fish. How many pets does Ava have in all?

4. # roses and # lilies are in a vase. How many flowers are in the vase?

5. There are # biscuits on the plate and # cakes. How many sweets are there to eat?

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Counting forwards by 2s – even numerals Counting forwards by 2s – odd numerals Odd & Even numeral identification (PPT

available) What number (subitising, one-to-one correspondence) Next even number? Next odd number? +0 + 1 +10

By the end of this unit, students will be able to: Count by 2’s (even & odd numbers) Add 2 to numerals, regardless of order (full set

shown below)

2 + 0

2 + 1

2 + 2

2 + 3

2 + 4

2 + 5

2 + 6

2 + 7

2 + 8

2 + 9

2 + 10

0 + 2

1 + 2

3 + 2

4 + 2

5 + 2

6 + 2

7 + 2

8 + 2

9 + 2

10 + 2

Equipment Required Manipulatives Addition Facts Grid Writing Materials Digit and Numeral Deck Numeral Patterns ALL (odd and even) Addition Facts ALL Deck (+2) Worded Presentations Deck Addition (5 examples in unit,


Demonstration Script Odd and Even NumeralsSay, “Count by 2’s, starting at 2 and make the model for this”

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Say “These are called even numbers. Even numbers end in 0, 2, 4, 6, 8”Say, “Make 28. It ends in 8, it is called an even number.” Say, “Make 54. It ends in 4, it is called an even number.”Say, “Make 154. It also ends in 4, so it is called an even number.”Say, “Count by 2’s, starting at 1 and make the model for this” Say “These are called odd numbers. Odd numbers end in 1, 3, 5, 7, 9”Say, “Make 25. It ends in 5, it is called an odd number.” Say, “Make 73. It ends in 3, it is called an odd number.”Say, “Make 273. It also ends in 3, so it is called an odd number.”

These counting patterns may require some review before introducing the concept of +2, it is recommended to not introduce this concept until the odd & even identification is clear.

Add 2Begin with the blocks still on the table in odd and even representations (see above).Say, “Point to #” (student points to matching block)Say, “Which number is two bigger than / 2 more than / 2 larger than / plus 2 / add 2?(if required) Say, “Let’s check by adding a two block to #”

Repeat with any numeral 1-10 until student is confidently identifying the next number before working on a clear desk space and introducing writing.

Say, “We have 4 (place the 4 block on table) and add two (add a two block to the 4) – how many do we have?”

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Say, “Write this” Say, “If I change the order of the numerals (show with writing) does the answer change?” (answer – no)

Say, “Write this”

Say, “How else can I write these additions?”

Continue demonstrations with all addition facts below:2 + 0

2 + 1

2 + 2

2 + 3

2 + 4

2 + 5

2 + 6

2 + 7

2 + 8

2 + 9

2 + 10

0 + 2

1 + 2

3 + 2

4 + 2

5 + 2

6 + 2

7 + 2

8 + 2

9 + 2

10 + 2

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This teaching cycle can best be described by the following diagram. Going forward you’ll begin with making and saying to introduce the concept. Then you’ll introduce writing, initially by adding or subtracting the required element, then

demonstrating the commutative or associative property and finally by representing both vertically and horizontally.

Key MessageWhen we add two to any number it is the next odd or even number (so we have to know odd or even 1st)


1. There are # boys in the pool and # girls in the pool. How many children are in the pool?

2. # birds are in the tree and # are on the ground eating seeds. How many birds altogether?

3. Charlotte lost # drink bottles at school. She found # of them. How many are still lost?

4. # people are in line. # more people join the line. How many people are waiting?

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5. I drew # pictures yesterday. Today I drew # more. How many have I drawn altogether?


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Extension: Larger Numbers – Levelling UpReview 4 + 2 = 6 from previous demonstration before proceeding.Then make 40 + 20 with ten blocks. Say “We have 4 tens or 40 and add 2 tens or 20, how many do we have”Prompting in counting 4 – 6 for odd and adding 4 tens – 6 tens – 60

Then make 400 + 200 with hundreds blocks.Say “We have 4 hundred or 400 and add 2 hundreds or 200, how many do we have”Prompting in counting 4 – 6 for odd and adding 4 hundreds – 6 hundreds – 600

In this first presentation of larger numbers, we’re introducing the connection between the relationship in the units moving across to tens and hundreds by simply labelling the numerals correctly. Only present these questions as Numeral + 20 / 200 … the commutative property can be reinforced in subsequent lessons.

Key MessageWe add numerals with the same value

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Unit 9: Using Known Facts to Solve for Unknown (Missing Addends) BackgroundSolving for an unknown value or finding the missing addend is important as it:

reinforces the addition facts prepares for subtraction familiarises the student with algebra (please don’t

introduce symbols or letters)

It begins as a language activity, manipulating the language for addition, before moving to an extension of the written formats (vertical & horizontal, order doesn’t change the answer). It works towards introducing the subtraction algorithm.

Retrieval Practice Make – Say - Record Numerals Next Number? +0 + 1 + 10 + 2

By the end of this unit, students will be able to: Apply known addition facts to solve for the

unknown value.

0 + _ = 0

0 + _ = 1

0 + _ = 2

0 + _ = 3

0 + _ = 4

0 + _ = 5

0 + _ = 6

0 + _ = 7

0 + _ = 8

0 + _ = 9

0 + _ =10

1 + _ = 1

2 + _ = 2

3 + _ = 3

4 + _ = 4

5 + _ = 5

6 + _ = 6

7 + _ = 7

8 + _ = 8

9 + _ = 9

10+_ =10

1 + _ = 2

1 + _ = 3

1 + _ = 4

1 + _ = 5

1 + _ = 6

1 + _ = 7

1 + _ = 8

1 + _ = 9

1 + _ =10

1 + _ =11

2 + _ = 3

3 + _ = 4

4 + _ = 5

5 + _ = 6

6 + _ = 7

7 + _ = 8

8 + _ = 9

9 + _ =10

10+_ =11

2 + _ = 4

2 + _ = 5

2 + _ = 6

2 + _ = 7

2 + _ = 8

2 + _ = 9

2 + _ =10

2 + _ =11

2 + _ =12

3 + _ = 5

4 + _ = 6

5 + _ = 7

6 + _ = 8

7 + _ = 9

8 + _ =10

9 + _ =11

10+_ =12

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Addition & Subtraction Facts Intervention Handbook10+_ =13

10+_ =14

10+_ =14

10+_ =16

10 _ =17

10+ _=18

10+ _=19

10+_ =20

3 + _ =13

4 + _ =14

5 + _ =15

6 + _ =16

7 + _ =17

8 + _ =18

9 + _ =19

Equipment Required Manipulatives Writing Materials Missing Addends Facts ALL Decks (+0, +1, +2, +10) Worded Presentations Deck Addition (need to be

converted to missing addend, subtraction deck may be substituted)

Demonstration Script Using known addition facts above, use the following language prompts before moving to written representations in the student’s book.

What # plus # is the same as #

Make the known piece with blocks

Make the whole piece with blocks

See the answer Build the answer Say the answer Write the answer

Continue demonstrations using the addition facts below (without duplicates):0 + _ = 0

0 + _ = 1

0 + _ = 2

0 + _ = 3

0 + _ = 4

0 + _ = 5

0 + _ = 6

0 + _ = 7

0 + _ = 8

0 + _ = 9

0 + _ =10

1 + _ = 1

2 + _ = 2

3 + _ = 3

4 + _ = 4

5 + _ = 5

6 + _ = 6

7 + _ = 7

8 + _ = 8

9 + _ = 9

10+_ =10

1 + _ = 2

1 + _ = 3

1 + _ = 4

1 + _ = 5

1 + _ = 6

1 + _ = 7

1 + _ = 8

1 + _ = 9

1 + _ =10

1 + _ =11

2 + _ = 3

3 + _ = 4

4 + _ = 5

5 + _ = 6

6 + _ = 7

7 + _ = 8

8 + _ = 9

9 + _ =10

10+_ =11

2 + _ 2 + _ 2 + _ 2 + _ 2 + _ 2 + _ 2 + _ 2 + _ 2 + _

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Addition & Subtraction Facts Intervention Handbook= 4 = 5 = 6 = 7 = 8 = 9 =10 =11 =12

3 + _ = 5

4 + _ = 6

5 + _ = 7

6 + _ = 8

7 + _ = 9

8 + _ =10

9 + _ =11

10+_ =12

10+_ =13

10+_ =14

10+_ =14

10+_ =16

10 _ =17

10+ _=18

10+ _=19

10+_ =20

3 + _ =13

4 + _ =14

5 + _ =15

6 + _ =16

7 + _ =17

8 + _ =18

9 + _ =19


1. Xander is wrapping # presents. He has already wrapped #. How many more does he need to wrap?

2. Our teacher is printing # booklets. He has printed # so far. How many more to print?

3. I am making sandwiches for # people. I have made # so far. How many more do I need to make?

4. Of the # rooms in the house, # have carpet, how many do not have carpet?

5. # people are invited to a party and # have arrived. How many people are we waiting for?

RecordingThis skill doesn’t involve a tick off at the end – it is the introduction of subtraction.

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Unit 10: Addition Facts + 9Retrieval Practice

Make – Record – Say Numerals (focus on teens) Count backwards from 20 Number before? +0 +1 +10 + 2 Missing Addends


shown below)

9 + 0

9 + 1

9 + 2

9 + 3

9 + 4

9 + 5

9 + 6

9 + 7

9 + 8

9 + 9

9 + 10

0 + 9

1 + 9

2 + 9

3 + 9

4 + 9

5 + 9

6 + 9

7 + 9

8 + 9

9 + 9

10 + 9

Equipment Required Manipulatives Addition Facts Grid Writing Materials Digit and Numeral Deck Numeral Patterns ALL (add 10, number before) Addition Facts ALL Deck (+9) Missing Addends ALL Deck (+9) Worded Presentations Deck Addition (5 examples in unit,



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Place the 9 and 10 blocks next to each other

Say “9 is very close to 10, it is only 1 away.”Say, “Because you already know how to add 10, we’ll use this to help you quickly add 9 to numbers – because they’re only one different.”

The process you’ll model for + 9 is to +10 (this relies on student’s quickly identifying teens as a place value function of tens and units) and then counting back 1 numeral.

Repeat with the addition facts below until the student is confidently adding 10 and counting back one numeral, working on a clear desk space before introducing writing or commutative property.0 + 9

1 + 9

2 + 9

3 + 9

4 + 9

5 + 9

6 + 9

7 + 9

8 + 9

9 + 9

10 + 9

Then the familiar process below of changing the order of the addends and writing in vertical and horizontal representations can occur with the remaining addition facts.60© Learning Links


9 + 0

9 + 1

9 + 2

9 + 3

9 + 4

9 + 5

9 + 6

9 + 7

9 + 8

9 + 9

9 + 10

Key MessageWhen we add nine to any numeral it is just 1 less than adding 10 (we add 10 then go back one or go back

one first then add 10)


1. Michelle picked # flower. Her dad gave her # more flowers. How many flowers does Michelle have altogether?

2. There are # people on a bus. # more get on. How many people are there on the bus now?

3. Our car has four tyres. There is a spare in the boot. How many tyres do we have altogether?

4. Nina has # dolls. Her mum buys her # more. How many does she have now?

5. Andrew had already saved # dollars. He earnt # more this week. How much money does he have now?


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Extension: Larger Numbers – Levelling UpReview 3 + 9 = 12 from previous demonstration before proceeding.Then make 30 + 90 with ten blocks.

Say “We have 3 tens or 30 and add 9 tens or 90, how many do we have?”Say, “As 3 plus 9 was 12, 3 tens plus 9 tens will be 12 tens” Say, “Check this” (count blocks)Say, “There are too many 10 blocks in this place – we have 12 and can only have 9, 9 tens are 90 – what do we have when we add one more 10 to 90? (check 100 as answer)“Say, “Yes, 100. So, we have moved to the next place and will use a hundreds block to make this number” (check correct place value representation)Say, “What number do we have now? Write this down” 62© Learning Links


It is unlikely you have enough hundreds blocks in your manipulatives kit. However, the pattern of 3 + 9 can still be linked to 300 + 900 using a place value chart and numeral cards.

Key MessageWe add numerals with the same value

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Unit 11: Addition Facts - DoublesRetrieval Practice

Make – Record – Say Numerals Counting forwards +0 +1 +10 + 2 Missing Addends + 9

By the end of this unit, students will be able to: Add the set of doubles (full set shown below,

italics are facts previously covered)

0 + 0

1 + 1

2 + 2

3 + 3

4 + 4

5 + 5

6 + 6

7 + 7

8 + 8

9 + 9

10+ 10

Equipment Required Manipulatives Addition Facts Grid Writing Materials Numeral Patterns ALL Deck (Doubles) Addition Facts ALL Decks (Doubles) Missing Addends ALL Deck (Doubles) Worded Presentations Deck Addition (specific doubles

questions included in deck)

Demonstration Script Say, “There is a group of addition facts which cut our grid in half – these are known as the doubles.”Say, “Some of these you already know” (refer to chart, coloured in).

0 + 0 = 0

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1 + 1 = 22 + 2 = 4

10 + 10 = 209 + 9 = 18

Say, “We have some new ones to add.”

Complete demonstration for all new doubles.0 + 0

1 + 1

2 + 2

3 + 3

4 + 4

5 + 5

6 + 6

7 + 7

8 + 8

9 + 9

10+ 10

Encourage the student to notice the pattern of doubles, the sums are increasing by 2 (because each pair of addends have increased by one) – so knowing even numeral counting patterns keep helping.

Also ensure you recognise there is not another way to write these facts as these are the same numbers.

Key MessageAdding doubles are a special group of numbers we remember.

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1. Amy and Amber are identical twins. They are each # years old. What is their combined age?

2. My sister and I each have # ribbons. How many ribbons do we have altogether?

3. There are 2 boxes of # pencils. How many pencils are there altogether?

4. Two cats are sleeping. They each have 4 legs. How many legs do they have altogether?

5. Two families have # children each. How many children altogether?

RecordingColour, tick, add stamps to the Doubles facts on the Addition Facts Grid when you’re comfortable this is appropriate.

Extension: Larger Numbers – Levelling UpExtend knowledge of doubles by modelling any of the following.66© Learning Links

Addition & Subtraction Facts Intervention Handbook10 + 10

20 + 20

30 + 30

40 + 40

50 + 50

60 + 60

70 + 70

80 + 80

90 + 90

100+100

200+200

300+300

400+400

500+500

600+600

700+700

800+800

900+900

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Unit 12: Addition Facts - Almost Doubles (Associative Property)RationaleHaving a strong understanding and recall of doubles allows for some relationships to be modelled for new addition facts. The idea here isn’t to rote memorise these facts, but to encourage reasoning, thinking and using known facts to derive at the answer quickly. The premise of this is that the previous skills of next number and doubles need to be firm, they must be absolute known facts for this to work (hence, not rushing through previous skills).

Retrieval Practice Make – Record – Say Numerals Next Number +0 +1 +10 + 2 Missing Addends + 9 + Doubles

By the end of this unit, students will be able to:Add the set of close doubles (there is not a full set, only shown facts require this additional strategy)

1 + 0

2 + 1

3 + 2

4 + 3

5 + 4

6 + 5

7 + 6

8 + 7

9 + 8

10 + 9

11+10

0 + 1

1 + 2

2 + 3

3 + 4

4 + 5

5 + 6

6 + 7

7 + 8

8 + 9

9 + 10

10+11

Equipment Required Manipulatives Addition Facts Grid Writing Materials

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Digit and Numeral Deck Numeral Patterns ALL Deck (Doubles + 1) Addition Facts Deck (Doubles + 1) Missing Addends ALL Deck (Doubles + 1) Worded Presentations Deck Addition (5 examples in unit,

but deck can be randomised)Demonstration Script Say, “Just as we used our add 10 facts to quickly add 9, we’re going to use our doubles facts to learn new addition facts”Say, “When you know the doubles fact 4 + 4 = 8 (make with blocks), then you can quickly answer 4 + 5 = 9 because it is just one more or the next number” (make & check)

Say, “These are sometimes called ‘near doubles’ or ‘doubles neighbours. We’ll call them ‘close doubles’”

This fact family introduces a new property – the associative property which an extension of the commutative property. The associative property states we can regroup or re-associate the addends in a problem without affecting the sum (4 + 5 is the same as 4 + 4 + 1 – both equal 9).

Complete demonstration for all close doubles.4 + 3 5 + 4 6 + 5 7 + 6 8 + 7 9 + 83 + 4 4 + 5 5 + 6 6 + 7 7 + 8 8 + 9

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Please note – 1 + 0, 2 + 1, 3 + 2, 9 + 8, 10 + 9 are already covered with previous learning (+0, +1, +2, +9, +10), you can use these with this strategy but ensure to show both methods to reinforce there are multiple ways to come to the sum.

Key MessageKnowing how to add doubles helps us add close doubles quickly.


1. Will has # cards in his collection. Tim’s collection is # greater than Will’s. How many cards does Tim have?

2. Adam has # bats. Luke has # more bats than Adam. How many bats does Luke have?

3. At the beach Henry saw # crabs. Lisa saw # more than Henry. How many did Lisa see?

4. Gary had # scarves. He bought # more. How many scarves does he have now?

5. Ann makes # necklaces. Sarah makes # more than Ann. How many necklaces does Sarah make?

6. Cliff has # books and Ryder has # books for the fair. How many books will they donate?

RecordingColour, tick, add stamps to the Close Doubles facts on the Addition Facts Grid when you’re comfortable this is appropriate.

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Extension: Larger Numbers – Levelling UpExtend knowledge of doubles by modelling any of the following (only facts for this property are included).40 + 30 50 + 40 60 + 50 70 + 60 80 + 70 90 + 8030 + 40 40 + 50 60 + 50 60 + 70 70 + 80 80 + 90300 + 400

400 + 500

500 + 600

600 + 700

700 + 800

800 + 900

400 + 300

500 + 400

600 + 500

700 + 600

800 + 700

900 + 800

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Unit 13: Addition Facts - Adding to 10Adding to 10 is a common addition fact family, sometimes the main or only fact family focussed on and is often referred to as “Friends of 10”, “Bridging to 10”. It is a powerful fact family, like Doubles, in that it can be applied to much larger numbers quickly.

Retrieval Practice Make – Record – Say Numerals Count forwards to 10 +0 +1 +10 + 2 Missing Addends + 9 + Doubles + Almost Doubles

By the end of this unit, students will be able to: Add the set of facts to 10 (only 4 require

attention, the full set is included)

10 + 0

9 + 1

8 + 2

7 + 3

6 + 4

5 + 5

4 + 6

3 + 7

2 + 8

1 + 9

0 + 10

Equipment Required Manipulatives Addition Facts Grid Writing Materials Digit and Numeral Deck Numeral Patterns ALL Deck (Add to 10) Addition Facts Deck (Add to 10) Missing Addends ALL Deck (Remaining Facts) Worded Presentations Deck Addition (specific add to 10

questions included)

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Demonstration Script Say, “We’ll be revising how to get to 10 (reach 10, make 10, add to 10) to help us quickly add larger numbers” Say, “Ten is such an important number, because our number system is based on 10 or deci – there can only be 9 of any numeral type in a place and once we reach 10 of that type we move to the next value – this is how you’ve been making numbers throughout this whole intervention.”Say, “Many of these ‘add to 10 facts’ you already know (make these first)”

10 + 09 + 18 + 25 + 5

Say, “There are just 2 more to learn”

Repeat for the 4 + 6 = 10 fact.

Activities to consolidate this addition fact (the full set) include:

Build a wall with blocks to orally rehearse the pattern (10 – 1 & 9 – 2 + 8 – 3 & 7 …)

Fill the gaps (with blocks, paper & pencil)

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Flip Cards (turn a card with 0-10, say the matching numeral and then move on a board, collect tokens …)

I have you need (deck of numeral cards 0-10, take a card and say “I have 3, you need (7)”

Here are the facts to use for demonstrations and activities.10 + 0

9 + 1

8 + 2

7 + 3

6 + 4

5 + 5

4 + 6

3 + 7

2 + 8

1 + 9

0 + 10

Key MessageKnowing what numbers add to 10 helps us add bigger numbers.


1. There are 10 children in the family. # have put away their clothes. How many more need to put their clothes away?

2. There were 10 floats in the pool. # have been taken out of the pool. How many are still in the pool?

3. Liam has 10 different hats. He has left # at school. How many are still at home?

4. We need 10 people to play the game. # people are ready. How many more need to come to play?

5. There will be 10 candles on my birthday cake. We can only find #. How many more candles do we need to find?

6. I have 10 fingers on my hand. # fingers have paint on them. How many fingers are clean?

RecordingColour, tick, add stamps to the Add to 10 facts on the Addition Facts Grid when you’re comfortable this is appropriate.

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Extension: Larger Numbers – Levelling Up100 + 0

90 + 10

80 + 20

70 + 33

60 + 40

50 + 50

40 + 60

30 + 70

20 + 80

10+90

0+100

Unit 14: Remaining Addition FactsBy this stage of the intervention, there are a handful of addition facts that are remaining to be learnt or linked to some other known facts.

3 + 53 + 63 + 84 + 74 + 85 + 75 + 86 + 8

There are some patterns and groupings that can assist when modelling these remaining facts. You’ll notice the strategies being used rely heavily on doubles and 10 (either adding 10 or add to 10).

3 + 5 known double 3 & add 277© Learning Links


3 + 6 1 less than known add to 10 (4 + 6 4 - 1 + 6)

3 + 8 1 more than known add to 10 (2 + 8 2 + 1 + 8)

4 + 7 1 more than known add to 10 (3 + 7 3 + 1 + 7)1 more than known add to 10 (4 + 6 4 + 7 + 1)


5 + 7 known double 5 & add 22 more than known add to 10 (3 + 7 3 + 2 + 7)

5 + 8 2 less than add 10 (5 + 8 5 + 10 – 2)

6 + 8 known double 6 & add 22 less than add 10 (6 + 8 6 + 10 – 2)

Retrieval Practice Make – Record – Say Numerals +0 +1 +10 + 2 Missing Addends + 9 + Doubles + + Almost Doubles + to 10

By the end of this unit, students will be able to: Add the remaining addition facts

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3 + 5 3 + 6 3 + 8 4 + 7 4 + 8 5 + 7 5 + 8 6 + 85 + 3 6 + 3 8 + 3 7 + 4 8 + 4 7 + 5 8 + 5 8 + 6

Equipment Required Manipulatives Addition Facts Grid Writing Materials Digit and Numeral Deck Addition Facts ALL Deck (Remaining Facts) Missing Addends ALL Deck (Remaining Facts) Worded Presentations Deck Addition (5 examples in unit,


Demonstration Script Say, “There are 8 addition facts left” Make – Say – Write the addition facts.

Key MessageI’m almost there!


1. Wally picked # strawberries on Sunday and another # strawberries on Monday. How many strawberries has he picked?

2. Ricky bakes # muffins for the sale and Sophie baked # more muffins. How many did they bake altogether?

3. Isla played # games and her brother played # more games. How many games did they play altogether?

4. If I hold up # fingers on one hand and # fingers on the other hand, how many fingers am I holding up?

5. Dad bought # kilograms of sausages and # kilograms of bacon for the BBQ. How many kilograms of food did he buy altogether?

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RecordingColour, tick, add stamps to the remaining facts on the Addition Facts Grid when you’re comfortable this is appropriate.

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Unit 15: Subtraction Facts with 0 & 1 BackgroundSubtraction is simply the opposite or inverse of addition. If a student knows addition facts and can solve for an unknown sum, then they are already subtracting. Where possible, introduce these together so that the learning is transferrable. Use your discretion as to whether to complete the entire addition modules and then cycle back around to repeat for subtraction or teach in tandem.

The language we'll use for subtraction initially is "difference" then take away, minus, less subtract – but eventually we’re looking to interchange the language.

There are some differences in physically placing blocks on the table for addition and subtraction that can enhance understanding. This has already been introduced to students in the previous unit in solving for an unknown numeral.

When adding we recommend placing blocks horizontally, next to each other – this helps to visually represent the numbers getting larger, counting along a number line …

When subtracting we recommend placing blocks horizontally, but under each other to visually represent there is an amount missing and this is the number we’re finding.

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During demonstrations horizontal and vertical representations can be used to reflect the horizontal representations of algorithms. However, during initial teaching stick to one, then add the other if

you require.Retrieval Practice

Make – Say – Record Numerals Counting + 0 + 1 Operations (will depend on whether you introduce this at

the end of all subtraction, hence all addition is included or whether you can begin to introduce subtraction earlier)

By the end of this unit, students will be able to: Subtract 0 from numerals (full set shown

below) Subtract numerals with a difference of 0 (full

set shown below) Subtract 1 from numerals (full set shown below) Subtract numerals with a difference of 1 (full set shown

below)

1 - 1

2 - 2

3 - 3

4 - 4

5 - 5

6 - 6

7 - 7

8 - 8

9 - 9

10 – 10

0 - 0

1 – 0

2 – 0

3 – 0

4 – 0

5 – 0

6 – 0

7 – 0

8 – 0

9 – 0

10 – 0

3 - 2

4 - 3

5 - 4

6 - 5

7 - 6

8 - 7

9 - 8

10 - 9

11 – 10

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2 - 1

3 – 1

4 – 1

5 – 1

6 – 1

7 – 1

8 – 1

9 – 1

10 – 1

11 - 1

Equipment Required Manipulatives Subtraction Facts Grid Writing Materials Digit and Numeral Decks Numeral Patterns ALL (0 and number before?) Missing Addends ALL (0 and 1) Subtraction Facts ALL Deck (0 and 1) Worded Presentations Deck Subtraction (5 examples in

unit, but deck can be randomised)

Subtraction Facts are taught in this intervention to relate closely to the known addition facts. As the commutative property does not apply to subtraction (order of digits will change the difference) we group subtraction facts of -0 and -1

as well as those that equal 0 & 1. We begin subtraction questions by considering the related addition facts.

Each session will still involve make – say – record, using the manipulatives, however we are making the subtraction problem as its related missing addend problem to support students to retrieve known addition facts to solve subtraction facts. As we’re connecting known addition facts with subtraction facts, we will do a little more talking and writing if teaching addition & subtraction in tandem.

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Demonstration Script The script for subtraction is a little more complex, as it involves initially rewording the problem as an addition problem for missing addend applications. This modification is scripted in detail below, although it maintains the instructional routine of materials, talking and writing throughout.

Say, “Subtraction is the opposite of addition, we can use our known addition facts to quickly retrieve subtraction facts when we need them”.

ZeroSay, “Our +0 addition facts will help us retrieve subtraction facts”Say, “We’re going to find the difference between 4 and 0 or 4 - 0” (say & write subtraction problem)Say, “4 minus 0 means what numeral plus 0 is the same as 4? (rephrase as a missing addend problem)Re-write the problem (_ + 0 = 4)Make and Remake using manipulativesSay subtraction answer “The difference between 4 and 0 is 4”Record this problem and answer

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Continue with more – 0 before introducing differences that equal 00 - 0

1 – 0

2 – 0

3 – 0

4 – 0

5 – 0

6 – 0

7 – 0

8 – 0

9 – 0

10 – 0

Key MessageWhen we subtract 0 from a numeral, the difference is unchanged as we have taken nothing away.

Say, “Our +0 addition facts will help us retrieve more subtraction facts”Say, “We’re going to find the difference between 3 and 3 or 3 - 3” (say & write subtraction problem)Say, “3 minus 3 means what numeral plus 3 is the same as 3? (rephrase as a missing addend problem)Re-write the problem (_ + 3 = 3)Make and Remake using manipulativesSay subtraction answer “The difference between 3 and 3 is 3”Record this problem and answer.

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Continue with more differences that equal 00 – 0

1 - 1

2 - 2

3 - 3

4 - 4

5 - 5

6 - 6

7 - 7

8 - 8

9 - 9

10 – 10

Key MessageWhen we subtract the same numeral from itself, we have taken it all away and there is nothing left - the difference

is zero.

OneSay, “Our +1 addition facts will help us retrieve subtraction facts”Say, “We’re going to find the difference between 5 and 1 or 5 - 1” (say & write subtraction problem)Say, “5 minus 1 means what numeral plus 1 is the same as 5? (rephrase as a missing addend problem)Re-write the problem (_ + 1 = 5)Make and Remake using manipulativesSay subtraction answer “The difference between 5 and 1 is 4”Record this problem and answer

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Continue with more – 1 before introducing differences that equal 12 - 1

3 – 1

4 – 1

5 – 1

6 – 1

7 – 1

8 – 1

9 – 1

10 – 1

11 - 1

2 - 1

Key MessageWhen we subtract 1 it is the number before, because when we add 1 it is the number after, they are opposites.

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Say, “Our +1 addition facts will help us retrieve more subtraction facts”Say, “We’re going to find the difference between 5 and 4 or 5 - 4” (say & write subtraction problem)Say, “5 minus 4 means what numeral plus 4 is the same as 5? (rephrase as a missing addend problem)Re-write the problem (_ + 4 = 5)Make and Remake using manipulativesSay subtraction answer “The difference between 5 and 4 is 1”Record this problem and answer

Continue with more differences that equal 13 - 2

4 - 3

5 - 4

6 - 5

7 - 6

8 - 7

9 - 8

10 - 9

11 – 10

Key MessageWhen we subtract a number that is the number before it, the answer is 1 as they are only one number apart.

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At this time, it is very important to explain that the commutative property only applies to addition of whole numbers (1 – 3 is not the same as 3 – 1). But, because addition is commutative (order doesn’t change the sum) we can use this to help

with subtraction, 3 – 1 can be solved by knowing 2 + 1 = 3 or 1 + 2 = 3. These addition facts lead to two related and true subtraction facts (3 – 1 = 2 and 3 – 2 = 1) but only one will be correct to answer the question 3 – 1.

Please also don’t tell students we cannot take 3 away from 1, because we can – it is a negative difference and students learn this in later years. Also steer away from incorrect language of take the smallest number from the biggest number – focus on the relationships and connections to known facts.


1. There are # bananas. The gorilla eats # bananas. How many bananas are left?

2. Savannah has # strawberries. She gives Sally # oranges. Savannah has # oranges left.

3. There are # apples in the fruit basket. Harry takes out # apple. How many apples are left?

4. Alice and Mary like cats. Mary has # cats and Alive has # cat. Mary has # more cats than Alice.

5. When we were fishing, we caught # fish but had to throw # back. How many fish did we have to bring home?

RecordingColour, tick, add stamps to the 0 and 1 facts on the Subtraction Facts Grid when you’re comfortable this is appropriate. This may take several sessions to review and consolidate. Please use your discretion as to whether subtraction facts are introduced at this stage of the intervention or whether they are held until all addition facts are known.

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Unit 16: Subtraction Facts with 10Retrieval Practice

Make – Say – Record Numerals Count forwards and backwards by 10 + 10 Operations (will depend on whether you

introduce this at the end of all subtraction, hence all addition is included or whether you can begin to introduce subtraction earlier)



set shown below)

10 – 0

11 – 1

12 – 2

13 – 3

14 – 4

15 – 5

16 – 6

17 – 7

18 – 8

19 – 9

20 - 10

10 – 10

11 - 10

12 – 10

13 – 10

14 – 10

15 – 10

16 – 10

17 – 10

18 – 10

19 – 10

Equipment Required Manipulatives Subtraction Facts Grid Writing Materials Digit and Numeral Decks Numeral Patterns ALL (10) Missing Addends ALL (10) Subtraction Facts ALL Deck (10) Worded Presentations Deck Subtraction (5 examples in


Demonstration Script Review +10 facts Begin the demonstration cycle below focussing initially on subtraction problems involving subtract 10, then add subtraction problems that have a difference of 10.

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Complete demonstrations for the following.10 – 10

11 - 10

12 – 10

13 – 10

14 – 10

15 – 10

16 – 10

17 – 10

18 – 10

19 – 10

10 – 0

11 – 1

12 – 2

13 – 3

14 – 4

15 – 5

16 – 6

17 – 7

18 – 8

19 – 9

20 - 10

Key MessageWhen we subtract ten from any numeral it is the tens that change by just one less ten.


1. # fish are swimming in the lake, # are caught. How many are left?

2. There are # marbles. # are red, the rest are green. How many marbles are green?

3. # bees are in the hive. # fly away. How many bees are left?

4. # people got onto the bus, then # got off at the next stop. How many people are left in the bus?

5. There are # cows in the paddock. # have eaten. How many cows are still eating?

RecordingColour, tick, add stamps to the 10 facts on the Subtraction Facts Grid when you’re comfortable this is appropriate.

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Make – Say – Record Numerals Counting odd and even numerals (forwards &

backwards) + 2 Operations (will depend on whether you




set shown below)

2 - 0

3 - 1

4 - 2

5 - 3

6 - 4

7 - 5

8 - 6

9 - 7

10 - 8

11 - 9

12 – 10

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4 – 2

5 - 2

6 – 2

7 – 2

8 – 2

9 – 2

10 – 2

11 – 2

12 - 2

Equipment Required Manipulatives Subtraction Facts Grid Writing Materials Digit and Numeral Decks Numeral Patterns ALL (odd and even) Missing Addends ALL (2) Subtraction Facts ALL Deck (2) Worded Presentations Deck Subtraction (5 examples in


Demonstration Script Review +2 facts Begin the demonstration cycle below focussing initially on subtraction problems involving subtract 2, then add subtraction problems that have a difference of 2.

Initial demonstrations with following.4 – 2

5 - 2

6 – 2

7 – 2

8 – 2

9 – 2

10 – 2

11 – 2

12 - 2

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Complete demonstrations with all iterations.2 - 0

3 - 1

4 - 2

5 - 3

6 - 4

7 - 5

8 - 6

9 - 7

10 - 8

11 - 9

12 – 10

4 – 2

5 - 2

6 – 2

7 – 2

8 – 2

9 – 2

10 – 2

11 – 2

12 - 2

Key MessageWhen we subtract 2, it is the odd or even number before.When we subtract two numbers with a

difference of 2, they are two decreasing odd or even numeral pairs.


1. There are # bats on the wire. # bats fly away. How many birds are on the wire now?

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2. Sue has # slices of oranges. She eats # slices. How many slices are left?

3. There are # pages to read in my book. I have read # pages so far. How many more pages do I need to read?

4. Alison is # years old. Her brother is # years old. What is the difference in their ages?

5. There are # spaces for eggs in a carton. I have used # eggs. How many eggs are left?

RecordingColour, tick, add stamps to the 2 facts on the Subtraction Facts Grid when you’re comfortable this is appropriate.

Extension: Larger Numbers – Levelling UpProceed to extend subtraction facts to larger numbers (30 – 20, 300 – 200 …)

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Make – Say – Record Numerals Count forwards and backwards by 10 Number before + 9 Operations (will depend on whether you




set shown below)

9 – 9

10 – 9

11 – 9

12 – 9

13 – 9

14 – 9

15 – 9

16 – 9

17 – 9

18 – 9

19 - 9

9 - 0

10 - 1

11 - 2

12 - 3

13 - 4

14 - 5

15 - 6

16 - 7

17 - 8

18 - 9

19 - 10

Equipment Required Manipulatives Subtraction Facts Grid Writing Materials Digit and Numeral Decks Numeral Patterns ALL (9) Missing Addends ALL (9) Subtraction Facts ALL Deck (9) Worded Presentations Deck Subtraction (5 examples in


Demonstration Script Review +9 facts

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Begin the demonstration cycle below focussing initially on subtraction problems involving subtract 9, then add subtraction problems that have a difference of 9.

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Say, “Subtracting 9 is often considered a difficult subtraction, here we will link to our +9 facts to support.”

Complete demonstrations for the following, ensuring you write all related facts in both vertical and horizontal representations.9 – 9

10 – 9

11 – 9

12 – 9

13 – 9

14 – 9

15 – 9

16 – 9

17 – 9

18 – 9

19 - 9

9 - 0

10 - 1

11 - 2

12 - 3

13 - 4

14 - 5

15 - 6

16 - 7

17 - 8

18 - 9

19 - 10

Key MessageWhen we subtract 9 from any numeral, we can subtract 10 and then add one more (because 10 was 1 too many).


1. There are # trucks. # drive off. How many trucks are left?

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2. Mum hade # sandwiches. # have been eaten already. How many sandwiches are left?

3. Lucy had # balloons. # popped. Lucy has # balloons left.4. Matt won # points in the game and Andy won # points.

What is the difference in their scores?5. In a family # children are boys and # children are girls.

How many more boys than girls are there in the family?RecordingColour, tick, add stamps to the 9 facts on the Subtraction Facts Grid when you’re comfortable this is appropriate.

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Unit 19: Subtract with DoublesRetrieval Practice

Make – Say – Record Numerals + Doubles Operations (will depend on whether you


By the end of this unit, students will be able to: Recognise the subtraction facts from addition

doubles facts.

0 – 0

2 – 1

4 – 2

6 - 3

8 – 4

10 – 5

12 – 6

14 – 7

16 – 8

18 – 9

20 - 10

Equipment Required Manipulatives Subtraction Facts Grid Writing Materials Digit and Numeral Decks Numeral Patterns ALL (Doubles) Missing Addends ALL (Doubles) Subtraction Facts ALL Deck (Doubles) Worded Presentations Deck Subtraction (specific doubles


Demonstration Script Review +Doubles facts Say, “By knowing our + Doubles facts, we can quickly retrieve subtraction facts.”



Complete demonstrations for the following, ensuring you write facts in both vertical and horizontal representations.0 – 0

2 – 1

4 – 2

6 - 3

8 – 4

10 – 5

12 – 6

14 – 7

16 – 8

18 – 9

20 - 10

Key MessageKnowing our add doubles facts helps us answer subtraction questions.


1. My brothers Archer and Fletcher are twins. Their combined age is #. How old are each of my brothers?

2. My sister and I have the same number of books in our rooms. How many books do we each have?

3. There are 2 boxes with the same number of pencils. Altogether there are # pencils. How many pencils go into each box?



4. The same number of people are in both rooms at the cinema. There are # people altogether. How many people are in each room?

5. Two families have the same number of pets. How many pets does each family have?



RecordingColour, tick, add stamps to the Doubles facts on the Subtraction Facts Grid when you’re comfortable this is appropriate.

Extension: Larger Numbers – Levelling UpProceed to extend subtraction facts to larger numbers (60 – 30, 600 - 300 …)



Unit 20: Subtraction Facts from 10Retrieval Practice

Make – Say – Record Numerals + 10 Operations (will depend on whether you


By the end of this unit, students will be able to:Subtract numerals from 10 (all should be addressed in this group as they are the inverse of adding to 10, critical for bigger numbers)

10 – 0

10 – 1

10 – 2

10 – 3

10 – 4

10 – 5

10 – 6

10 – 7

10 – 8

10 – 9

10 - 10

Equipment Required Manipulatives Subtraction Facts Grid Writing Materials Digit and Numeral Decks Numeral Patterns ALL (to 10) Missing Addends ALL (to 10) Subtraction Facts ALL Deck (from 10) Worded Presentations Deck Subtraction (specific 10-


Demonstration Script Review + facts Say, “By knowing our + 10 facts – all the numeral pairs that add to 10, we can quickly retrieve subtraction facts.”



Complete demonstrations for the following, ensuring you write facts in both vertical and horizontal representations.10 – 0

10 – 1

10 – 2

10 – 3

10 – 4

10 – 5

10 – 6

10 – 7

10 – 8

10 – 9

10 - 10

Key MessageOur facts to 10 will help with both addition and subtraction.











RecordingColour, tick, add stamps to the Subtract from 10 facts on the Subtraction Facts Grid when you’re comfortable this is appropriate.

Extension: Larger Numbers – Levelling UpProceed to extend subtraction facts to larger numbers (100 – 70, 1000 – 700 …)



Unit 21: Remaining Subtraction FactsYou’ll notice some deviation from the order of the addition facts from here, there are far less patterns to assist the remaining subtraction facts except for linking to the addition fact. The focus for these remaining facts is to use known addition facts to extrapolate and retrieve the related subtraction facts.

There are two key relationships to draw on here:

Doubles and either one more or one less Making 10 and adding a bit more (to make a teen number)

These facts can be separated by the subtrahend (number being subtracted from) or the minuend (number being subtracted)

Remaining Facts by MinuendSubtract 3

7 – 38 – 3

9 – 311 – 3

Build on the relationship that double 3 is 67 is one more than 6 (difference is one more than 3 [4]) 8 is 2 more than 6 (difference is two more than 3 [5])

Build on the fact 3 + 7 = 10 9 is 1 less than 10 (difference is one less than 7 [6]) 11 is 1 more than 10 (difference is one more than 7 [8])

Subtract 4

7 – 49 – 4

11 – 412 – 4

Build on the relationship that double 4 is 87 is one less than 8 (difference is one less than 4 [3]) 9 is 1 more than 8 (difference is one more than 4 [5])

Build on the fact 4 + 6 = 1011 is 1 more than 10 (difference is one more than 6 [7])



12 is 2 more than 10 (difference is one more than 6 [8])

Subtract 5

8 – 59 – 5

Subtract 5

11 – 512 – 513 – 5

Build on the relationship that double 5 is 108 is two less than 10 (difference is two less than 5 [3]) 9 is 1 less than 10 (difference is one less than 5 [4]) 11 is 1 more than 10 (difference is one more than 5 [6])

Build on the fact 5 + 5 = 1011 is 1 more than 10 (difference is one more than 5 [6]) 12 is 2 more than 10 (difference is two more than 5 [7]) 13 is 3 more than 10 (difference is three more than 5 [8])

Subtract 6

9 – 611 – 613 – 614 – 6

Build on the fact 6 + 4 = 109 is 1 less than 10 (difference is one less than 4 [3])11 is 1 more than 10 (difference is one more than 4 [5]) 13 is 3 more than 10 (difference is three more than 4 [7]) 14 is 4 more than 10 (difference is four more than 4 [8])

Build on the relationship that double 6 is 1211 is 1 less than 12 (difference is one less than 6 [5]) 13 is 1 more than 12 (difference is one more than 6 [7]) 14 is 2 more than 12 (difference is two more than 6 [8])



Subtract 7

11 – 712 – 7

13 – 715 – 7

Build on the fact 7 + 3 = 1011 is 1 more than 10 (difference is one more than 3 [4]) 12 is 2 more than 10 (difference is two more than 3 [5])

Build on the relationship that double 7 is 1413 is 1 less than 14 (difference is one less than 7 [6]) 15 is 1 more than 14 (difference is one more than 7 [8])

Subtract 8

11 – 812 – 813 – 8

14 – 815 – 8


Build on the relationship that double 8 is 1614 is 2 less than 16 (difference is two less than 8 [6]) 15 is 1 less than 16 (difference is one less than 8 [7])

Remaining Facts by Subtrahend7 – 47 – 3

These are related facts 3 + 4 = 7, 4 + 3 = 7 and 7 – 3 = 4 and 7 – 3 = 47 – 4 can be double 4 is 8 less 1 (3)7 – 3 can be double 3 is 6 and 1 more (4)

8 – 58 - 3

These are related facts 3 + 5 = 8, 5 + 3 = 8 and 8 – 3 = 5 and 8 – 5 = 38 – 5 can be double 5 is 10 less 2 (3)8 – 3 can be double 3 is 6 and 2 more (5)



9 – 59 - 4

These are related facts 4 + 5 = 9, 5 + 4 = 9 and 9 – 5 = 4 and 9 – 5 = 49 – 5 can be double 5 is 10 less 1 (4)9 – 5 can be 10 – 5 is 5 and we started with 1 too many, so subtract 1 (4)9 – 4 can be double 4 is 8 and 1 more (5)9 – 4 can be 10 – 4 is 6 and we started with 1 too many, so subtract 1 (5)These facts can also be addressed with other “9” facts

9 – 39 - 6

These are related facts 3 + 6 = 9, 6 + 3 = 9 and 9 – 3 = 6 and 9 – 6 = 39 – 3 can be 10 – 3 is 7 and we started with 1 too many, so subtract 1 (6)9 – 6 can be 10 – 6 is 4 and we started with 1 too many, so subtract 1 (3)These facts can also be addressed with other “9” facts

11 – 811 – 3

11 – 711 – 4

11 – 611 – 5

This group of related facts can be retrieved with the relationship 11 = 10 + 111 – 8 can be 8 & 2 make 10 and we need 1 more (3)11 – 7 can be 7 & 3 make 10 and we need 1 more (4)11 – 6 can be 6 & 4 make 10 and we need 1 more (5)11 – 6 can also be double 6 is 12 less 1 (5)11 – 5 can be 5 & 5 make 10 and we need 1 more (6)11 – 5 can also be double 5 is 10 add 1 (6)11 – 4 can be 4 & 6 make 10 and we need 1 more (7)11 – 3 can be 3 & 7 make 10 and we need 1 more (8)

12 – 812 – 4

12 – 7

This group of related facts can be retrieved with the relationship 12 = 10 + 212 – 8 can be 8 & 2 make 10 and we need 2 more (4)



12 – 5 12 – 7 can be 7 & 3 make 10 and we need 2 more (5)12 – 5 can be 5 & 5 make 10 and we need 2 more (7)12 – 5 can also be double 5 is 10 add 2 (7)12 – 4 can be 4 & 6 make 10 and we need 2 more (8)



13 – 813 – 5

13 – 713 – 6

This group of related facts can be retrieved with the relationship 13 = 10 + 313 – 8 can be 8 & 2 make 10 and we need 3 more (5)13 – 7 can be 7 & 3 make 10 and we need 3 more (6)13 – 7 can also be double 7 is 14 subtract 1 (6)13 – 5 can be 5 & 5 make 10 and we need 3 more (8)13 – 5 can also be double 5 is 10 add 3 (8)

14 – 814 – 6

This group of related facts can be retrieved with the relationship 14 = 10 + 414 – 8 can be 8 & 2 make 10 and we need 4 more (6)14 – 8 can also be double 8 is 16 and subtract 2 (6)14 – 6 can be 6 & 4 make 10 and we need 4 more (8)14 – 6 can also be double 6 is 12 add 2 (8)

15 – 815 – 7

This group of related facts can be retrieved with the relationship 15 = 10 + 515 – 8 can be 8 & 2 make 10 and we need 5 more (7)15 – 8 can also be double 8 is 16 and subtract 1 (7)15 – 7 can be 7 & 3 make 10 and we need 5 more (8)15 – 7 can also be double 7 is 14 add 1 (8)

Retrieval Practice Make – Say – Record Numerals Operations (will depend on whether you


By the end of this unit, students will be able to:



Subtract numerals by linking to known addition facts

7 – 3

8 – 3

9 – 3

11 – 3

7 – 4

9 – 4

11 – 4

12 – 4

9 – 5

11 – 5

12 – 5

13 – 5

9 – 6

11 – 6

13 – 6

14 – 6

11 – 7

12 – 7

13 – 7

15 – 7

11 – 8

12 – 8

13 – 8

14 – 8

15 - 8



Equipment Required Manipulatives Subtraction Facts Grid Writing Materials Digit and Numeral Decks Numeral Patterns ALL (to 10) Missing Addends ALL (to 10) Subtraction Facts ALL Deck (from 10) Worded Presentations Deck Subtraction (5 examples in



1. Mum made # cupcakes. I ate #. How many are left?2. There are # balls altogether. # of them are tennis balls.

How many basketballs are there?3. Penny has # rice crackers. She eats #. How many rice

crackers does she have left?4. Richard has # stickers. Blake has # stickers. How many

fewer stickers does Blake have than Richard?5. John has # books. He has # more books than his brother.

How many books does his brother have?6. Jenny collects # flowers. Erin collects # fewer flowers than

Jenny. How many flowers does Erin collect?7. Linda has # stamps. She has # more than Rebecca. How

many stickers does Rebecca have?

RecordingColour, tick, add stamps to the remaining facts on the Subtraction Facts Grid when you’re comfortable this is appropriate.





Where to now?Completion of this intervention, through the introduction of all addition facts and the related subtraction facts, provides the foundation for future mathematics learning.

Students will progress throughout this intervention at a pace they need, mastery is critical and they need to be provided with enough opportunities for them to understand these concepts and be able to retrieve the facts when needed.

Additional supports beyond this intervention include:

iPad apps that can be controlled for the addend or minuend.

Board Games using the deck of known facts for recall and progression through the board.

Recall of facts – oral or written (please don’t time these rehearsals, knowing the facts is more important than speed) – see here for printing instructions

Retrieval activities to consolidate link between strategy and question types, simply write / type a question in the

empty box for the student to select the strategy. (Retrieval Presentation Deck available).



Strategy boxes can also be left blank for students to use their own wording to explain how they would approach this question.

A Retrieval Presentation Deck is available for this intervention. It has been set up as a presentation deck, identical to all other decks for presenting. The deck can be displayed in screen share with Annotate functionality or can be printed 9 to a page for a single sheet (you could print a set of these to populate with questions ahead of time so they are ready for use.





Second Pathway: Tandem Addition & Subtraction FactsIn this second pathway a modified scope is suggested. This relies on the detailed scripts in the previous sections of this handbook. In this second pathway, the emphasis is on a numeral and the addition and subtraction facts related to this, including missing addend and extensions with place value.

This second pathway assumes digit formation, numeral identification and counting is firm. Where this is not the case the first pathway is advised as it will progress more gradually, increasing in complexity at a slower pace.

The second pathway is designed to solidify the relationships between the addition and subtraction facts by introducing these in tandem, knowing one fact will allow the student to access multiple facts. This has several advantages for students who require additional support:

Builds confidence in the expanding facts known by forming connections between addition and subtraction;

Provides spaced interleaved retrieval practice every session, these principles of learning are well demonstrated as effective learning practices (see The Learning Scientists, Rosenshine’s Principles);

Reduces time wasted repeating teaching cycles; and Acknowledges there is already less time available for

these students as they already have gaps in learning.

The overall structure of this second pathway includes the following sequence, always maintaining the teaching model:

1. Focus Digit / Numeral2. Make with materials3. Addition Facts Strategy4. Commutative Property (order doesn’t matter in addition)


https://www.teachertoolkit.co.uk/wp-content/uploads/2018/10/Principles-of-Insruction-Rosenshine.pdf

https://www.learningscientists.org/

https://www.learningscientists.org/


5. Vertical & horizontal representations6. Missing Addend (introduction to / prerequisite for

subtraction)7. Links to Subtraction Facts8. Questions with units (blocks & numerals)9. Questions with tens (blocks & numerals)10. Questions with hundreds (blocks & numerals)11. Worded presentations

Additional Retrieval activities for all stages of this second pathway can be found here.

Fact Family 1: ZeroEnsure you have reviewed Units 1-4 in the first pathway before beginning with Zero. Place Value, Counting Patterns and Subitising (of the materials you’re using) should still be included within the retrieval practice at the beginning of each session.

Zero represents no items when we’re counting. The numeral 0 holds the place where there is nothing in that place (e.g., 10 is 1 ten and 0 units, 100 is 1 hundred 0 tens and 0 units, 101 is 1 hundred 0 tens and 1 unit).

Complete demonstrations for addition and subtraction using the teaching model.

Key Messages1.When we add zero to any numeral

the sum is the same numeral.



2.When we subtract 0 from a numeral, the difference is unchanged as we have taken nothing away.

3. When we subtract the same numeral from itself, we have taken it all away and there is nothing left - the difference is zero.

0 Addition Facts0 + 0

0 + 1

0 + 2

0 + 3

0 + 4

0 + 5

0 + 6

0 + 7

0 + 8

0 + 9

0 + 10

1 + 0

2 + 0

3 + 0

4 + 0

5 + 0

6 + 0

7 + 0

8 + 0

9 + 0

10 + 0

0 Missing Addends0 + _ = 0

0 + _ = 1

0 + _ = 2

0 + _ = 3

0 + _ = 4

0 + _ = 5

0 + _ = 6

0 + _ = 7

0 + _ = 8

0 + _ = 9

0 + _ =10

1 + _ = 1

2 + _ = 2

3 + _ = 3

4 + _ = 4

5 + _ = 5

6 + _ = 6

7 + _ = 7

8 + _ = 8

9 + _ = 9

10+_ =10

0 Subtraction Related Facts0 - 0

1 – 0

2 – 0

3 – 0

4 – 0

5 – 0

6 – 0

7 – 0

8 – 0

9 – 0

10 – 0

1 - 1

2 - 2

3 - 3

4 - 4

5 - 5

6 - 6

7 - 7

8 - 8

9 - 9

10 – 10



Worded Presentations1. The door opened once but wouldn’t open again. How

many times did the door open?2. I ate # grapes before dinner. My dad wouldn’t let me have

any more. How many grapes did I eat?3. Brianna collected # points at school last week. This week

is school holidays, and no points can be collected. How many points does Brianna have?

4. Christian ate # potatoes. He asked for more, but there were none left. How many potatoes did he eat?

5. It didn’t rain yesterday. Today it is raining. For how many days has it rained?

6. There are # bananas. The gorilla eats # bananas. How many bananas are left?

7. Savannah has # strawberries. She gives Sally # oranges. Savannah has # oranges left.

8. There are # apples in the fruit basket. Harry takes out # apple. How many apples are left?

9. Alice and Mary like cats. Mary has # cats and Alive has # cat. Mary has # more cats than Alice.

10. When we were fishing, we caught # fish but had to throw # back. How many fish did we have to bring home?

The demonstrations for Unit 9 (Missing Addends) may need to be included and repeated to improve the connections between

addition and subtraction facts.



Fact Family 2: OneOne represents 1 item when we’re counting.


Key Messages1.When we add one to any numeral

it is the next counting numeral.2.We can change the order of whole

numerals when adding without changing the answer.

3.When we subtract 1 it is the number before, because when we add 1 it is the number after, they are opposites.

4.When we subtract a number that is the number before it, the answer is 1 as they are only one number apart.


1 + 1

1 + 2

1 + 3

1 + 4

1 + 5

1 + 6

1 + 7

1 + 8

1 + 9

1 + 10

0 + 1

2 + 1

3 + 1

4 + 1

5 + 1

6 + 1

7 + 1

8 + 1

9 + 1

10 + 1


1 + _ = 3

1 + _ = 4

1 + _ = 5

1 + _ = 6

1 + _ = 7

1 + _ = 8

1 + _ = 9

1 + _ =10

1 + _ =11

2 + _ = 3

3 + _ = 4

4 + _ = 5

5 + _ = 6

6 + _ = 7

7 + _ = 8

8 + _ = 9

9 + _ =10

10+_ =11


3 – 1

4 – 1

5 – 1

6 – 1

7 – 1

8 – 1

9 – 1

10 – 1

11 - 1



3 - 2

4 - 3

5 - 4

6 - 5

7 - 6

8 - 7

9 - 8

10 - 9

11 – 10

Extensions with Place ValueEnsure you also use materials and numerals to extend this strategy for students for maximum understanding and transference (6 + 1 = 7, 60 + 10 = 70 (6 tens + 1 ten = 7 tens) …



Worded PresentationsThe list of worded presentations below can be used for most of the fact families in subsequent sections. Where a specific list of worded presentations is recommended, they will appear in the section.

Addition1. There are # bears in my room and I find # outside. How

many altogether?2. I have # red pencils and # yellow pencils. There are #

pencils altogether.3. # apples are green and # are red. How many in all?4. Max sharpened # pencils before recess and # after recess.

How many pencils did he sharpen today?5. Trish is # years old. How old will she be in # years?6. The boy has # cars. He gets # more for his birthday. How

many cars does he have now?7. # cars were in the car park when we arrived with our car.

How many cars are there now?8. Ava has # birds. She also has # fish. How many pets does

Ava have in all?9. # roses and # lilies are in a vase. How many flowers are in

the vase?10. There are # biscuits on the plate and # cakes. How many

sweets are there to eat?11. There are # boys in the pool and # girls in the pool. How

many children are in the pool?12. # birds are in the tree and # are on the ground eating

seeds. How many birds altogether?13. Charlotte lost # drink bottles at school. She found # of

them. How many are still lost?14. # people are in line. # more people join the line. How

many people are waiting?15. I drew # pictures yesterday. Today I drew # more. How

many have I drawn altogether?16. Michelle picked # flower. Her dad gave her # more

flowers. How many flowers does Michelle have altogether?17. There are # people on a bus. # more get on. How many

people are there on the bus now?18. Our car has four tyres. There is a spare in the boot. How

many tyres do we have altogether?



19. Nina has # dolls. Her mum buys her # more. How many does she have now?

20. Andrew had already saved # dollars. He earnt # more this week. How much money does he have now?

21. Will has # cards in his collection. Tim’s collection is # greater than Will’s. How many cards does Tim have?

22. Adam has # bats. Luke has # more bats than Adam. How many bats does Luke have?

23. At the beach Henry saw # crabs. Lisa saw # more than Henry. How many did Lisa see?

24. Gary had # scarves. He bought # more. How many scarves does he have now?

25. Ann makes # necklaces. Sarah makes # more than Ann. How many necklaces does Sarah make?

26. Cliff has # books and Ryder has # books for the fair. How many books will they donate?

27. Wally picked # strawberries on Sunday and another # strawberries on Monday. How many strawberries has he picked?

28. Ricky bakes # muffins for the sale and Sophie baked # more muffins. How many did they bake altogether?

29. Isla played # games and her brother played # more games. How many games did they play altogether?

30. If I hold up # fingers on one hand and # fingers on the other hand, how many fingers am I holding up?

31. Dad bought # kilograms of sausages and # kilograms of bacon for the BBQ. How many kilograms of food did he buy altogether?

Missing Addends1. Xander is wrapping # presents. He has already wrapped #.

How many more does he need to wrap?2. Our teacher is printing # booklets. He has printed # so far.

How many more to print?3. I am making sandwiches for # people. I have made # so far.

How many more do I need to make?4. Of the # rooms in the house, # have carpet, how many do

not have carpet?5. # people are invited to a party and # have arrived. How

many people are we waiting for?



Subtraction1. There are # bananas. The gorilla eats # bananas. How many

bananas are left?2. Savannah has # strawberries. She gives Sally # oranges.

Savannah has # oranges left.3. There are # apples in the fruit basket. Harry takes out #

apple. How many apples are left?4. Alice and Mary like cats. Mary has # cats and Alive has #

cat. Mary has # more cats than Alice.5. When we were fishing, we caught # fish but had to throw #

back. How many fish did we have to bring home?6. # fish are swimming in the lake, # are caught. How many

are left?7. There are # marbles. # are red, the rest are green. How

many marbles are green?8. # bees are in the hive. # fly away. How many bees are left?9. # people got onto the bus, then # got off at the next stop.

How many people are left in the bus?10. There are # cows in the paddock. # have eaten. How

many cows are still eating?11. There are # bats on the wire. # bats fly away. How many

birds are on the wire now?12. Sue has # slices of oranges. She eats # slices. How many

slices are left?13. There are # pages to read in my book. I have read #

pages so far. How many more pages do I need to read?14. Alison is # years old. Her brother is # years old. What is

the difference in their ages?15. There are # spaces for eggs in a carton. I have used #

eggs. How many eggs are left?16. There are # trucks. # drive off. How many trucks are left?17. Mum hade # sandwiches. # have been eaten already.

How many sandwiches are left?18. Lucy had # balloons. # popped. Lucy has # balloons left.19. Matt won # points in the game and Andy won # points.

What is the difference in their scores?20. In a family # children are boys and # children are girls.

How many more boys than girls are there in the family?21. Mum made # cupcakes. I ate #. How many are left?22. There are # balls altogether. # of them are tennis balls.

How many basketballs are there?



23. Penny has # rice crackers. She eats #. How many rice crackers does she have left?

24. Richard has # stickers. Blake has # stickers. How many fewer stickers does Blake have than Richard?

25. John has # books. He has # more books than his brother. How many books does his brother have?

26. Jenny collects # flowers. Erin collects # fewer flowers than Jenny. How many flowers does Erin collect?

27. Linda has # stamps. She has # more than Rebecca. How many stickers does Rebecca have?



Fact Family 3: TenOur number system is based on 10 (known as deci), there are only 10 digits (0-1-2-3-4-5-6-7-8-9) which form all of the numerals used to represent numbers. Ten represents 10 items when we’re counting. Only one digit (0-9) can be in any place in a numeral, once we reach the numeral 10 we have two numerals, the 1 represents the 10 block and the 0 means there are no units in the number.

Ten is introduced early in this pathway as it provides additional opportunities to consolidate familiarity and confidence with the teens. Students often struggle to count by 2’s after 10 as they are still learning and becoming comfortable with the teen numbers. Introducing 10 at this stage aims to reduce this issue.

Complete demonstrations for addition and subtraction using the teaching model below.

Key Messages1.When we add ten to any numeral

it is the tens that change by just one more ten.

2.When we subtract 1 it is the number before, because when we add 1 it is the number after, they are opposites.

3.When we subtract a number that is the number before it, the answer is 1 as they are only one number apart.


10 + 1

10 + 2

10 + 3

10 + 4

10 + 5

10 + 6

10 + 7

10 + 8

10 + 9

10+ 10

0 + 10

1 + 10

2 + 10

3 + 10

4 + 10

5 + 10

6 + 10

7 + 10

8 + 10

9 + 10



10 Missing Addends10+_ =13

10+_ =14

10+_ =14

10+_ =16

10 _ =17

10+ _=18

10+ _=19

10+_ =20

3 + _ =13

4 + _ =14

5 + _ =15

6 + _ =16

7 + _ =17

8 + _ =18

9 + _ =19


3 – 1

4 – 1

5 – 1

6 – 1

7 – 1

8 – 1

9 – 1

10 – 1

11 - 1

3 - 2

4 - 3

5 - 4

6 - 5

7 - 6

8 - 7

9 - 8

10 - 9

11 – 10

Fact Family 4: TwoTwo represents 2 items when we’re counting. When counting by 2’s we are also counting by odd or even number patterns.


Key Messages1.When we add two to any number

it is the next odd or even number (so we have to know odd or even 1st)

2.When we subtract 2, it is the odd or even number before.

3.When we subtract two numerals with a difference of 2, they are two decreasing odd or even numeral pairs.

2 Addition Facts2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 +



0 1 2 3 4 5 6 7 8 9 100 + 2

1 + 2

3 + 2

4 + 2

5 + 2

6 + 2

7 + 2

8 + 2

9 + 2

10 + 2


2 + _ = 5

2 + _ = 6

2 + _ = 7

2 + _ = 8

2 + _ = 9

2 + _ =10

2 + _ =11

2 + _ =12

3 + _ = 5

4 + _ = 6

5 + _ = 7

6 + _ = 8

7 + _ = 9

8 + _ =10

9 + _ =11

10+_ =12


3 – 1

4 – 1

5 – 1

6 – 1

7 – 1

8 – 1

9 – 1

10 – 1

11 - 1

3 - 2

4 - 3

5 - 4

6 - 5

7 - 6

8 - 7

9 - 8

10 - 9

11 – 10

Related facts and odd and even numerals are the most efficient strategies for subtracting 2, however the answer can still be derived by simply counting back 2!

Extensions with Place ValueEnsure you also use materials and numerals to extend this strategy for students for maximum understanding and transference (6 + 2 = 8, 60 + 20 = 80 (6 tens + 2 tens = 8 tens) …

Fact Family 5: NineAlthough working with 9 uses the related facts of 10, these are separated by the facts of 2 to provide time to consolidate the facts of 10 before manipulating these.




Key Messages1.When we add nine to any numeral

it is just 1 less than adding 10 (we add 10 then go back one or go back one first then add 10)

2.When we subtract 9 from any numeral, we can subtract 10 and then add one more (because 10 was 1 too many).


9 + 1

9 + 2

9 + 3

9 + 4

9 + 5

9 + 6

9 + 7

9 + 8

9 + 9

9 + 10

0 + 9

1 + 9

2 + 9

3 + 9

4 + 9

5 + 9

6 + 9

7 + 9

8 + 9

9 + 9

10 + 9


9 + _ = 10

9 + _ = 11

9 + _ = 12

9 + _ = 13

9 + _ = 14

9 + _ = 15

9 + _ = 16

9 + _ = 17

9 + _ = 18

9 + _ = 19

3 + - = 12

4 + _ = 13

5 + _ = 14

6 + _ = 15

7 + _ = 16

8 + _ = 17

9 + _ = 18

9 Subtraction Related Facts9 – 9

10 – 9

11 – 9

12 – 9

13 – 9

14 – 9

15 – 9

16 – 9

17 – 9

18 – 9

19 - 9

9 - 0

10 - 1

11 - 2

12 - 3

13 - 4

14 - 5

15 - 6

16 - 7

17 - 8

18 - 9

19 - 10




Fact Family 6: DoublesComplete demonstrations for addition and subtraction using the teaching model.

Key Messages1.Adding doubles are a special

group of numbers we remember.2.Knowing our add doubles facts

helps us answer subtraction questions.

Double Addition Facts0 + 0

1 + 1

2 + 2

3 + 3

4 + 4

5 + 5

6 + 6

7 + 7

8 + 8

9 + 9

10+ 10

Doubles Missing Addends0 + _ = 0

1 + _ = 2

2 + _ = 4

3 + _ = 6

4 + _ = 8

5 + _ =10

6 + _ =12

7 + _ =14

8 + _=16

9 + _ =18

10+ _=20

_ + 0 = 0

_ + 1 = 2

_ + 2 = 4

_ + 3 = 6

_ + 4 = 8

_ + 5 =10

_ + 6 =12

_ + 7 =14

_ + 8=16

_ + 9 =18

_+ 10=20

Doubles Subtraction Related Facts0 – 0

2 – 1

4 – 2

6 - 3

8 – 4

10 – 5

12 – 6

14 – 7

16 – 8

18 – 9

20 - 10

As Doubles is such a helpful fact to know the whole set is included here for review, the new ones for teaching are 3+3, 4+4, 5+5, 6+6, 7+7, 8+8.

Worded Presentations



Addition1. Amy and Amber are identical twins. They are each # years

old. What is their combined age?2. My sister and I each have # ribbons. How many ribbons do

we have altogether?3. There are 2 boxes of # pencils. How many pencils are

there altogether?4. Two cats are sleeping. They each have 4 legs. How many

legs do they have altogether?5. Two families have # children each. How many children

altogether?

Subtraction1. My brothers Archer and Fletcher are twins. Their combined

age is #. How old are each of my brothers?2. My sister and I have the same number of books in our

rooms. How many books do we each have?3. There are 2 boxes with the same number of pencils.

Altogether there are # pencils. How many pencils go into each box?

4. The same number of people are in both rooms at the cinema. There are # people altogether. How many people are in each room?

5. Two families have the same number of pets. How many pets does each family have?




Fact Family 7: Making & Subtracting from 10Adding to 10 is a common addition fact family, sometimes the main or only fact family focussed on and is often referred to as “Friends of 10”, “Bridging to 10”. It is a powerful fact family, like Doubles, in that it can be applied to much larger numbers quickly.


Key Messages1.Knowing what numbers add to 10

helps us add bigger numbers.2.Our facts to 10 will help with

both addition and subtraction.

Making Ten Addition Facts10 + 0

9 + 1

8 + 2

7 + 3

6 + 4

5 + 5

4 + 6

3 + 7

2 + 8

1 + 9

0 + 10

1 Missing Addends0+ _ =10

1+ _ =10

2+ _ =10

3+_ =10

4 + - =10

5+ _ =10

6+ _ =10

7+ _ =10

8+ _ =10

9+ _ =10

10+_ =10

Subtraction from Ten Related Facts10 – 0

10 – 1

10 – 2

10 – 3

10 – 4

10 – 5

10 – 6

10 – 7

10 – 8

10 – 9

10 - 10

Worded PresentationsAddition & Subtraction








6. I have 10 fingers on my hand. # fingers have paint on them. How many fingers are clean?

Extensions with Place ValueEnsure you also use materials and numerals to extend this strategy for students for maximum understanding and transference (6 + 4 = 10, 60 + 40 = 100 (6 tens + 4 tens = 10 tens 100) …



Fact Family 8: Almost DoublesHaving a strong understanding and recall of doubles allows for some relationships to be modelled for new addition facts. The idea here isn’t to rote memorise these facts, but to encourage reasoning, thinking and using known facts to derive at the answer quickly. The premise of this is that the previous skills of next number and doubles need to be firm, they must be absolute known facts for this to work (hence, not rushing through previous skills).


Key Messages1.Knowing how to add doubles helps

us add and subtract close doubles quickly.

Almost Doubles Addition Facts4 + 3 5 + 4 6 + 5 7 + 6 8 + 7 9 + 83 + 4 4 + 5 5 + 6 6 + 7 7 + 8 8 + 9


5 + _ = 9

6 + _ = 11

7 + _ = 13

8 + _ = 15

9 + _ = 17

3 + _ = 7

4 + _ = 9

5 + _ = 11

6 + _ = 13

7 + _ = 15

8 + _ = 17

Almost Doubles Subtraction Related Facts7 - 3 9 - 4 11 - 5 13 - 6 15 - 7 17 - 87 - 4 9 - 5 11 - 6 13 - 7 15 - 8 17 - 9



Only the new facts related to this strategy are included here, there are more efficient strategies for other facts.



Fact Family 9: Remaining FactsThere are now a small set of addition and subtraction facts remaining to be learnt and linked to other related facts.

There are some patterns that can be utilised here (see detailed lists below), at this stage of the program students are encouraged to be using known facts to help them retrieve these when needed.

This may be a set of facts that are recalled by rote if appropriate for the student.


Key MessagesI’m almost there!

Remaining Addition Facts3 + 5 3 + 6 3 + 8 4 + 7 4 + 8 5 + 7 5 + 8 6 + 8

3 + 5 known double 3 & add 2

3 + 6 1 less than known add to 10 (4 + 6 4 - 1 + 6)


4 + 7 1 more than known add to 10 (3 + 7 3 + 1 + 7)1 more than known add to 10 (4 + 6 4 + 7 + 1)




5 + 7 known double 5 & add 22 more than known add to 10 (3 + 7 3 + 2 + 7)

5 + 8 2 less than add 10 (5 + 8 5 + 10 – 2)

6 + 8 known double 6 & add 22 less than add 10 (6 + 8 6 + 10 – 2)

Remaining Missing Addends3 + _ = 8

3 + _ = 9

3 + _ = 11

4 + _ = 11

4 + _= 12

5 + _ = 12

5 + _ = 13

6 + _ = 14

5 + _ = 8

6 + _ = 9

8 + _ = 11

7 + _ = 11

8 + _= 12

7 + _ = 12

8 + _ = 13

8 + _ = 14

Remaining Subtraction Related Facts8 – 3 9 – 3 11 – 3 11 – 4 12 – 4 12 – 5 13 – 5 14 – 68 – 5 9 - 6 11 - 8 11 - 7 12 - 8 12 - 7 13 - 8 14 - 8

Remaining Facts by MinuendSubtract 3

8 – 3

9 – 311 – 3

Build on the relationship that double 3 is 68 is 2 more than 6 (difference is two more than 3 [5])

Build on the fact 3 + 7 = 10 9 is 1 less than 10 (difference is one less than 7 [6]) 11 is 1 more than 10 (difference is one more than 7 [8])

Subtract 4

11 – 412 – 4

Build on the fact 4 + 6 = 1011 is 1 more than 10 (difference is one more than 6 [7]) 12 is 2 more than 10 (difference is one more than 6 [8])

Subtract 5142© Learning Links


8 – 5

11 – 512 – 513 – 5

Build on the relationship that double 5 is 108 is two less than 10 (difference is two less than 5 [3])


Subtract 6

9 – 614 – 6

Build on the fact 6 + 4 = 109 is 1 less than 10 (difference is one less than 4 [3])14 is 4 more than 10 (difference is four more than 4 [8])

Build on the relationship that double 6 is 1214 is 2 more than 12 (difference is two more than 6 [8])

Subtract 7

11 – 712 – 7

Build on the fact 7 + 3 = 1011 is 1 more than 10 (difference is one more than 3 [4]) 12 is 2 more than 10 (difference is two more than 3 [5])

Subtract 8

11 – 812 – 813 – 8

14 – 8


Build on the relationship that double 8 is 1614 is 2 less than 16 (difference is two less than 8 [6])





Session Planning Form AChild’s Name Starting Date

Retrieval PracticeCounting Last Weeks’

ConceptPrevious Weeks’ Concept

New Concept

Modelling & Demonstration

Independent Practice

Worded Questions

Retrieval PracticeNew Concept Other (errors in beginning

retrieval practice)

Next Steps?



Session Planning Form BChild’s Name Starting Date

Teach Retrieval Practice

Comments

Pre-RequisitesCounting Numerals (Digits)Place Value (Teens, Decades, Making)Counting Patterns (Forwards, Backwards)Counting Concepts (Subitising)Addition+ 0

+ 1

+ 10

+ 2

Missing Addend Concept+9



+ Doubles

+ Almost Doubles+ to 10

Remaining Facts3 + (5, 6, 8)4 + (7, 8)5 + (7, 8)6 + 8Subtraction - with 0 & 1

- with 10

- with 2

- with 9

- with Doubles

- from 10

Remaining Facts-3 (7, 8, 9, 11)-4 (7, 9, 11, 12)-5 (8, 9, 11, 12, 13)-6 (9, 11, 13, 14)-7 (11, 12, 13, 15)



-8 (11, 12, 13, 14, 15)



Resource SummaryThe core resources for this entire intervention have been provided for you in the Downloads section. The resources have been created mainly as presentation decks (PowerPoint files that can be opened in any presentation program, e.g., Google docs). The decks are complete sets, in the order of the first pathway of the program and in chronological order (0-9 where appropriate).

Explained earlier in the handbook, to review how to use the decks:

1. Download files to your computer to have a local copy2. Make a copy and name this for your student3. Select the slides the student needs (i.e., delete slides not

covered or required)

To use decks virtually:a. Present slides in screen share in Zoom (when delivering

online tutoring)b. Present slides from iPad (when delivering face to face to

reduce paper wastage)

To use decks in physical form, go to Print menu on your computer to select the layout function to choose how many slides to print to a page to create:

a. flashcards (recommend 4-6 per page) before cuttingb. worksheets (recommend 16 per page) before printing

The resources available for this intervention include: This handbook! Digit and Numeral Deck (lists numerals 0-20) Counting Grid from 0 (counting grid with teens and

decades expressed in place value form) MAB Colouring (if further review of numeral identification

is required) Place Value (presentation deck with labels and grids) Numeral Patterns ALL (lists counting patterns in multiple

formats) Addition Facts Grid (Word file to print and record student

progress visually)



Addition Facts ALL (complete list of addition facts for learning without answers)

Retrieval Presentation Deck (slides with types of retrieval tasks to display and insert numerals quickly)

Retrieval Practice Page (common retrieval types on a single page)

Worded Presentations Addition (set of worded problems for numerals to be inserted)

Missing Addends Facts Grid (Word file to print and record student progress visually)

Missing Addends ALL (complete list of all missing addend addition facts for retrieval tasks)

Subtraction Facts Grid (Word file to print and record student progress visually)

Subtraction Facts ALL (complete list of subtraction facts for learning without answers)

Worded Presentations Subtraction (set of worded problems for numerals to be inserted)

All Facts 2nd Pathway (complete set of addition, missing addend, subtraction grouped according to fact family (0, 1, 10 …)

Please note: Additional commercial resources have been added to the Downloads section for Digit Formation and Subitising. These will be replaced with Learning Links resources in the future.


Documents

Table of Contents - learninglinkshub.org.au · Web viewMathematics has a very precise vocabulary and the language of mathematics in a broader sense requires specific instruction