Page 1 of 39

Outcome: MA3-7NA compares, orders and calculates with fractions, decimals and percentages

Rationale:

Students will read and study the information required. They will attempt the warmup questions and then select a

coloured level on the column provided to practise the skill that is not too easy or too hard for them to achieve

(generate at least 3 of their own each day). Students have support links to access for further explanations where

needed. Teachers will check their performance and give feedback or recommendations where feasible. Once they feel

confident on one colour, they are encouraged to attempt the next (left to right) at their own pace.

On the 5th lesson of the week, students will engage in problem solving questions based on their current

understanding. It is not required that they solve all the problems but they must attempt one at least.

Students will also have Mentals booklets where they can time themselves when completing the questions. Students

are encouraged to research unfamiliar words or concepts where necessary.

Page 2 of 39

Essential core understanding:

Page 3 of 39

Page 4 of 39

Warm up

Page 5 of 39

Task: Look at the coloured columns on the next page. Have a go at showing your understanding on the coloured skill

that you think you can do. Look at the examples provided and remember to make your own numbers where they are

not provided. Show me at least three different ones to demonstrate your understanding.

Tip: Read the column thoroughly, everything typed is there to help you, if it’s too hard then move to the left column.

Page 6 of 39

Week 1 Lesson 1-4 Choose one column to work on- not too easy, not too hard. You can work on one to the right of your selection the following lesson if you feel confident to try it.

F D 13 Equivalent Fractions

Can you show me 3 other fractions equal to a half?

F D 13 Equivalent Fractions

Can you show me other fractions equivalent to two

thirds?

F D 29 Percentages related to Hundredths as Fractions and Decimals

Can you represent hundredths in fractions and decimals?

F D 30

Can you round the original price of items to the nearest dollar and then find the price after a 50% discount?

Equivalent means equal value. The fractions below show equal value to a half.

Example working out

1. 1

2=

1×2

2×2=

2

4

2. 3

6=

3×2

6×2=

6

12

(Tip: denominator will be a multiple of two)

We know that 2

3=

4

6=

8

12

But how do we know that all these fractions are equal to

two thirds? Example working out

Choose a numerator 10 If 10 is two thirds of the denominator then I will need to first halve it to find one third. 10 ÷ 2 = 5 Then I will multiply it by 3 to find the denominator.

5x3= 15

𝑇ℎ𝑒𝑟𝑒𝑓𝑜𝑟𝑒 10

15 𝑖𝑠 𝑒𝑞𝑢𝑖𝑣𝑎𝑙𝑒𝑛𝑡 𝑡𝑜 𝑡𝑤𝑜

𝑡ℎ𝑖𝑟𝑑𝑠.

Fractions can be represented as decimals and percentages.

Percent is another word for the

fraction one hundredth. The symbol

looks like this %

Select a number to create a hundredth and record it as a

fraction, decimal and percentage. Select where it would go on this

number line and draw it.

Example

Look up the prices of some items, round them to the

nearest dollar and then halve it to find the discounted price.

(if you can demonstrate this level easily then move on to the red level for week 2)

Page 7 of 39

Week 1 Day 5

Problem Solving Questions- Yellow and Blue Level

Page 8 of 39

Week 1 Day 5

Problem Solving Questions- Green and Red Level

Page 9 of 39

Fraction Wall- Week 2 Yellow (option of cutting and pasting fractions or drawing)

Page 10 of 39

Week 2 Blue level This multiplicative Place Value Chart can help you make the relational connections.

Page 11 of 39

Week 2 Day 5 Problem Solving Questions Red column

Week 2 Lesson 1-4 Choose one column to work on. If this week’s concepts are too complicated you can work on a different concept from last week. FD 14 Equivalent Fractions on a Number Line

Can you place the fractions on page 9 on a number line?

FD 16- Cents as a fraction of a dollar

Can you investigate money as decimal, and describe cents as fractions of dollars. (Refer to page 10.)

(If you worked on this level last week then move on to

the red level for week 1 then week 2)

FD 30 Can you round the original price of items to the nearest dollar and then find the price after a 25% discount?

Draw a number line between one and zero Place halves, quarters and eighths on the number line. What fractions are in the same place? How can you explain how you know they are equivalent? (fraction wall, relationship between the denominator and numerator, common place on a number line) It has been started it for you:

(note: the fraction wall is pasted for demonstration, you are not required to cut it out unless it helps deepen your understanding)

1- Select an amount of money including cents and dollars. Record the dollars as wholes and cents as fractions of a dollar.

Example

$3.52=3 𝑜𝑛𝑒𝑠 𝑑𝑜𝑙𝑙𝑎𝑟𝑠 +5

10𝑑𝑜𝑙𝑙𝑎𝑟 +

2

100 𝑑𝑜𝑙𝑙𝑎𝑟 𝑎𝑛𝑑 $3.52 = 3.52 𝑑𝑜𝑙𝑙𝑎𝑟𝑠

2- Select coins. Record each as a decimal fraction and as a fraction of a dollar.

Example

50 cents recorded as 0.5 dollars

or 5

10 dollars or

5

100 𝑑𝑜𝑙𝑙𝑎𝑟𝑠 or

1

2 𝑑𝑜𝑙𝑙𝑎𝑟

3- Add two or more coins and record their sum as a decimal and as a fraction of a dollar.

Example

e.g. 50 cents + 20 cents = 0.7

dollars, or 7

10 dollar or

7

100 dollar

Look up the prices of some items, round them to the

nearest dollar and then follow the steps to find the discounted

price after a 25% reduction

Extension: find 20%, 70%, 40% and 33% off some items in a brochure or on a website. Write some of your own problems to solve.

Page 12 of 39

Blue column

Page 13 of 39

Yellow column

Support Links (You are not limited to these, there are many examples

on the internet, stick to the ones that help you understand the

concepts):

Equivalent fractions:

https://www.youtube.com/watch?v=nQKQn2kiNDI

https://www.youtube.com/watch?v=cFDP_bbfW7s

Equivalent Fractions on a number line:

https://www.youtube.com/watch?v=Su4DKLbK8mA

Percentages:

https://www.youtube.com/watch?v=CbyZLlyenLg

https://www.youtube.com/watch?v=uXZ895FMzZ8

https://www.youtube.com/watch?v=ty12FGhxQEw

Calculating Discounts:

https://www.youtube.com/watch?v=ty12FGhxQEw

https://www.youtube.com/watch?v=WYWPuG-8U5Q

Page 14 of 39

*Important*: You will cover two

strands in the following weeks. This means you will need to divide your weekly focus to demonstrate

your understanding ( 2 lessons on chance, 2 lessons on discounts)

Outcomes: uses appropriate methods to collect data and constructs, interprets and evaluates data displays, including dot plots. MA3-18SP

conducts chance experiments and assigns probabilities as values between 0 and 1 to describe their outcomes MA3-19SP

Resources needed: Two dice (if you cannot access these, use the template on the following page and follow the steps

on https://www.firstpalette.com/craft/paper-dice.html to make your own. Alternatively, type in ‘interactive dice’ on google and

select one to use.)

Page 15 of 39

Page 16 of 39

Support links for Chance in week 3 and 4:

Yellow column> Introduction to chance https://www.youtube.com/watch?v=TedbpetdzBE

Probability songs: https://www.youtube.com/watch?v=ToPYHnRROVI

https://www.youtube.com/watch?v=au8hf0-A27s

Probability https://www.youtube.com/watch?v=KzfWUEJjG18

https://www.youtube.com/watch?v=vGcmjINp1x8

Displaying Data on a line: https://www.youtube.com/watch?v=mHCBtKFhV8M

https://www.youtube.com/watch?v=QJCQL794G1U Using a spinner https://www.youtube.com/watch?v=3QmNvODlnt8 https://www.youtube.com/watch?v=7KcKrOTRSqY

Page 17 of 39

Warm up

Page 18 of 39

Page 19 of 39

Chance Week 3 You will need to complete 2 lessons a week from this table and then the other 2 from the “Discounts” table.

S & P 16 Can you identify the outcomes of a chance experiment and list probabilities using fractions.

S & P 17 Can you trial a chance experiment then use the data to predict outcomes of future trials?

S & P 17 Can you use the data from dice combinations predict the chances on

larger trials?

S & P 17 Can you use the data from a different chance experiment to predict chances in larger trials? (if this is too tricky then start back from the blue)

1. Use the counters on page 23 (you can use 3 different colour lollies instead or real counters). Colour the rest of the counters using either green, yellow or red.

2. Predict how much you have of each colour. I think I have 23 red, 12 blue and 6 green.

3. Tally the amount of counters you have in a table.

Example:

4. Did your prediction match the actual data?

5. Make given probabilities using fractions. Example:

Show that the sum of your fractions = 1

My fractions should add to 50

50

Frequency means how often an outcome occurs. Step 1: Draw a base line and number it 2 to 12. Roll your dice 20 times, after each roll record the sum that occurs through a cross on your line plot. Example:

4 + 1 = 5 so I recorded a cross on 5

Roll again, 1 + 1= 2 so I recorded a cross on 2... repeat

20 times… Step 2: use your data to predict what sum is most likely to occur in future frequencies.

Example: My data above shows a frequency of 1 on 2, 3 and 4, a frequency of 3 on 5 and a frequency of 2 on 6. Therefore 5 has the greatest frequency. Step 3: Draw another line to conduct another trial with 30 rolls. Were the predicted and actual frequencies similar or different? Did the same sum have the greatest frequency? Was it what you predicted? Were your predictions likely but not certain? Explain.

Step 1: use your dice to continue gathering data on all possible dice combinations and record your data. The first 3 have been done for you.

Answer the questions (full sentences):

1. How many sum combinations make 5? Are there four combinations that add to make 5?

Count your total amount of combinations (you should have recorded 36 possible combinations altogether) Your results should show 6 out of 36 combinations have a sum of 7.

2. If we rolled the dice 6 times would we predict we’d roll one sum of 7?

3. Does one combination make the sum of two?

How many times do you predict we would get the other sums if we rolled the dice 100 times?

1. Make a spinner or use one freely available on the internet (where numbers/ colours/ symbols are freely recorded on the internet)

2. Conduct a chance experiment

using a small number of trials, recording the frequencies in a dot/line plot.

3. Use the frequencies to predict

the frequencies in a larger trial

4. Conduct the larger trial

5. Compare the frequencies from the two trials

6. Compare your predicted frequencies from your actual frequencies

7. Identify differences, explaining that trials and predictions are likely but not certain.

Use the data to predict frequencies in much larger trials of 50, 100, 200 and

1000.

Page 20 of 39

Week 3 Problem Solving

Blue column Red column

Page 21 of 39

Week 3 Chance Problem Solving

Yellow column Green column

Page 22 of 39

Discounts Week 3 You will need to complete 2 lessons a week from this table and then the other 2 from the ‘chance’ table.

F D 29 (if this level is too hard then revise blue and yellow column from week 1 and 2)

Can you represent hundredths in fractions and decimals?

F D 30 Can you round the original price of items to the nearest dollar and then find the price after a 50% discount?

FD 30 Can you round the original price of items to the nearest dollar and then find the price after a 25%

discount?

FD 30 MF 13 Can you apply your strategies to find 75% off discounts?

Fractions can be represented as decimals and percentages.

Percent is another word for the

fraction one hundredth. The symbol

looks like this %

Select a number to create a

hundredth and record it as a fraction, decimal and percentage. Select

where it would go on this number line and draw it.

Example:

Look up the prices of some items in a brochure or on a website, round them to the

nearest dollar and then halve it to find the discounted price.

Find one quarter of the amount

Example:

Therefore $22.50 x 3= $66 + 1.50

(mentally, I added the dollars first and then the cents)

Or You could subtract it from the total

$90-$22.50= $67.50

(mentally, I will subtract using place value 9 tens – 2 tens =7 tens, 7 tens – 2

ones= 68 - 0.50 = $67.50)

Select some items from a website or brochure and find the discounted price after a 25% reduction. Show both ways

to check your answers.

1 Pick an item from a brochure or website. Record its price.

2 Multiply 25% of the price by 3 to find the 75% that will be paid.

3 Subtract 25% from the original price to find the 75% that will be paid.

Extension: If you attempted to find 75% of some prices in week 2 then compare the strategy you used to the one below. You may have/ have not followed the same steps. Record your findings.

Page 23 of 39

Counters for week 3 yellow column

Page 24 of 39

Chance Week 4 You will need to complete 2 lessons a week from this table and then the other 2 from the “Discounts” table.

S & P 17 Can you conduct another chance experiment and use the data

from small trials to predict larger ones?

S & P 18 Can you use data to create a fair game of chance where the organiser has a greater chance of winning?

If the green and red column are too challenging then go back to week 3 chance lessons. If this is you, you will need to continue with Problem Solving questions from week 3.

Conduct a chance experiment tossing 1,2,3 or 4 coins. Using a small number of trials, recording the results in line/ dot plot. Use the frequencies to predict the frequencies in a larger trial. Conduct the larger trial. Compare the frequencies from the 2 trials. Compare your predicted frequencies from your actual frequencies. Identify differences, explaining that trials and predictions are likely but not certain. Use the data from your trials to predict the frequencies in much larger trials of 50, 100, 200 and 1000.

(Remember 7 was the most likely sum when rolling two dice) Can you design a game where the sum of 7 might increase your chances of winning? For example: in this coin toss game below, using a smaller coin will increase the organiser’s chance of not landing on a line when they compete with a friend.

Can you describe the probability of each outcome as a fraction and decimal on a number line? For example: The possibility of landing on heads in the game above is half.

You might describe the possibility of landing on a 7 in your game? Or on a2. Use the combinations from last week’s column to help you.

Page 25 of 39

Week 4 Chance Problem Solving

Green Column

Page 26 of 39

Red column (2 pages of questions)

Page 27 of 39

Page 28 of 39

Discounts Week 4 You will need to complete 2 lessons a week from this table and then the other 2 from the “Chance” table.

Choose a column to work on from week 1, 2 or “discounts week 3”.

FD 30 Can you round the original price of items to the nearest dollar and then find the price after a 25% discount?

FD 30 MF 13 Can you apply your strategies to find 75% off discounts?

FD 30 MF 13 Can you work out the discounted price by multiplying 10% of a number?

Alternatively, you can use your knowledge of fractions to attempt matching the parts of a whole using decimals on page 31. Write in the fractions that match your

decimals e.g. 0.20= 𝟐𝟎

𝟏𝟎𝟎

Find one quarter of the amount

Example:

Therefore $22.50 x 3= $66 + 1.50

(mentally, I added the dollars first and then the cents)

Or You could subtract it from the total

$90-$22.50= $67.50

(mentally, I will subtract using place value 9 tens – 2 tens =7 tens, 7 tens – 2

ones= 68 - 0.50 = $67.50)

Select some items from a website or brochure and find the discounted price

after a 25% reduction Show both ways to check your answers.

4 Pick an item from a brochure or website. Record its price.

5 Multiply 25% of the price by 3 to find the 75% that will be paid.

6 Subtract 25% from the original price to find the 75% that will be paid.

Extension: If you attempted to find 75% of some prices in week 2 then

compare the strategy you used to the one below. You may have/ have not

followed the same steps. Record your findings.

Example:

Then see if you can work out 30%, 20% and 80% off by first dividing your number

to find 10%

Example:

If you extended yourself in week 2 and practised finding discounts for 70% then compare the strategy you used to the one demonstrated below. Did you take the same steps? Explain.

Page 29 of 39

Week 3 and 4 Discounts Problem Solving All columns can attempt

Page 30 of 39

Page 31 of 39

Page 32 of 39

You are required to complete 2 lessons from each “week 5” table.

Support links: You should all be linked to Google Classroom by now so codes to support links will be shared online.

Essential Vocabulary for Number Patterns:

Pattern: has a part that repeats.

Terms: numbers and fractions in the patterns.

A multiple of a number is any product of that number and an integer(whole). For example, the multiples of 5 include 5

x 0, 5 x 1, 5 x 2, 5 x 3, and so on.

Remember if blue column is too hard then start back from the yellow until you are confident with yellow.

If red is too hard then go back to green until you understand the green column concept. Teachers want you to

demonstrate your understanding on paper using your own examples.

Page 33 of 39

Week 5 Warm up: (won’t be necessary if you are working on green and red level this week)

PA 13 Demonstration and Example: 2, 4 , 6, 8, ____12, 14, ____......

This a number pattern with missing elements. How could I find the missing number? How could I describe it?

I could record the terms on a number line.

How much did I add each time? I added 2, so the pattern repeats by adding 2.

Once you have done a few, challenge yourself to repeatedly subtract to create patterns starting from any number and describe them.

EXAMPLE: 17, 15, 13, 11. I have repeatedly subtracted 2.

8+2= 10, 14+2= 16. I have identified the missing elements.

Your turn: Record a number pattern that repeats by adding 2,3, 5 or 6. Follow the same steps to describe the pattern and identify missing elements.

You could use these if you like:

1,3,5,7__, 11, __...

5, 10, ___, 20, ___, 30, 35, 40…

1,4,7, ___, 13, 16,___...

17 15 13

-2 -2 -2

11

Page 34 of 39

Week 5- warm up

Identify the number pattern and complete it

on the hundreds chart.

What boxes will I colour? How much do I need

to add each time? Hmmm…

Page 35 of 39

Week 5 Lesson 1-2 Number Patterns. Choose the column that is not too easy, not too hard.

PA 24 Use multiplication to identify the rules and terms in multiplication.

PA 24 Patterns of non-multiples, Rule and Terms through multiplication.

PA 28 Can you create and describe a pattern using fractions that are multiples of the first

term?

PA 28 Can you create and describe patterns using decimals that are not multiples of the first term?

Example 1: When repeatedly adding the number we start from, then we are using multiples of that number. Term 1= 1 x 5 Term 2= 2x5

Term 3= 3x5 and so on.. To work out the tenth term what

do you think we have to do? If you said 10 x 5 = 50 then you are correct. The tenth term will be 50. What will the 11th term be? What will the 12th? Example 2

50 is our first term. Our pattern repeats by subtracting 5. How did we get our first term? We subtracted 5 from 55(55-5=50) How could we use multiplication to describe the terms?

How can we work out the tenth term? Term 10: 10 X 5, subtract from 55= 5. Work out the 11th and 12th term using multiplication. Record number patterns skip counting forwards and backwards by 2, 3, 4, 5, 6, 7, 8 or 9. Describe a rule using multiplication like I have above.

. Example: How can I use multiplication to describe non-multiples of 5?

To work out the tenth term I will multiply. 10x5=50 and then add 2, 50+2= 52. Term 10=52. Can you work out the 11th term in the example? Your turn to create number patterns that increase and decrease starting from a different number (not the number that repeats) and record the terms and describe a rule. Decreasing pattern example:

(See PA 24 video 2 for further explanation of the thinking process.)

Let’s start our number pattern with a fraction (the first term) and keep adding that same fraction to create a number pattern that shows multiples of that fraction. Example:

How can I describe the way my pattern repeats? Example:

Now try it backwards, subtract by the same fraction on a number line to show how it repeats backwards. Example:

Choose a different term to start from then follow the steps above to create a pattern with the same rule. Now try recording and describing an increasing and decreasing pattern using a different fraction that is a multiple of the

first term. E.g.+ 3

4 and -

3

4 on a line.

I have started at 0.3 and increased by repeatedly adding 0.3. Therefore, I have demonstrated multiples of 0.3. Have a go. Show me terms that increase and decrease and describe the rule. (if you started lesson 1 in this column, please show that you can use fractions to create a pattern as well) I will now investigate patterns with decimals that are not multiples of the first term. Example:

Then I can start at 4 and repeatedly subtract by 0.3.

Have a go at creating increasing and decreasing patterns using decimals that are not multiples of first term. Describe.

Page 36 of 39

Week 5 Problem Solving Number Patterns Red column

Green column

Page 37 of 39

Week 5 Problem Solving Number Patterns Blue column and yellow

Yellow column

Page 38 of 39

Week 5 Lesson 3-4. Statistics and Probability/ Chance continued. Choose the column that is not too easy, not too hard. (If yellow is too hard then go back to week 3 yellow column on page 19 of your booklet)

S & P 17 Can you trial a chance experiment then use the data to predict outcomes of future trials?

S & P 17 Can you use the data from dice combinations predict the chances on larger trials?

S & P 18 Playing games to engage in a deeper understanding of fair/ unfair chance games.

S & P 18 Can you use data to create a game where everyone has a fair chance of winning?

Frequency means how often an outcome occurs. Step 1: Draw a base line and number it 2 to 12. Roll your dice 20 times, after each roll record the sum that occurs through a cross on your line plot. Example:

4 + 1 = 5 so I recorded a cross on 5

Roll again, 1 + 1= 2 so I recorded a cross on 2... repeat

20 times… Step 2: use your data to predict what sum is most likely to occur in future frequencies.

Example: My data above shows a frequency of 1 on 2, 3 and 4, a frequency of 3 on 5 and a frequency of 2 on 6. Therefore 5 has the greatest frequency. Step 3: Draw another line to conduct another trial with 30 rolls. Were the predicted and actual frequencies similar or different? Did the same sum have the greatest frequency? Was it what you predicted? Were your predictions likely but not certain? Explain.

Step 1: use your dice to continue gathering data on all possible dice combinations and record your data. The first 3 have been done for you.

Answer the questions (full sentences):

4. How many sum combinations make 5? Are there four combinations that add to make 5?

Count your total amount of combinations (you should have recorded 36 possible combinations altogether) Your results should show 6 out of 36 combinations have a sum of 7.

5. If we rolled the dice 6 times would we predict we’d roll one sum of 7?

6. Does one combination make the sum of two?

How many times do you predict we would get the other sums if we rolled the dice 100 times?

Let’s trial a chance game. Make and play this game: A horse race with each horse numbered 2 to 12. When we roll 2 dice, whichever horse’s number is rolled, move two spaces forward. Answer these questions: If you chose horse number 7, would you have a greater chance of winning? Why or why not? (Tip: if unsure, go back to blue column to collate data) Your answer should explain why this is an unfair game based on the data from possible dice combinations. Now play and see if your prediction was correct. Who actually won? List some games of chance that you know. E.g. Monopoly. Do those games present an equal chance of winning for each player? Why?/ Why not? (use fractions, decimals and percentages to support your chance explanations, you can draw a number line to refer to if you like.)

You have investigated how public games of chance may not be fair. This week we will investigate fair games. Demo/ Example: Looking back at all the possible combinations when rolling two dice, we can see there is a 50% chance of rolling an even number and a 50% chance of rolling an odd. Based on this data, my game gives players an equal chance of winning.

Page 39 of 39

Week 5 Chance Problem Solving

Yellow and blue:

Go back and complete any Chance/ Statistics and Probability Problem solving questions you haven’t answered. If you

have completed all the ones you can do, then you can write your own to solve this week.

Green and Red: