5th Grade 5th - CST Curriculum Talk · A math journal, or problem solving notebook as they are sometimes referred to, is a book in which students record their math work and thinking

5th Grade Math Journals contains 90 math journal tasks

aligned with the Common Core State Standards. All tasks are

based on a problem solving approach and provide valuable

opportunities for students to organize, clarify and reflect on

their thinking while developing key mathematical skills and

understandings.

www.k-5mathteachingresources.com

5th GradeMATH JOURNALS5th

Contents

1. What are Math Journals? .................................................................................. ....... 1-6

2. Overview of Tasks .................................................................................................. 7-12

3. Math Journal Task Labels .................................................................................. 13-102

4. Resources .............................................................................. ............................. 103-109

Coordinate Grid Paper (Tasks 7, 8, 9, and 85) Cm Grid Paper (Task 55) Triangles Pack (Tasks 87 and 88) Geoboard Paper 5x5 and 7x7 (Task 89)

5. Math Rubric Samples ............................................................ ............................ 110-119- Sample 1 Student Copy- Sample 2 Student Copy- Sample 1 Classroom Display Copy- Sample 2 Classroom Display Copy

6. User License ............................................................ ........................................... 120-121

What Are Math Journals?

A math journal, or problem solving notebook as they are sometimes referred to, is a book inwhich students record their math work and thinking. Math journals can be used to:

Record the solutions to math problems: When solving problems in a math journal,students are expected to record their strategy and thought processes, as well assolutions.

Write about learning: At times students may be asked to reflect on their math learning.For example, students may be asked to write about "what you already know about ......" atthe beginning of a unit, or "what you did today, what you learned, and any questions youhave", or "the three most important things you learned in this unit and why."

By dating entries a math journal provides a chronological record of the development of astudent’s mathematical thinking throughout the year.

Why Use Math Journals?

While students learn how to "do" math, they must also learn how to articulate what they arelearning. It is important to provide many opportunities for students to organize and recordtheir work without the structure of a worksheet. Math journals support learning because, inorder to get their ideas on paper, students must organize, clarify, and reflect on their thinking.Initially many students will need support and encouragement in order to communicate theirideas and thinking clearly on paper but, as with any skill, the more they practice the easier itwill become.

Math Journals also serve as invaluable assessment resources that can inform classroominstruction. Requiring students to communicate their reasoning processes provides a usefulinsight into what a child understands, how s/he approaches ideas and what misconceptions s/hehas.

What Are The Characteristics of a Good Math Journal Question?

A Good Math Journal Question ….

builds in differentiation by allowing for multiple entry points, strategies, and recordingtechniques thereby allowing all students to work at their individual level of thinking,

provides the opportunity for students to learn by moving beyond what they already knowwhen answering a question, and the teacher to learn about each student from the

1

attempt,

may have more than one solution or a variety of possible solution paths that range fromsimple to complex,

requires more than just remembering a fact or reproducing a skill,

provides opportunities for students to represent their mathematical ideas using modelsand written language,

provides opportunities for students to justify their reasoning and evaluate the reasoningof others,

has clear, concise directions.

The most important thing to consider when developing a math journal question is whether thequestion involves significant mathematics. Closed questions such as, “There are two bowls ofapples. Each bowl has eight apples. How many apples in all?” do little to develop mathematicalthinking if the student can answer the question before even getting back to her seat. Thestudent may spend 15 minutes drawing and coloring apples but the math thinking is limited.Changing the question from a closed to an open format such as, “There are 16 apples to put intobowls. Each bowl must have the same number of apples. Show as many different solutions as youcan.” creates greater potential to stimulate mathematical thinking and reasoning.

How Are Math Journal Sessions Structured?

A variety of math journal tasks have been included in this E-book. Some tasks can be used asquick warm up tasks. Others are suitable for independent practice or group work, as a Think-Pair Share, or as homework or assessment tasks. More involved tasks can be as used as themain task during the math block.

When used as the main task during the math block the math journal session would typicallyconsist of three main components: before, during and after. During the before phase, or mini-lesson, the role of the teacher is to mentally prepare students for the task, ensure thatstudents understand the task and establish expectations. In order to prepare students for thetask some teachers like to model a similar problem, in a large class math journal while othersprefer to pose the task right away and then have students brainstorm a list of possible solutionstrategies. If you do decide to model a task it is important that you take care not to underminestudents' thought processes by telling them what to do, or by discouraging them from makingsense of alternative strategies or solutions. To ensure that students understand a task theteacher may discuss certain vocabulary involved in the task or have students explain what theproblem is asking in their own words. Establishing expectations from the outset for mathjournal sessions is crucial. Asking students to record their thinking on paper using diagrams,

2

numbers, or words places an emphasis on process, indicating to students that their thinking is asimportant as the answers.

In the during, or Student Activity stage, encourage students to use their own ideas. Differentstrategies and recording methods should be valued. This is a time for the teacher to listen andfind out how students are approaching a problem. The teacher may confer with individuals orsmall groups of students and record anecdotal notes, or use questioning to guide studentsneeding extra support.

The after phase, or Share component, is a crucial component of the math journal session whereacademic talk between, and among, students is promoted. Several students may be selected toshare their solutions and justify their reasoning. Selecting students who have used differentstrategies, models, or recording styles will provide models for other students of possible newapproaches to try at another time. The teacher's role in creating an environment wherestudents come ready to think, listen, share, and evaluate both their own and the reasoning oftheir peers is critical. Building this environment takes time, patience, and consistency.Strategies such as moving to a specific location in the classroom to gather for the share, usingappropriate wait time after asking a question, accepting all ideas and answers regardless ofobvious errors, and having students share their work with a partner before the whole classShare all encourage student communication. Early in the year a chart of Math Talk stems canprovide a useful support to scaffold students' interactions during the Share. Possible stemsinclude:

I agree with ___ because ……I disagree with ___ because ……I also noticed ……I’d like to build on what …. said ……I didn’t understand ……I think what …... meant is ……I predict that …..My strategy was …...I think a more efficient strategy would be ....Another possible strategy would be ...Can you say more about … ...?Why do you think that?How do you know that?Can you explain that in another way?Can you prove that?

Can Math Journal Tasks Be Revisited During The Year?

Repeating, or revisiting tasks, allows students to engage with tasks at a deeper level. On thefirst occasion the student may be focused on ‘how to do’ the task. Subsequent visits provide anopportunity for students to communicate their reasoning more clearly. Making slight variations

3

to an open ended task or changing the materials used to complete a task helps to maintaininterest while providing time for students to further develop skills and concepts. For example, aquestion such as, ‘Which is larger, 2.9 or 2.13? Explain your reasoning' can be revisited manytimes during the course of the year by simply changing the decimals. Similarly, 'You divide twonumbers and the quotient is 2.5. What might the two numbers be?' can be revisited by changingthe problem to 'You multiply two numbers and the product is .....'

You may decide to provide opportunities for students to revisit tasks by introducing mathjournal tasks to the whole class and then placing similar tasks in centers for students to revisitat other times during the year. Another option is to choose one journal task and repeat itseveral times throughout the year, with slight variations, as a record of the development ofmath skills and understandings for student portfolios.

How Often Should I Use Math Journals in My Class?

This is entirely up to the individual teacher. Some teachers use them several times a week.Other teachers who have more restrictions on their math sessions due to using a mandatedcurriculum set aside one session per week for math journals and then select a journal task thatcorrelates with the current unit of study. You may choose to use some tasks as quick warm ups,or as homework or assessment tasks. The important thing is to ensure that students are beinggiven regular opportunities throughout the year to record their mathematical thinking in a waywhich makes sense to them.

What Type Of Book Should My Students Use As A Math Journal?

At the K-5 level many teachers use a blank notebook as the math journal so that students arenot restricted by lines and have the space to choose whether to use diagrams, numbers, wordsor a combination of these to record their thinking.

Content: This E-book contains 90 math journal tasks. Content for all tasks is aligned with theCommon Core State Standards. See the provided tables for an outline of the focus domain andCommon Core Standard for each task.

In addition to the standards that describe content, there are eight Common Core StateStandards focusing on mathematical practice, which are implicit in many of the math journaltasks in this E-book. These are:

Mathematical Practices:1. Make sense of problems and persevere in solving them.2. Reason abstractly and quantitatively.3. Construct viable arguments and critique the reasoning of others.4. Model with mathematics.

4

http://astore.amazon.com/k5matteares-20?_encoding=UTF8&node=26

5. Use appropriate tools strategically.

6. Attend to precision.

7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning.

Different mathematical practices will be brought out in different tasks, depending on how the

teacher presents the tasks and approaches student responses. For example, the open-ended

nature of these tasks require students to make sense of the question before they select a

strategy to solve the problem. This will be supported by skillful teaching moves but can be

undermined if the teacher removes the demand for student sense making by telling students

how to solve a problem, or expecting all students to solve the problem in the same way.

Many of the tasks require that students use a mathematical model (drawings, charts, graphs,

equations etc.) and/or construct viable arguments by explaining their thinking and justifying

their conclusions. Other tasks require students to reason abstractly and quantitatively by

attending to the meaning of quantities, not just how to compute them, and knowing and flexibly

using different properties of operations. Some tasks encourage students to look closely to

discern patterns, structures and mathematical relationships. Students should be expected to

attend to precision by communicating precisely using mathematical language and carefully

formulated explanations. If students are given the opportunity to share their solutions and

strategies at the conclusion of the math journal session opportunities arise to critique the

reasoning of others. Allowing students to make their own decisions as to which mathematical

tools are appropriate for a given situation is also important. The teacher's role is to ensure that

a variety of tools and recording paper are available should students choose to use them, rather

than telling students which tools to use for a given task.

Math Rubric

A rubric can be a powerful tool for both teaching and assessment. Use of a rubric can improve

student performance, as well as monitor it, by making teachers' expectations clear and by

showing students how to meet these expectations. The result is often marked improvements in

the quality of student work and in learning. Two sample Math Rubrics, suitable for use with

math journal tasks, are included in this E-Book. You may like to choose one to use with your

class or use them as a model to design your own. Make an enlarged copy for display in the

classroom and have students paste a smaller copy inside the front cover of their math journal

for easy reference.

Printing the Tasks:

The 90 math journal tasks are formatted so that you can print them on mailing labels (Avery

Standard, 5160). Just print and pass out for students to peel and stick at the top of their

math journal page. If you experience any difficulty printing the labels try the following:

1. Verify that you have a current version of Adobe Acrobat Reader. To

determine the version of Adobe Acrobat, open Adobe from your desktop or

start menu, click on help, and then About Acrobat Reader. Download an

update to your reader from the Adobe Reader download page on Adobe's

website.

2. When in the Preview Labels screen click the Print icon.

3. Under Page Handling make sure Page Scaling is set to None and Auto-

Rotate and Center is not selected.

4. Click OK.

Placing the labels in student journals provides information for parents, teachers and

administrators as to what task the student was working on. The Avery Standard 5160

label is used in order to give students as much blank space on the page as possible to

record their thinking. Teachers may find it useful to write each task on a chart or

whiteboard before introducing it so that students see the task in large print before

beginning work.

Resources

Resources have been included for use with the following math journal tasks:

Coordinate Grid Paper (Tasks 7, 8, 9, and 85)

Cm Grid Paper (Task 55)

Triangles Pack (Tasks 87 and 88)

Geoboard Paper 5x5 and 7x7 (Task 89)

In addition, our website offers a wide range of free math center task cards and resources

suitable for use in 5th Grade classrooms. Please see the links below as a starting point.

http://www.k-5mathteachingresources.com/5th-grade-number-activities.html http://www.k-5mathteachingresources.com/5th-grade-geometry.html http://www.k-5mathteachingresources.com/5th-grade-measurement-and-data.html

http://www.adobe.com/

http://www.k-5mathteachingresources.com/5th-grade-number-activities.html

http://www.k-5mathteachingresources.com/5th-grade-geometry.html

http://www.k-5mathteachingresources.com/5th-grade-measurement-and-data.html



1 Operations and

Algebraic Thinking 5.OA1 Three students evaluated the numerical expression 7+ (8-3) x 2. Tom said the answer was 24. Nicole said

the answer was 17. Sam said the answer was 19. Who was correct? Why? Explain your thinking.

2 5.OA1 I wrote an equation using parentheses and all four operations with an answer of 25. What might the equation

have been?

3 5.OA1 Tom evaluated the expression 3 {5[10 + 5 (500—100) + 399] } and said that the answer was 36,135. Is Tom

correct? Justify your answer.

4 5.OA1 I wrote an equation using parentheses, brackets and braces with an answer of 268. What might the equation

have been?

5 5.OA2 How does the expression 6 x (4+5) compare to the expression 4+5. Explain your thinking.

6 5.OA2 Tom and Jack needed to write an expression for the steps “double 4 and then add 39.”

Jack wrote 2 (4 + 39). Tom wrote (2 x 4) + 39. Who is correct? Why?

7 5.OA3 Create an input-output table where the rule involves subtraction. Record your rule and graph the resulting

ordered pairs.

8 5.OA3 Given the rule s =t +3 and the starting number 0, create a table to show the first 5 terms in the sequence.

Graph the resulting ordered pairs.

9 5.OA3

10 Number and

Operations in Base

Ten

5.NBT1 Tom wrote 3,506,029 in expanded form like this: (3 x 1,000,000) + (5 x 100,000) + (6 x 10,000) + (2 x 10)

What errors did Tom make? Explain.

11 5.NBT1 There are two 4’s in 489,732,468. Name the place value of each 4 and explain how their values are related.

12 5.NBT2

13 5.NBT2

14 5.NBT2 Divide each of the following by 10, 100, and 1000: 67.8, 456.8, 531.20 Explain the pattern in the placement

of the decimal point when a decimal is divided by a power of 10.

15 5.NBT2 Use what you know about multiplying a decimal by a power of 10 to help solve the following problem: If 5

pounds of carrots cost $2.79, how much will 50 pounds cost? Explain your thinking.

7

Two bakers make cupcakes. Baker A uses a pan that holds 6 cupcakes. Baker B uses a pan that holds 12

cupcakes. Create an input-output table for each baker using 1,2,3,4 and 6 as the input values. Graph the

resulting ordered pairs. What do you notice?

Solve the following: 36x10=?, 36x100=?, 36x1000=? Explain the pattern in the number of zeros of the

product when multiplying a number by powers of 10.

Multiply each of the following by 10, 100, and 1000: 7.32, 38.5, .006. Explain the pattern in the placement of

the decimal point when a decimal is multiplied by a power of 10.

Task Domain Standard Math Journal Task (use Bookmarks tab to navigate to label pages)

16 Number and

Operations in Base

Ten

5.NBT2 At his first Art Show an artist sold a painting and a sculpture. He sold the painting for 10³ times as much

money as the sculpture. How much might he have sold each item for? Show three possible solutions.

17 5.NBT3a Give the large cube in a Base Ten set a value of 1, the flat a value of .1, the long a value of .01 and the small

cube a value of .001. Use 5 base ten blocks to represent a decimal. Record using a diagram, numerals, number

name and expanded form. Repeat.

18 5.NBT3a Write two different six digit decimals that have three digits on the left of the decimal point. Label the

place value of each digit. Write each decimal in word and expanded form.

19 5.NBT3b Which is larger 2.9 or 2.13? Explain your reasoning.

20 5.NBT3b Lisa said that 0.148 is greater than 0.52 because 148 is greater than 52. Is Lisa correct? Explain your

thinking.

21 5.NBT4 Turn over 5 numeral cards. Place a counter after the second numeral to represent a decimal point. Round the

number to the nearest hundredth using the following sentence frame and repeat 5 times:

__ is between __ and __ and is rounded to __.

22 5.NBT4 Two students rounded 2.467 to the nearest hundredth. Student A said the answer was 2.47. Student B said

the answer was 2.5. Who was correct? Explain your thinking.

23 5.NBT5 How could you break apart 242 to make 242 x 6 a simpler problem? Would this work for any number?

Explain. Support your reasoning with other examples.

24 5.NBT5 Create a word problem that could be solved by multiplying two factors that are between 100 and 500.

Explain how you would solve this problem.

25 5.NBT5 You multiply two numbers and the product is about 90 more than 31 x 63. What two numbers might you have

multiplied? Explain your thinking.

26 5.NBT5 Using the numbers 1, 2, 3, and 4 create the largest possible product and the smallest possible product. How

does the order of the digits affect the product?

27 5.NBT5 A giant panda eats up to 14 kilograms of bamboo per day. How many kilograms of bamboo will a zoo need to

feed a pair of pandas during the month of September?

28 5.NBT6 You divide a 4 digit whole number by a 2 digit divisor. There is no remainder. The sum of the digits in the

quotient is 9. What numbers might you have divided?

29 5.NBT6 Create a word problem that could be solved by dividing a three digit dividend by a 2 digit divisor. Explain

how you would solve the problem and check your answer.

30 5.NBT6 You divide two numbers and the quotient is 2.5. What might the two numbers be? Show at least 5 solutions.

8


31 Number and

Operations in

Base Ten

5.NBT6

32 5.NBT7 Show 5 possible solutions for each statement: a) the sum of 2 decimals is less than 1 b) the sum of 2 decimals is

equal to 1 c) the sum of 2 decimals is greater than 1

33 5.NBT7 Show 5 possible solutions for each statement: a) the difference between 2 decimals is less than 1 b) the

difference between 2 decimals is equal to 1 c) the difference between 2 decimals is greater than 1

34 5.NBT7 The difference between two decimals is 6.53. What might the two decimals be? Show 5 different solutions.

35 5.NBT7 Create and solve a word problem with a quotient of 3.4. How did you choose your numbers?

36 5.NBT7 I multiplied two numbers and got a product smaller than both factors. What might the two numbers be?

37 5.NBT7 Create a word problem involving multiplication of decimals in which the digits 3, 5, 7 and 2 appear. Show how you

would solve the problem.

38 5.NBT7 I spent $156 to enclose my garden at a cost of $6.50 per yard for fencing. Draw two possible plans for my

garden. Explain your reasoning.

39 Number and

Operations :

Fractions

5.NF1 1/a — 1/b = 1/c

How many different sets of numbers can you find that will make this a true sentence?

40 5.NF2 Create a word problem that can be solved by subtracting two fractions with unlike denominators. Explain how you

could use equivalent fractions to help solve the problem.

41 5.NF2 Two fractions are added together for a sum of 2/4. What might the two fractions be? Show at least 5 solutions.

42 5.NF2 The sum of two mixed numbers with unlike denominators is 5 8/10. What might the two mixed numbers be?

43 5.NF2 The difference between two mixed numbers with unlike denominators is 3 3/4. What might the two mixed

numbers be?

44 5.NF2 The total weight of three packages is ⅞lb. One package weighs 1/4lb. What might the other two packages weigh?

45 5.NF2 2/5 of the animals in a pet shop are dogs and 3/8 are cats. The rest of the animals are birds or mice. What

fraction of all the animals are dogs and cats? What fraction of all the animals are not dogs and cats? Explain.

9

A farmer grows 196kg of carrots. He sells them to a grocer who divides them into 5kg and 2kg bags. If the

grocer uses the same number of 2kg and 5kg bags, how many of each does he use? Explain your thinking.


46 Number and

Operations :

Fractions

5.NF3 4 friends share 7 small pizzas equally. How much pizza does each friend get? Represent your thinking using a

fraction model and an equation.

47 5.NF3 A baker is making 6 loaves of bread using 9 cups of milk. How much milk does she use per loaf? Represent your

thinking using a fraction model and an equation.

48 5.NF3 Tom and 7 friends share 2 liters of juice equally. How much juice does each person get? Represent your thinking

using a fraction model and an equation.

49 5.NF4a Three-fourths of a container of buttons are square. Two-thirds of the square buttons are red. What fraction of

the buttons are square and red? Represent your thinking using a fraction model and an equation.

50 5.NF4a Create a word problem for the equation 2/3 x 4/5. Show how you could solve the problem using a fraction model.

51 5.NF4a There are 20 muffins on a plate. 2/5 of the muffins are chocolate. 3/10 of the muffins are vanilla. The rest of

the muffins are blueberry. How many muffins are blueberry? Explain your thinking.

52 5.NF4a Show why 1/2 x 1/3 = 1/6 by dividing a rectangle. Repeat with other pairs of fractions with unlike denominators.

53 5.NF4a Tom says that ½ is the product of 3/5 x 5/6. Is Tom correct? Use a rectangular model and an equation to

prove your answer.

54 5.NF4a The product of two fractions with unlike denominators is less than ½. What might the two fractions be?

55 5.NF4b Draw a rectangle on cm grid paper with a length of 5½cm and a width of 3½cm. Find the area by counting unit

squares. Show that the answer is the same as would be found by multiplying the side lengths. Repeat for other

rectangles with fractional side lengths.

56 5.NF4b Mr. Smith wants to carpet a closet with carpet tiles. The closet is 5 meters long and half a meter wide. How

much carpet will he need? Represent your thinking with a rectangular model and an equation.

57 5.NF5a Ray digs a garden plot that is 30 feet wide and 20 feet long. Bill digs a garden plot that is half as wide, but has

the same length as Ray’s plot. How do the dimensions and area of the two garden plots compare?

58

59 You multiply a number by a fraction greater than 1. Will the product be more or less than the number you

multiplied by? Why?

60 5.NF6 Meg collected 2¾ of a bin of glass bottles to recycle. Liam collected 3 times as many bottles as Meg. How many

bins of bottles did Liam collect? Explain your thinking.

10

5.NF5b You multiply a fraction by ¾. Will the product be more or less than the number you multiplied by? Why?

5.NF5b

Task Domain Standard Math Journal Task (use Bookmark tab to navigate to label pages)

61 Number and

Operations :

Fractions

5.NF6 Create and solve two word problems involving multiplication of a fraction by a fraction. Represent each

problem using an equation and a fraction model.

62 5.NF6 Create and solve two word problems involving multiplication of a fraction by a mixed number. Represent each


63 5.NF6 The product of two mixed numbers is greater than 6 but less than 7. What might the two mixed numbers

be?

64 5.NF7a Tom and Ben solved the problem 1/5 ÷ 3 = ? Ben said the answer was 15/1. Tom said the answer was 1/15.

Who was correct? Use a fraction model to explain your reasoning.

65 5.NF7b Is the quotient of ½ ÷ 4 more, less, or equal to the quotient of 4 ÷ ½ ? Explain your thinking.

66 5.NF7c A bakery uses ⅛ of a barrel of oatmeal in each batch of cookies. On Monday the bakery used 3 barrels of

oatmeal. How many batches of cookies were made? Use a fraction model and an equation to represent the

problem.

67 5.NF7c A bird feeder holds 2 cups of birdseed. Dad is filling the bird feeder with a scoop that holds 1/6 of a cup.

How many scoops of birdseed will he need? Use a fraction model and an equation to represent the problem.

68 5.NF7c Create and solve a word problem involving division of a unit fraction by a whole number. Represent your


69 5.NF7c Create and solve a word problem involving division of a whole number by a unit fraction. Represent your


70 Measurement and

Data

5.MD1 Jim’s sleeping bag is 5 feet long. Jorge’s sleeping bag is 2 yards long. Steven’s sleeping bag is 68 inches long.

Whose sleeping bag is the longest? Explain your thinking.

71 5.MD1 Which is more: a) 2 yards or 7 feet? b) 4000mm or 3 meters? c) 3 pounds or 32 ounces? Explain your

thinking.

72 5.MD1 What is your arm span in millimeters/centimeters/decimeters/meters? If you find one measurement, how

can you find the others without measuring?

73 5.MD1 I placed one kilogram of sugar into four different sized bags. How much sugar might each of the bags

contain?

74 5.MD1 Dad is shopping for apples. He can buy a 3kg bag of apples for $4.00 or a 1500g bag for $2.25. Which is the

better buy? Explain.

75 5.MD1 Mike uses 120 pints of water to take a 5 minute shower. Dad uses 100 quarts for a 10 minute shower. Maria

uses 24.8 gallons for an 8 minute shower. Who uses the most gallons of water per minute? Explain.

11


76 Measurement and

Data 5.MD2 Create a line plot to display the data below. Choose a possible title and label the axis: Record three facts

about the data. Green: 5½ Red: 5⅛ Blue: 5¾ Purple: 5⅜ Orange: 4⅝ White: 5⅛

77 5.MD2 Collect 10 objects that are shorter than 5 inches in length. Measure each object to the nearest ⅛in.

Create a line plot to display your data. If you put all the objects together end to end what would be the

total length? Explain.

78 5.MD3, 5.MD4 Using cm cubes how many different rectangular prisms can you build with a volume of 24cm³ ? Record.

79 5.MD5a Build three different rectangular prisms using cm cubes. Find the volume of each cube by counting the

cubes. Describe any relationship that you notice between the length, width, and height of each prism and its

volume.

80 5.MD5b A rectangular prism has a volume of 72 cubic units. If one of its dimensions is 6, what might the other

dimensions be? Show three different solutions.

81 5.MD5b A storage container is 33m long, 16m wide, and 14m high. If half of the container is filled with boxes, how

much space is left? Explain your thinking.

82 5.MD5c Using cm cubes build two different solid figures, each composed of two non-overlapping right rectangular

prisms. Find the volume of each figure by adding the volumes of the non-overlapping parts. Record.

83 5.MD5c Joe is building a cage for his hamster. He attaches a 2ft by 3ft by 3ft cage to a larger cage that measures

4ft by 4ft by 3ft. What is the volume of the cage? Explain your thinking.

84 Geometry 5.G1 Draw two different quadrilaterals on a coordinate grid. Use ordered pairs to label the vertices. What is the

same/different about the two quadrilaterals?

85 5.G1 Lisa drew an isosceles triangle on a coordinate grid. One of the vertices was at the point (5,6). Where might

the other vertices have been?

86 5.G3 There are at least 3 different names that you can use for a 4-sided shape. What might the shape be? Draw

the shape and explain why it can have different names.

87 5.G3 Work with a partner. Measure the sides of 10 different triangles. Classify the triangles by the number of

congruent sides. Record your findings.

88 5.G3 Work with a partner. Measure the interior angles of 10 different triangles. Classify the triangles by the

measure of their largest interior angle. Record your findings.

89 5.G4 How many different quadrilaterals can you make on a geoboard? Which shapes are parallelograms? Which

shapes are not? Explain.

90 5.G4 What is the difference between the quadrilaterals in each pair below:

a) a square and a rectangle? b) a rectangle and a rhombus? c) a trapezoid and a parallelogram?

12


Three students evaluated the numerical expression

7+ (8-3) x 2. Tom said the answer was 24. Nicole

said the answer was 17. Sam said the answer was 19.

Who was correct? Why? Explain your thinking.





















































































































13

I wrote an equation using

parentheses and all four operations

with an answer of 25. What might

the equation have been?





















































































































14

Tom evaluated the expression

3 {5[10 + 5 (500—100) + 399] }

and said that the answer was 36,135.

Is Tom correct? Justify your answer.


3 {5[10 + 5 (500—100) + 399] }




3 {5[10 + 5 (500—100) + 399] }




3 {5[10 + 5 (500—100) + 399] }




3 {5[10 + 5 (500—100) + 399] }




3 {5[10 + 5 (500—100) + 399] }




3 {5[10 + 5 (500—100) + 399] }




3 {5[10 + 5 (500—100) + 399] }




3 {5[10 + 5 (500—100) + 399] }




3 {5[10 + 5 (500—100) + 399] }




3 {5[10 + 5 (500—100) + 399] }




3 {5[10 + 5 (500—100) + 399] }




3 {5[10 + 5 (500—100) + 399] }




3 {5[10 + 5 (500—100) + 399] }




3 {5[10 + 5 (500—100) + 399] }




3 {5[10 + 5 (500—100) + 399] }




3 {5[10 + 5 (500—100) + 399] }




3 {5[10 + 5 (500—100) + 399] }




3 {5[10 + 5 (500—100) + 399] }




3 {5[10 + 5 (500—100) + 399] }




3 {5[10 + 5 (500—100) + 399] }




3 {5[10 + 5 (500—100) + 399] }




3 {5[10 + 5 (500—100) + 399] }




3 {5[10 + 5 (500—100) + 399] }




3 {5[10 + 5 (500—100) + 399] }




3 {5[10 + 5 (500—100) + 399] }




3 {5[10 + 5 (500—100) + 399] }




3 {5[10 + 5 (500—100) + 399] }




3 {5[10 + 5 (500—100) + 399] }




3 {5[10 + 5 (500—100) + 399] }



15


parentheses, brackets and braces























































































































16

How does the expression 6 x (4+5)

compare to the expression 4+5.

Explain your thinking.
























































































17

Tom and Jack needed to write an

expression for the steps “double 4 and

then add 39.” Jack wrote 2(4 + 39). Tom

wrote (2 x 4) + 39. Who is correct? Why?





















































































































18

Create an input-output table where

the rule involves subtraction. Record

your rule and graph the resulting

ordered pairs.




ordered pairs.




ordered pairs.




ordered pairs.




ordered pairs.




ordered pairs.




ordered pairs.




ordered pairs.




ordered pairs.




ordered pairs.




ordered pairs.




ordered pairs.




ordered pairs.




ordered pairs.




ordered pairs.




ordered pairs.




ordered pairs.




ordered pairs.




ordered pairs.




ordered pairs.




ordered pairs.




ordered pairs.




ordered pairs.




ordered pairs.




ordered pairs.




ordered pairs.




ordered pairs.




ordered pairs.




ordered pairs.




ordered pairs.

19

Given the rule s =t+3 and the starting

number 0, create a table to show the

first 5 terms in the sequence. Graph

the resulting ordered pairs.





















































































































20

Two bakers make cupcakes. Baker A uses a pan that

holds 6 cupcakes. Baker B uses a pan that holds 12

cupcakes. Create an input-output table for each

baker using 1,2,3,4 and 6 as the input values. Graph

the resulting ordered pairs. What do you notice?


















































































































































21

Tom wrote 3,506,029 in expanded form

like this: (3 x 1,000,000) + (5 x 100,000) +

(6 x 10,000) + (2 x 10)



like this: (3 x 1,000,000) + (5 x 100,000) +

(6 x 10,000) + (2 x 10)



like this: (3 x 1,000,000) + (5 x 100,000) +

(6 x 10,000) + (2 x 10)



like this: (3 x 1,000,000) + (5 x 100,000) +

(6 x 10,000) + (2 x 10)



like this: (3 x 1,000,000) + (5 x 100,000) +

(6 x 10,000) + (2 x 10)



like this: (3 x 1,000,000) + (5 x 100,000) +

(6 x 10,000) + (2 x 10)



like this: (3 x 1,000,000) + (5 x 100,000) +

(6 x 10,000) + (2 x 10)



like this: (3 x 1,000,000) + (5 x 100,000) +

(6 x 10,000) + (2 x 10)



like this: (3 x 1,000,000) + (5 x 100,000) +

(6 x 10,000) + (2 x 10)



like this: (3 x 1,000,000) + (5 x 100,000) +

(6 x 10,000) + (2 x 10)



like this: (3 x 1,000,000) + (5 x 100,000) +

(6 x 10,000) + (2 x 10)



like this: (3 x 1,000,000) + (5 x 100,000) +

(6 x 10,000) + (2 x 10)



like this: (3 x 1,000,000) + (5 x 100,000) +

(6 x 10,000) + (2 x 10)



like this: (3 x 1,000,000) + (5 x 100,000) +

(6 x 10,000) + (2 x 10)



like this: (3 x 1,000,000) + (5 x 100,000) +

(6 x 10,000) + (2 x 10)



like this: (3 x 1,000,000) + (5 x 100,000) +

(6 x 10,000) + (2 x 10)



like this: (3 x 1,000,000) + (5 x 100,000) +

(6 x 10,000) + (2 x 10)



like this: (3 x 1,000,000) + (5 x 100,000) +

(6 x 10,000) + (2 x 10)



like this: (3 x 1,000,000) + (5 x 100,000) +

(6 x 10,000) + (2 x 10)



like this: (3 x 1,000,000) + (5 x 100,000) +

(6 x 10,000) + (2 x 10)



like this: (3 x 1,000,000) + (5 x 100,000) +

(6 x 10,000) + (2 x 10)



like this: (3 x 1,000,000) + (5 x 100,000) +

(6 x 10,000) + (2 x 10)



like this: (3 x 1,000,000) + (5 x 100,000) +

(6 x 10,000) + (2 x 10)



like this: (3 x 1,000,000) + (5 x 100,000) +

(6 x 10,000) + (2 x 10)



like this: (3 x 1,000,000) + (5 x 100,000) +

(6 x 10,000) + (2 x 10)



like this: (3 x 1,000,000) + (5 x 100,000) +

(6 x 10,000) + (2 x 10)



like this: (3 x 1,000,000) + (5 x 100,000) +

(6 x 10,000) + (2 x 10)



like this: (3 x 1,000,000) + (5 x 100,000) +

(6 x 10,000) + (2 x 10)



like this: (3 x 1,000,000) + (5 x 100,000) +

(6 x 10,000) + (2 x 10)



like this: (3 x 1,000,000) + (5 x 100,000) +

(6 x 10,000) + (2 x 10)


22

There are two 4’s in 489,732,468.

Name the place value of each 4 and

explain how their values are related.
























































































23

Solve the following:

36x10=?, 36x100=?, 36x1000=?

Explain the pattern in the number of zeros of

the product when multiplying a number by

powers of 10.


36x10=?, 36x100=?, 36x1000=?



powers of 10.


36x10=?, 36x100=?, 36x1000=?



powers of 10.


36x10=?, 36x100=?, 36x1000=?



powers of 10.


36x10=?, 36x100=?, 36x1000=?



powers of 10.


36x10=?, 36x100=?, 36x1000=?



powers of 10.


36x10=?, 36x100=?, 36x1000=?



powers of 10.


36x10=?, 36x100=?, 36x1000=?



powers of 10.


36x10=?, 36x100=?, 36x1000=?



powers of 10.


36x10=?, 36x100=?, 36x1000=?



powers of 10.


36x10=?, 36x100=?, 36x1000=?



powers of 10.


36x10=?, 36x100=?, 36x1000=?



powers of 10.


36x10=?, 36x100=?, 36x1000=?



powers of 10.


36x10=?, 36x100=?, 36x1000=?



powers of 10.


36x10=?, 36x100=?, 36x1000=?



powers of 10.


36x10=?, 36x100=?, 36x1000=?



powers of 10.


36x10=?, 36x100=?, 36x1000=?



powers of 10.


36x10=?, 36x100=?, 36x1000=?



powers of 10.


36x10=?, 36x100=?, 36x1000=?



powers of 10.


36x10=?, 36x100=?, 36x1000=?



powers of 10.


36x10=?, 36x100=?, 36x1000=?



powers of 10.


36x10=?, 36x100=?, 36x1000=?



powers of 10.


36x10=?, 36x100=?, 36x1000=?



powers of 10.


36x10=?, 36x100=?, 36x1000=?



powers of 10.


36x10=?, 36x100=?, 36x1000=?



powers of 10.


36x10=?, 36x100=?, 36x1000=?



powers of 10.


36x10=?, 36x100=?, 36x1000=?



powers of 10.


36x10=?, 36x100=?, 36x1000=?



powers of 10.


36x10=?, 36x100=?, 36x1000=?



powers of 10.


36x10=?, 36x100=?, 36x1000=?



powers of 10.

24

Multiply each of the following by 10, 100, and

1000: 7.32, 38.5, .006.

Explain the pattern in the placement of the

decimal point when a decimal is multiplied by a

power of 10.


1000: 7.32, 38.5, .006.



power of 10.


1000: 7.32, 38.5, .006.



power of 10.


1000: 7.32, 38.5, .006.



power of 10.


1000: 7.32, 38.5, .006.



power of 10.


1000: 7.32, 38.5, .006.



power of 10.


1000: 7.32, 38.5, .006.



power of 10.


1000: 7.32, 38.5, .006.



power of 10.


1000: 7.32, 38.5, .006.



power of 10.


1000: 7.32, 38.5, .006.



power of 10.


1000: 7.32, 38.5, .006.



power of 10.


1000: 7.32, 38.5, .006.



power of 10.


1000: 7.32, 38.5, .006.



power of 10.


1000: 7.32, 38.5, .006.



power of 10.


1000: 7.32, 38.5, .006.



power of 10.


1000: 7.32, 38.5, .006.



power of 10.


1000: 7.32, 38.5, .006.



power of 10.


1000: 7.32, 38.5, .006.



power of 10.


1000: 7.32, 38.5, .006.



power of 10.


1000: 7.32, 38.5, .006.



power of 10.


1000: 7.32, 38.5, .006.



power of 10.


1000: 7.32, 38.5, .006.



power of 10.


1000: 7.32, 38.5, .006.



power of 10.


1000: 7.32, 38.5, .006.



power of 10.


1000: 7.32, 38.5, .006.



power of 10.


1000: 7.32, 38.5, .006.



power of 10.


1000: 7.32, 38.5, .006.



power of 10.


1000: 7.32, 38.5, .006.



power of 10.


1000: 7.32, 38.5, .006.



power of 10.


1000: 7.32, 38.5, .006.



power of 10.

25

Divide each of the following by 10, 100, and

1000: 67.8, 456.8, 531.20


decimal point when a decimal is divided by a

power of 10.


1000: 67.8, 456.8, 531.20



power of 10.


1000: 67.8, 456.8, 531.20



power of 10.


1000: 67.8, 456.8, 531.20



power of 10.


1000: 67.8, 456.8, 531.20



power of 10.


1000: 67.8, 456.8, 531.20



power of 10.


1000: 67.8, 456.8, 531.20



power of 10.


1000: 67.8, 456.8, 531.20



power of 10.


1000: 67.8, 456.8, 531.20



power of 10.


1000: 67.8, 456.8, 531.20



power of 10.


1000: 67.8, 456.8, 531.20



power of 10.


1000: 67.8, 456.8, 531.20



power of 10.


1000: 67.8, 456.8, 531.20



power of 10.


1000: 67.8, 456.8, 531.20



power of 10.


1000: 67.8, 456.8, 531.20



power of 10.


1000: 67.8, 456.8, 531.20



power of 10.


1000: 67.8, 456.8, 531.20



power of 10.


1000: 67.8, 456.8, 531.20



power of 10.


1000: 67.8, 456.8, 531.20



power of 10.


1000: 67.8, 456.8, 531.20



power of 10.


1000: 67.8, 456.8, 531.20



power of 10.


1000: 67.8, 456.8, 531.20



power of 10.


1000: 67.8, 456.8, 531.20



power of 10.


1000: 67.8, 456.8, 531.20



power of 10.


1000: 67.8, 456.8, 531.20



power of 10.


1000: 67.8, 456.8, 531.20



power of 10.


1000: 67.8, 456.8, 531.20



power of 10.


1000: 67.8, 456.8, 531.20



power of 10.


1000: 67.8, 456.8, 531.20



power of 10.


1000: 67.8, 456.8, 531.20



power of 10.

26

Use what you know about multiplying a

decimal by a power of 10 to help solve the

following problem: If 5 pounds of carrots

cost $2.79, how much will 50 pounds cost?



















































































































































27

At his first Art Show an artist sold a painting

and a sculpture. He sold the painting for 10³

times as much money as the sculpture. How

much might he have sold each item for?

Show three possible solutions.


















































































































































28

Give the large cube in a Base Ten set a value of 1,

the flat a value of .1, the long a value of .01 and the

small cube a value of .001. Use 5 base ten blocks to

represent a decimal. Record using a diagram,

numerals, number name and expanded form. Repeat.


















































































































































29

Write 10 different decimal numbers

using the digits 3, 7, 2, 8, and 4.

Write each decimal in numeral, word

and expanded form.




and expanded form.




and expanded form.




and expanded form.




and expanded form.




and expanded form.




and expanded form.




and expanded form.




and expanded form.




and expanded form.




and expanded form.




and expanded form.




and expanded form.




and expanded form.




and expanded form.




and expanded form.




and expanded form.




and expanded form.




and expanded form.




and expanded form.




and expanded form.




and expanded form.




and expanded form.




and expanded form.




and expanded form.




and expanded form.




and expanded form.




and expanded form.




and expanded form.




and expanded form.

30

Which is larger 2.9 or 2.13?

Explain your reasoning.



























































31

Lisa said that 0.148 is greater than

0.52 because 148 is greater than 52.

Is Lisa correct? Explain your

thinking.




thinking.




thinking.




thinking.




thinking.




thinking.




thinking.




thinking.




thinking.




thinking.




thinking.




thinking.




thinking.




thinking.




thinking.




thinking.




thinking.




thinking.




thinking.




thinking.




thinking.




thinking.




thinking.




thinking.




thinking.




thinking.




thinking.




thinking.




thinking.




thinking.

32

Turn over 5 numeral cards. Place a counter after

the second numeral to represent a decimal point.

Round the number to the nearest hundredth using

the following sentence frame and repeat 5 times:



















































































































































33

Two students rounded 2.467 to the nearest

hundredth. Student A said the answer was

2.47. Student B said the answer was 2.5.

Who was correct? Explain your thinking.





















































































































34

How could you break apart 242 to make

242 x 6 a simpler problem? Would this

work for any number? Explain. Support

your reasoning with other examples.





















































































































35

Create a word problem that could be

solved by multiplying two factors that

are between 100 and 500. Explain how

you would solve this problem.





















































































































36

You multiply two numbers and the

product is about 90 more than 31 x 63.

What two numbers might you have






















































































































37

Using the numbers 1, 2, 3, and 4 create

the largest possible product and the

smallest possible product. How does the

order of the digits affect the product?





















































































































38

A giant panda eats up to 14 kilograms of

bamboo per day. How many kilograms of

bamboo will a zoo need to feed a pair of

pandas during the month of September?





















































































































39

You divide a 4 digit whole number by a

2 digit divisor. There is no remainder. The

sum of the digits in the quotient is 9. What

numbers might you have divided?





















































































































40


solved by dividing a three digit dividend by

a 2 digit divisor. Explain how you would

solve the problem and check your answer.





















































































































41

You divide two numbers and the

quotient is 2.5. What might the two

numbers be? Show at least 5

solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.

42

A farmer grows 196kg of carrots. He sells

them to a grocer who divides them into 5kg

and 2kg bags. If the grocer uses the same

number of 2kg and 5kg bags, how many of

each does he use? Explain your thinking.


















































































































































43

Show 5 possible solutions for each statement:

a) the sum of 2 decimals is less than 1

b) the sum of 2 decimals is equal to 1

c) the sum of 2 decimals is greater than 1





















































































































44

Show 5 possible solutions for each statement: a) the difference between 2 decimals is less than 1 b) the difference between 2 decimals is equal to 1 c) the difference between 2 decimals is greater

than 1


than 1


than 1


than 1


than 1


than 1


than 1


than 1


than 1


than 1


than 1


than 1


than 1


than 1


than 1


than 1


than 1


than 1


than 1


than 1


than 1


than 1


than 1


than 1


than 1


than 1


than 1


than 1


than 1


than 1

45

The difference between two

decimals is 6.53. What might the

two decimals be? Show 5 different

solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.

46

Create and solve a word problem

with a quotient of 3.4. How did

you choose your numbers?
























































































47

I multiplied two numbers and got a

product smaller than both factors.

What might the two numbers be?
























































































48

Create a word problem involving

multiplication of decimals in which the

digits 3, 5, 7 and 2 appear. Show how

you would solve the problem.





















































































































49

I spent $156 to enclose my garden at

a cost of $6.50 per yard for fencing.

Draw two possible plans for my






















































































































50

1/a — 1/b = 1/c

How many different sets of

numbers can you find that will make

this a true sentence?

1/a — 1/b = 1/c




1/a — 1/b = 1/c




1/a — 1/b = 1/c




1/a — 1/b = 1/c




1/a — 1/b = 1/c




1/a — 1/b = 1/c




1/a — 1/b = 1/c




1/a — 1/b = 1/c




1/a — 1/b = 1/c




1/a — 1/b = 1/c




1/a — 1/b = 1/c




1/a — 1/b = 1/c




1/a — 1/b = 1/c




1/a — 1/b = 1/c




1/a — 1/b = 1/c




1/a — 1/b = 1/c




1/a — 1/b = 1/c




1/a — 1/b = 1/c




1/a — 1/b = 1/c




1/a — 1/b = 1/c




1/a — 1/b = 1/c




1/a — 1/b = 1/c




1/a — 1/b = 1/c




1/a — 1/b = 1/c




1/a — 1/b = 1/c




1/a — 1/b = 1/c




1/a — 1/b = 1/c




1/a — 1/b = 1/c




1/a — 1/b = 1/c




51

Create a word problem that can be solved by

subtracting two fractions with unlike

denominators. Explain how you could use

equivalent fractions to help solve the

problem.





problem.





problem.





problem.





problem.





problem.





problem.





problem.





problem.





problem.





problem.





problem.





problem.





problem.





problem.





problem.





problem.





problem.





problem.





problem.





problem.





problem.





problem.





problem.





problem.





problem.





problem.





problem.





problem.





problem.

52

Two fractions are added together

for a sum of 2/4. What might the

two fractions be? Show at least 5

solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.




solutions.

53

The sum of two mixed numbers with

unlike denominators is 58/10. What

might the two mixed numbers be?
























































































54

The difference between two mixed

numbers with unlike denominators is 3¾.

What might the two mixed numbers be?
























































































55

The total weight of three packages is

⅞lb. One package weighs ¼lb. What

might the other two packages weigh?
























































































56

2/5 of the animals in a pet shop are dogs and

3/8 are cats. The rest of the animals are

birds or mice. What fraction of all the

animals are dogs and cats? What fraction of

all the animals are not dogs and cats? Explain.


















































































































































57

4 friends share 7 small pizzas equally.

How much pizza does each friend get?

Represent your thinking using a






















































































































58

A baker is making 6 loaves of bread using

9 cups of milk. How much milk does she use

per loaf? Represent your thinking using a






















































































































59

Tom and 7 friends share 2 liters of juice

equally. How much juice does each

person get? Represent your thinking






















































































































60

Three-fourths of a container of buttons are

square. Two-thirds of the square buttons are

red. What fraction of the buttons are square

and red? Represent your thinking using a



















































































































































61

Create a word problem for the

equation 2/3 x 4/5. Show how you

could solve the problem using a

fraction model.




fraction model.




fraction model.




fraction model.




fraction model.




fraction model.




fraction model.




fraction model.




fraction model.




fraction model.




fraction model.




fraction model.




fraction model.




fraction model.




fraction model.




fraction model.




fraction model.




fraction model.




fraction model.




fraction model.




fraction model.




fraction model.




fraction model.




fraction model.




fraction model.




fraction model.




fraction model.




fraction model.




fraction model.




fraction model.

62

There are 20 muffins on a plate. 2/5 of the

muffins are chocolate. 3/10 of the muffins

are vanilla. The rest of the muffins are

blueberry. How many muffins are blueberry?



















































































































































63

Show why 1/2 x 1/3 = 1/6 by dividing a

rectangle. Repeat with other pairs of

fractions with unlike denominators.
























































































64

Tom says that ½ is the product of

3/5 x 5/6. Is Tom correct? Use a

rectangular model and an equation to

prove your answer.




prove your answer.




prove your answer.




prove your answer.




prove your answer.




prove your answer.




prove your answer.




prove your answer.




prove your answer.




prove your answer.




prove your answer.




prove your answer.




prove your answer.




prove your answer.




prove your answer.




prove your answer.




prove your answer.




prove your answer.




prove your answer.




prove your answer.




prove your answer.




prove your answer.




prove your answer.




prove your answer.




prove your answer.




prove your answer.




prove your answer.




prove your answer.




prove your answer.




prove your answer.

65

The product of two fractions with

unlike denominators is less than ½.

What might the two fractions be?
























































































66

Draw a rectangle on cm grid paper with a length of 5½cm

and a width of 3½cm . Find the area by counting unit

squares. Show that the answer is the same as would be

found by multiplying the side lengths. Repeat for other



















































































































































67

Mr. Smith wants to carpet a closet with

carpet tiles. The closet is 5 meters long and

half a meter wide. How much carpet will he

need? Represent your thinking with a

rectangular model and an equation.


















































































































































68

Ray digs a garden plot that is 30 feet wide

and 20 feet long. Bill digs a garden plot that

is half as wide, but has the same length as

Ray’s plot. How do the dimensions and area of

the two garden plots compare?


















































































































































69

You multiply a fraction by ¾. Will

the product be more or less than

the number you multiplied by? Why?
























































































70

You multiply a number by a fraction

greater than 1. Will the product be

more or less than the number you

multiplied by? Why?




multiplied by? Why?




multiplied by? Why?




multiplied by? Why?




multiplied by? Why?




multiplied by? Why?




multiplied by? Why?




multiplied by? Why?




multiplied by? Why?




multiplied by? Why?




multiplied by? Why?




multiplied by? Why?




multiplied by? Why?




multiplied by? Why?




multiplied by? Why?




multiplied by? Why?




multiplied by? Why?




multiplied by? Why?




multiplied by? Why?




multiplied by? Why?




multiplied by? Why?




multiplied by? Why?




multiplied by? Why?




multiplied by? Why?




multiplied by? Why?




multiplied by? Why?




multiplied by? Why?




multiplied by? Why?




multiplied by? Why?




multiplied by? Why?

71

Meg collected 2¾ of a bin of glass bottles

to recycle. Liam collected 3 times as many

bottles as Meg. How many bins of bottles

did Liam collect? Explain your thinking.





















































































































72

Create and solve two word problems

involving multiplication of a fraction by a

fraction. Represent each problem using

an equation and a fraction model.





















































































































73



mixed number. Represent each problem

using an equation and a fraction model.





















































































































74

The product of two mixed numbers

is greater than 6 but less than 7.

What might the two mixed numbers

be?




be?




be?




be?




be?




be?




be?




be?




be?




be?




be?




be?




be?




be?




be?




be?




be?




be?




be?




be?




be?




be?




be?




be?




be?




be?




be?




be?




be?




be?

75

Tom and Ben solved the problem 1/5 ÷ 3 = ?

Ben said the answer was 15/1. Tom said the

answer was 1/15. Who was correct? Use a

fraction model to explain your reasoning.





















































































































76

Is the quotient of ½ ÷ 4 more, less,

or equal to the quotient of 4 ÷ ½ ?

























































































77

A bakery uses ⅛ of a barrel of oatmeal in each

batch of cookies. On Monday the bakery used 3

barrels of oatmeal. How many batches of cookies

were made? Use a fraction model and an

equation to represent the problem.


















































































































































78

A bird feeder holds 2 cups of birdseed. Dad

is filling the bird feeder with a scoop that

holds 1/6 of a cup. How many scoops of

birdseed will he need? Use a fraction model

and an equation to represent the problem.


















































































































































79


involving division of a unit fraction by a

whole number. Represent your problem






















































































































80


involving division of a whole number by a

unit fraction. Represent your problem






















































































































81

Jim’s sleeping bag is 5 feet long. Jorge’s

sleeping bag is 2 yards long. Steven’s sleeping

bag is 68 inches long. Whose sleeping bag is

the longest? Explain your thinking.





















































































































82

Which is more: a) 2 yards or 7 feet?

b) 4000mm or 3 meters? c) 3 pounds or

32 ounces? Explain your thinking.
























































































83

What is your arm span in millimeters/

centimeters/decimeters/meters? If you

find one measurement, how can you find

the others without measuring?





















































































































84

I placed one kilogram of sugar into

four different sized bags. How much

sugar might each of the bags

contain?




contain?




contain?




contain?




contain?




contain?




contain?




contain?




contain?




contain?




contain?




contain?




contain?




contain?




contain?




contain?




contain?




contain?




contain?




contain?




contain?




contain?




contain?




contain?




contain?




contain?




contain?




contain?




contain?




contain?

85

Dad is shopping for apples. He can buy

a 3kg bag of apples for $4.00 or a

1500g bag for $2.25. Which is the






















































































































86

Mike uses 120 pints of water to take a 5

minute shower. Dad uses 100 quarts for a 10

minute shower. Maria uses 24.8 gallons for an

8 minute shower. Who uses the most gallons

of water per minute? Explain.


















































































































































87

Create a line plot to display the data below.

Choose a possible title and label the axis:

Record three facts about the data.

Green: 5½ Red: 5⅛ Blue: 5¾ Purple: 5⅜

Orange: 4⅝ White: 5⅛


















































































































































88

Collect 10 objects that are shorter than 5in.

in length. Measure each object to the nearest

⅛in. Create a line plot to display your data. If

you put all the objects together end to end

what would be the total length? Explain.


















































































































































89

Using cm cubes how many different

rectangular prisms can you build

with a volume of 24cm³? Record.
























































































90

Build three different rectangular prisms using

cm cubes. Find the volume of each cube by

counting the cubes. Describe any relationship

that you notice between the length, width, and

height of each prism and its volume.


















































































































































91

A rectangular prism has a volume of 72

cubic units. If one of its dimensions is 6,

what might the other dimensions be?

Show three different solutions.





















































































































92

A storage container is 33m long, 16m

wide, and 14m high. If half of the

container is filled with boxes, how much

space is left? Explain your thinking.





















































































































93

Using cm cubes build two different solid

figures, each composed of two non-

overlapping right rectangular prisms. Find the

volume of each figure by adding the volumes

of the non-overlapping parts. Record.


















































































































































94

Joe is building a cage for his hamster. He

attaches a 2ft by 3ft by 3ft cage to a larger

cage that measures 4ft by 4ft by 3ft. What

is the volume of the cage? Explain your

thinking.





thinking.





thinking.





thinking.





thinking.





thinking.





thinking.





thinking.





thinking.





thinking.





thinking.





thinking.





thinking.





thinking.





thinking.





thinking.





thinking.





thinking.





thinking.





thinking.





thinking.





thinking.





thinking.





thinking.





thinking.





thinking.





thinking.





thinking.





thinking.





thinking.

95

Draw two different quadrilaterals on a

coordinate grid. Use ordered pairs to label

the vertices. What is the same/different

about the two quadrilaterals?





















































































































96

Lisa drew an isosceles triangle on a

coordinate grid. One of the vertices was

at the point (5,6). Where might the

other vertices have been?





















































































































97

There are at least 3 different names that

you can use for a 4-sided shape. What

might the shape be? Draw the shape and

explain why it can have different names.





















































































































98

Work with a partner. Measure the sides

of 10 different triangles. Classify the

triangles by the number of congruent

sides. Record your findings.





















































































































99

Work with a partner. Measure the interior

angles of 10 different triangles. Classify the

triangles by the measure of their largest

interior angle. Record your findings.





















































































































100

How many different quadrilaterals

can you make on a geoboard? Which

shapes are parallelograms? Which






















































































































101

What is the difference between the

quadrilaterals in each pair below:

a) a square and a rectangle?

b) a rectangle and a rhombus?

c) a trapezoid and a parallelogram?


















































































































































102

103

104

105

Copy several sets onto card, laminate and cut out for Triangle Packs.

A

B

C D

106

E

J

H

F

I

G

107

__________________________________________________________________________________________________________ __________________________________________________________________________________________________________ __________________________________________________________________________________________________________

108

109

I solved the problem correctly using an efficient strategy.

My explanation is very clear and logical. I used math vocabulary effectively.

I included evidence that I checked my work for accuracy.

I solved the problem correctly using an appropriate strategy.

My explanation is reasonably clear. I used some math vocabulary.

I solved part of the problem correctly or made some small errors. I used a strategythat was partially useful, but did not lead to a correct solution.

Some parts of my explanation are clear. I used little math vocabulary.

I gave no answer or an incorrect answer. My strategy is inappropriate.

I did not include an explanation or my explanation is unclear or irrelevant.

My work shows that I have a thorough understanding of this math concept.

My work shows that I have a good understanding of this math concept.

My work shows some understanding of this math concept.

My work shows that I need more help to understand this math concept.

110


I modeled the problem using a very clear drawing or diagram, chart, graph, or equation.

My explanation is very clear and accurate. I used precise math vocabulary,supported my predictions and conclusions with proof and evaluated thereasonableness of my solution.


I modeled the problem using a clear drawing or diagram, chart, graph, or equation.

My explanation is reasonably clear and accurate. I used some math vocabulary,supported my predictions and conclusions with proof and evaluated thereasonableness of my solution.

I solved part of the problem correctly or made some small errors. I used a strategythat was partially useful, but did not lead to a correct solution.

I attempted to model the problem using a clear drawing or diagram, chart, graph, orequation.

Some parts of my explanation are clear. I tried to use math vocabulary andattempted to support my descriptions and conclusions with proof.

I gave no answer or an incorrect answer. My strategy was inappropriate.

I did not model the problem using a drawing or diagram, chart, graph, or equation.

I did not include an explanation or my explanation is unclear or irrelevant.

My work shows that I have a thorough understanding of this math concept.

My work shows that I have a good understanding of this math concept.

My work shows some understanding of this math concept.

My work shows that I need more help to understand this math concept.

111


My explanation is very clear and logical. I usedmath vocabulary effectively.

I included evidence that I checked my work for accuracy.

My work shows a thorough understanding of the mathin this task.

112

I solved the problem correctly using an appropriatestrategy.

My explanation is reasonably clear. I used some mathvocabulary.

My work shows a good understanding of the mathin this task.

113

I solved part of the problem correctly or made somesmall errors. I used a strategy that was partially useful,but did not lead to a correct solution.

Some parts of my explanation are clear. I used littlemath vocabulary.

My work shows some understanding of the mathin this task

114

I gave no answer or an incorrect answer. My strategyis inappropriate.

I did not include an explanation or my explanation isunclear or irrelevant.

My work shows that I need more help to understandthe math in this task.math in this task.

115


I modeled the problem using a very clear drawing or diagram,chart, graph, or equation.

My explanation is very clear and accurate. I used precisemath vocabulary, supported my predictions and conclusionswith proof and evaluated the reasonableness of my solution.

My work shows a thorough understanding of the math in this task.

116


I modeled the problem using a clear drawing or diagram,chart, graph, or equation.

My explanation is reasonably clear and accurate. I usedsome math vocabulary, supported my predictions andconclusions with proof and evaluated the reasonableness ofmy solution.

My work shows a good understanding of the math in this task.

117

I solved part of the problem correctly or made some smallerrors. I used a strategy that was partially useful, but didnot lead to a correct solution.

I attempted to model the problem using a drawing or diagram,chart, graph, or equation.

Some parts of my explanation are clear. I tried to use mathvocabulary and attempted to support my descriptions andconclusions with proof.

My work shows some understanding of the math in this task.

118

I gave no answer or an incorrect answer. My strategy wasinappropriate.

I did not model the problem using a drawing or diagram,chart, graph, or equation.

I did not include an explanation or my explanation is unclearor irrelevant.

My work shows that I need more help to understand the math inthis task.

119

Single User License

K-5 MATH TEACHING RESOURCES LLC, (“K5MTR”) agrees to grant, and the user (“you,” “user,” “your”) agrees to

accept, a nonexclusive license to use the downloadable math resources, math games, hands-on math activities, and math

workbooks available by and through K5MTR (collectively, “eBook”), under the terms and conditions of this eBook License

Agreement (“Agreement”). Your use of the eBook constitutes your agreement to the terms and conditions set forth in this

Agreement. This Agreement, or any part thereof, cannot be changed, waived, or discharged other than by a statement in

writing signed by you and K5MTR. Please read the entire Agreement carefully. BY DOWNLOADING OR OTHERWISE

USING ANY OF THE EBOOKS, USER AGREES TO BE BOUND BY THIS AGREEMENT.

1. eBook Usage. The K5MTR eBook may be used by one user. The user of the eBook shall be subject to all of the terms of

this Agreement, whether or not a license was purchased by the user or the user was the original downloader.

2. Printing. You may only print pages of the eBook, in connection with the lawful use of such pages on connection with a

classroom, home schooling, or other teaching environment, for which you are responsible for providing mathematics related

instruction. Other than the above, you may not print pages and/or distribute eBook content to others.

3. Copyright, Use and Resale Prohibitions. K5MTR retains all rights not expressly granted to you in this Agreement. The

content, and related documentation in the eBook are protected by copyright laws and international copyright treaties, as well

as other intellectual property laws and treaties. Nothing in this Agreement constitutes a waiver of K5MTR’s rights. K5MTR

will not be responsible for performance problems due to circumstances beyond its reasonable control. Other than as stated

in this Agreement, you may not copy, print, modify, remove, delete, augment, add to, publish, transmit, sell, resell, license,

create derivative works from, or in any way exploit any of the eBook’s content, in whole or in part, in print or electronic

form, and you may not aid or permit others to do so. You may not use the eBook or the content therein for commercial

purposes. The unauthorized use or distribution of copyrighted or other proprietary content is illegal and could subject the

purchaser to substantial damages. Purchaser will be liable for any damage resulting from any violation of this Agreement.

4. No Transfer. This license is not transferable by the eBook purchaser unless such transfer is approved in advance by

K5MTR. Provided, however, that the purchaser of a “standard option” manual subscription may give his or her copy of the

eBook to a coworker to use, in which case the coworker will be subject to the terms and conditions of this Agreement.

5. Marks of Ownership. You must not remove or alter any mark of ownership, copyright, trademark or other property

right which is embodied in the eBook including its documentation and the physical or digital material in which the eBook is

stored when supplied to you.

6. Limitation of Liability and Disclaimer of Warranty. The eBook, any content provided therein, or any counsel or

advice provided by any member of K5MTR’s staff or any principal of K5MTR, are in no way substitutes for assistance

from trained, licensed, certified, and qualified education professionals. If the assistance of a trained educator is required,

the services of a competent professional person should be sought.

THE EBOOK IS PROVIDED “AS IS” AND K5MTR DOES NOT MAKE ANY WARRANTY OR REPRESENTATION,

EITHER EXPRESS OR IMPLIED, TO THE EBOOK, INCLUDING ITS QUALITY, ACCURACY, PERFORMANCE,

MERCHANTABILITY, OR FITNESS FOR A PARTICULAR PURPOSE. YOU ASSUME THE ENTIRE RISK AS TO

THE RESULTS AND PERFORMANCE OF THE EBOOK. K5MTR DOES NOT WARRANT, GUARANTEE, OR

MAKE ANY REPRESENTATIONS REGARDING THE USE OF, OR THE RESULTS OBTAINED WITH THE EBOOK

(INCLUDING BUT NOT LIMITED TO INCREASING, ENHANCING, OR OTHERWISE IMPROVING THE MATH

AND ARITHMETIC CAPABILITIES, TEST SCORES, OR PERFORMANCE OF ANY PERSON), IN TERMS OF

ACCURACY, CORRECTNESS OR RELIABILITY, OR COMPLIANCE WITH ANY EDUCATIONAL OR ACADEMIC

RULES, REGULATIONS, OR LAW IN ANY JURISDICTION. In no event will K5MTR be liable for indirect, special,

incidental, or consequential damages arising out of delays, errors, omissions, inaccuracies, or the use or inability to use the

eBook, or for interruption of the eBook, from whatever cause. This will apply even if K5MTR has been advised that the

possibility of such damage exists. Specifically, K5MTR is not responsible for any costs, including those incurred as a result

of lost profits or revenue, poor academic performance, loss of data, the cost of recovering such programs or data, the cost of

any substitute program, claims by third parties, or similar costs. In no case will K5MTR’s liability exceed the amount of

license fees paid.

7. Hold Harmless / Indemnification. You agree to defend, indemnify and hold K5MTR and any third party provider

harmless from and against all third party claims and damages (including reasonable attorneys’ fees) regarding your use of

the eBook, unless the claims or damages are due to K5MTR’s or any third party provider’s gross negligence or willful

misconduct or arise out of an allegation for which K5MTR is obligated to indemnify you.

8. Compliance with Law. Any use of the eBook must be lawful and you expressly agree to avoid any use that is potentially

or actually unlawful that could constitute a criminal offense, give rise to civil liability or otherwise violate any applicable

local, state, national or international law, regulation or judicial ruling.

9. Governing Law. If there is any dispute arising out of the eBook, by using the eBook, you expressly agree that any such

dispute shall be governed by the laws of the State of New York, U.S.A. and the federal laws of the United States of

America, without regard to its conflict of law provisions and excluding that body of law known as conflicts of law and the

United Nations Convention on Contracts for the Sale of Goods. You expressly agree to submit to the exclusive jurisdiction

of the exclusive jurisdiction of and venue in the federal and state courts located in New York County, New York, U.S.A.

Use of the EBook is unauthorized in any jurisdiction that does not give effect to all provisions of this Section 9.

10. Severability. If any provision of this Agreement or the application thereof to any person or circumstance shall be

invalid or unenforceable to any extent, the remainder of this Agreement and the application of such provisions to other

persons or circumstances shall not be affected thereby and shall be enforced to the greatest extent permitted by law.

11. Entire Agreement. It is hereby acknowledged that this Agreement constitutes the entire agreement between the parties

pertaining to the subject matter hereof, and supersedes in their entirety any and all written or oral agreements previously

existing between the parties with respect to such subject matter.

Documents

5th Grade 5th - CST Curriculum Talk · A math journal, or problem solving notebook as they are sometimes referred to, is a book in which students record their math work and thinking