Teacher Resource Book

AchieveMath

Teacher Resource Book Levels 3–5

Teacher Resource BookLevels 3–5

Contents

Fluency Routines . . . . . . . . . . . . . . . . . . . . . . 3

Discourse Routines . . . . . . . . . . . . . . . . . . . 15

Resources . . . . . . . . . . . . . . . . . . . . . . . . . . 49

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3©2021 Levels 3–5 Fluency Routines

Fluent retrieval of basic arithmetic facts is essential to math proficiency . Students should have mastered addition and subtraction of whole numbers through 20 by the end of Level 2, and they will continue to need to rely on fluent use of these facts to manipulate larger whole numbers, fractions, and decimals . In addition, by the end of Level 3, students should be able to fluently multiply and divide within 100 and be fluent in multiplying all single-digit factors . Achieving fluency with these facts will enable them to accurately and efficiently engage with more complex operations, including those involving rational numbers, and to solve novel problems .

The following fluency routines are designed to help students in Levels 3–5 continue to develop number sense, enhance their understanding of the relationships within the number system, and attain automaticity with all arithmetic facts . These routines push students to think about the relationships between and among numbers and to use this understanding to develop strategies for using these relationships in increasingly complex mathematics, including manipulating rational numbers and solving multi-step word problems . Discussion after routines allows classmates to share their ideas and the visual or mathematical structures they used to complete the routine .

Every AchieveMath lesson includes a recommended fluency routine, and students should spend at least 6 minutes of every class working to become fluent in fact retrieval and enhance their number sense . If you feel your students would benefit from a different routine than the one outlined in the lesson, use the descriptions that follow to construct your own activity .

Fluency Routines Levels 3–5

ContentsChoral Counting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Count Around the Circle . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Double-More . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Forehead Numbers/Back-to-Back . . . . . . . . . . . . . . . . . . . . . 6

Math Dice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Mental Math . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Multi-More . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Number Bonds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Number Talks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Number Triangles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Quick Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11

Ratio Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11

Start and Stop Counting . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

True or False . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Ways to Make a Number . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

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4 Levels 3–5 Fluency Routines ©2021

Choral Counting

Materials: none required

Steps

1 . Assign students a counting sequence or skip-counting interval and a direction for counting (forward or backward) .

2 . Assign students a starting point . You may also assign students an ending point .

3 . Students say the counting sequence aloud together . You may choose to join in or not, depending on the amount of support students need .

4 . After completing the Choral Counting routine, have students discuss:• Why is this counting sequence important?• Is this counting sequence difficult? Why or why not?

Use this routine:• When students are learning a new counting sequence .• When students are struggling to master an important counting sequence .

Optional models and manipulatives:• Hundred chart• Number lines• Open number lines • Number triangles

Count Around the Circle


Steps

1 . Have students sit in a circle .

2 . Assign students a starting number, counting interval or sequence, and a direction . You may also provide students a context for their counting and manipulatives or visual supports to represent that context . (For example, if everyone is bringing 6 cupcakes to a party, how many will all of us bring?)

3 . Have students estimate the ending number of a single time (or multiples times) around the circle . Ask students to explain the reasoning for their estimates . Students may comment on the reasonableness of their peers’ estimates . Allow students to revise their estimates as they count .

4 . One student starts the counting sequence, then each student going around the circle says the next number . Allow students adequate time and appropriate tools (manipulatives or visual supports) to contribute the next number in the sequence .

5 . If students struggle with the sequence, you may switch to Choral Counting .

6 . After completing the Count Around the Circle routine, have students discuss:• Why is this counting sequence important?• Is this counting sequence difficult? Why or why not?• What numbers in the counting sequence were difficult? Why?• Was your estimate correct? Why?

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Use this routine:• To reinforce important counting sequences and skip-counting patterns .• To help students notice number patterns .• When students need practice making and justifying reasonable estimates .

Optional models and manipulatives:• 10-frames• Hundred chart• Number lines• Open number lines

Double-More

Materials: playing cards (with face cards removed)

Steps

1 . Pair students . If you have an odd number, you may work with a student .

2 . Give each pair a deck of cards with the face cards removed (or face cards may be assigned a value of 10) . Tell students that aces have a value of 1 .

3 . One student deals the cards so that each student has an equal number of cards .

4 . Each student plays two cards and adds them . The student with the larger sum gets all four cards . If the sums are equivalent, students keep their own cards .

5 . At the end of the game, students count their cards to see who has more . Students may then deal the cards and play again .

6 . After completing the Double-More routine, have students discuss: • What cards were easy to add? What cards were difficult?• What strategies did you use to add the cards?

Use this routine:• As students master their addition facts to 20 .

Optional models and manipulatives:• 10-frames and manipulatives• Number bonds• Addition chart

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Forehead Numbers/Back-to-Back

Materials: playing cards (with face cards removed), or whiteboards and markers

Steps

1 . Put students into groups of three and give each group a deck of cards .

2 . One student is designated the Calculator . The other two students each draw a card and immediately put it to their forehead without looking at it . They can see the other student’s card but not their own .

3 . The Calculator announces either the sum or product of the numbers on the two cards along with whether it is the sum or the product .

4 . The first student to correctly guess the card on their forehead wins both cards .

5 . If neither student can figure out their number, the Calculator gives the product or sum, whichever they did not give initially .

6 . For the next round, another student is the Calculator .

7 . After completing the Forehead Numbers/Back-to-Back routine, have students discuss:• How did you use your friend’s number to find your number?• Was it easier to figure out your number when you had the sum or the product?• Did you like guessing or being the Calculator better? Why?

Variation: In the Back-to-Back variation of the routine, the whole class can play . Choose two students to stand back-to-back at the board and one to be the Calculator . The students at the board each write a number (within an assigned range) that the other cannot see . The Calculator announces the sum, the product, or both, and the first student to guess their peer’s number remains at the board; the Calculator and the other student sit down . Choose another student to face off at the board and a new Calculator .

Use this routine:• As students master addition and multiplication facts . • As students understand compensation .• As students make the connection between addition and subtraction and multiplication and division .

Optional models and manipulatives:• Part-part-whole tape diagrams• Number bonds• Number triangles

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Math Dice

Materials: polyhedral dice, six-sided dice

Steps

1 . Pair students . If you have an odd number, you may work with a student or you may assign one group of three .

2 . Give each pair one polyhedral die and at least five six-sided dice .

3 . One student rolls the polyhedral die, and the other rolls the six-sided dice .

4 . Working together, students make the number on the polyhedral die using at least two of the six-sided dice and any operation they are familiar with (add, subtract, multiply, divide, use exponents, etc .) .

5 . After they have found as many combinations as they can (using the six-sided dice multiple times, if necessary), the pair rolls the dice again, swapping who rolls the polyhedral die and who rolls the six-sided dice .

6 . After completing the Math Dice routine, have students discuss:• What were some ways you made the target number that involved more than two dice?• Was it easier to make the target number when it was a big number or a small number?

Use this routine:• As students become more flexible adding and subtracting numbers and finding sums and differences

in multiple ways .• As students master addition and subtraction facts to 20 .• As students become more flexible multiplying and dividing numbers and finding products and

quotients in multiple ways .• As students master multiplication and division facts within 100 .• As students think about the relationships between and among numbers and operations .

Optional models and manipulatives: • Open number lines

Mental Math


Steps

1 . Tell students that you will display a problem that they will solve independently and silently, using only their brains .

2 . Display the problem . Tell students to put their thumbs up when they think they have an answer .

3 . Allow students to share both their answer and their process for finding the problem . Have students discuss:• What strategies did you use to solve the problem(s) in your head?• How were the problems connected?• Did you hear any strategies that you might use in the future?

Variation: This routine may be done with just one problem (which will be accompanied by extensive discussion) or with multiple problems that are connected in some way, in which case students may try to employ the strategies other students have suggested .

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Use this routine: • As students memorize arithmetic facts .• As students complete operations with larger numbers . • As students work with structures for word problems . • As students internalize visual representations for math concepts .• As students understand the base-10 system and the rational number system .

Optional models and manipulatives: You may employ relevant visual supports as students describe their strategies and mental images . For example, if a student describes constructing a mental number line, draw what the student describes . Or, if a student describes deconstructing one of the addends to make a friendly number, draw number bonds to show this strategy .

Multi-More

Materials: playing cards (with face cards removed)

Steps

1 . Pair students . If you have an odd number, you may work with a student .

2 . Give each pair a deck of cards with the face cards removed (or face cards may be assigned a value of 10) . Tell students that aces have a value of 1 .

3 . One student deals the cards so that each student has an equal number of cards .

4 . Each student plays two cards and multiplies them . The student with the larger product gets all four cards . If the products are equivalent, students keep their own cards .

5 . At the end of the game, students count their cards to see who has more . Students may then deal the cards and play again .

6 . After completing Multi-More, have students discuss: • What kinds of cards allowed you to win a hand?• Were there times you were surprised that you won a hand? What surprised you?• Were there times you struggled to multiply your numbers? What tools did you use to help you?

Use this routine:• As students master their multiplication facts .

Optional models and manipulatives:• Multiplication table• Hundred chart• Number lines• Number triangles

Number Bonds

Materials: number bonds, pencils; optional: copy paper

Steps

1 . Prepare number bond pages, or use the ones provided in the Student Book . You may use the Number Bonds reproducible or draw number bonds on copy paper . Depending on the focus, the number bonds may have unknowns in any position .

2 . Distribute number bond pages to students .

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3 . Students complete their number bonds, either in pairs or independently .

4 . Students compare their number bonds with another student or pair, noticing and discussing differences .

5 . After completing the Number Bonds routine, have students discuss:• Which number bonds were most challenging? Why?• How did you solve a number bond with the unknown as the whole? • How did you solve a number bond with the unknown as a part?

Variations: • Instead of (or in addition to) completing the number bonds, students may write equations with an

unknown in any position (using symbols or letters for the unknown) and solve . • You may choose to make custom number bond pages for students based on their specific needs .

Use this routine: • As students master addition and subtraction facts to 20 .• As students conceptualize part-part-whole relationships .• As students conceptualize the relationship between addition and subtraction .• As students begin to use letter variables to write equations .

Optional models and manipulatives: • 10-frames• Number lines• Hundred chart

Number Talks

Materials: copy paper, pencils; if students will work in small groups, provide chart paper and crayons; optional: manipulatives

Steps

1 . Present students with a number, an expression, or an equation with no context .

2 . Working as a class or in pairs or small groups, students come up with everything they can about the number, expression, or equation . This may include decompositions, factors, multiples, and visual representations . You may allow students to use manipulatives if you choose .

3 . As a class, discuss the different representations students came up with for numbers or different procedures and visuals students used to simplify or solve . Have students discuss:• What representations did you use for your number?• What are some interesting things you noticed about your number? • What procedure did you use to solve the problem?• How is your procedure different from your neighbors’?• Why did you use the visual representation you chose?• How did you know your answer was reasonable?

Use this routine: • To help students think flexibly about numbers and their relationships .• To analyze different representations of numbers . • To analyze procedures for solving problems .

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Optional models and manipulatives:• Base-10 drawings• 10-frames• Number bonds• Number lines • Open number lines • Place value charts• Place value drawings• Tape diagrams • Number triangles• Factor rainbows• Factor trees

Number Triangles

Materials: number triangles, pencils

Steps

1 . Prepare number triangle pages, or use the ones provided in the Student Book . You may use the Number Triangle reproducible or draw number triangles on copy paper . Depending on the focus, the number triangles may have unknowns in any position .

2 . Distribute number triangle pages to students .

3 . Students complete their number triangles, either in pairs or independently .

4 . Students compare their number triangles with another student or pair, noticing and discussing differences .

5 . After completing the Number Triangles routine, have students discuss:• Which number triangles were most challenging? Why?• How did you solve a number triangle with the unknown as the whole? • How did you solve a number triangle with the unknown as a part?

Variation: Students may write equations with an unknown in any position (using symbols or letters for the unknown) and solve .

Use this routine:• As students master multiplication and division facts . • As students conceptualize the relationship between multiplication and division . • As students begin to use letter variables to write equations .

Optional models and manipulatives:• Arrays• Number lines• Multiplication tables• Hundred charts

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Quick Images

Materials: Quick Image cards

Steps

1 . Locate the Quick Image cards in the Teacher Lesson Manual . Be sure that all students can see the images .

2 . Show students the first Quick Image card for a few seconds .

3 . Have students tell the value they saw and explain how they were able to identify it so quickly .

4 . If you are showing a string of Quick Image cards, have students compare and contrast the different images and identify how they are related .

5 . After completing the Quick Images routine, have students discuss:• How were you able to identify the image so quickly? • What helped you identify the value on the card?• What were the differences among the images you saw?• How were they similar?

Use this routine:• As students learn to subitize values .• As students see relationships among values .• As students learn to use visual representations of numbers . • As students learn to unitize numbers .

Ratio Tables

Materials: a way to display the rule, pattern, scenario, or equation; whiteboards and markers

Steps

1 . Display a rule, pattern, scenario, or equation .

2 . Working as a whole class or in pairs using whiteboards, students complete the ratio table for the situation presented .

3 . Students may complete multiple, related ratio tables and/or be given multiple rules, patterns, scenarios, or equations .

4 . After completing the Ratio Tables routine, have students discuss:• How did you complete the table? • What is the relationship among the values on the table?• If you completed multiple tables, what is the relationship between the tables?

Use this routine:• As students are mastering multiplication facts .• As students are learning about equations and variables .• As students are learning about number patterns and number rules .

Optional models and manipulatives:• Number triangles• Multiplication tables• Hundred chart• Number lines

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Start and Stop Counting


Steps

1 . Have students sit in a circle .

2 . Assign a starting point, an ending point, a direction, and an interval to use for counting . You may ask students to predict who will say the last number or how many times the count will go around the circle before getting to the ending number .

3 . Students take turns as the counting goes around the circle . Counting continues until the ending number is reached .

4 . After completing the Start and Stop Counting routine, have students discuss:• Was it difficult to remember the ending number as you counted?• Was it difficult to keep track of the interval as you counted? Why or why not?• What was similar about all the numbers that you said?

Use this routine: • As students learn different counting sequences .• As students learn to skip-count .• As students employ counting up and counting down as strategies in addition and subtraction .

Optional models and manipulatives: • 10-frames • Number lines• Open number lines

True or False

Materials: a way to display the equations or inequalities, or index cards and envelopes

Steps

1 . Display an equation or inequality . Have students decide if it is true or false . Students must defend their classification .

2 . After completing the True or False routine, have students discuss:• How could you tell if an equation/inequality was true or false?• How could you make this false equation/inequality true?• How are these equations/inequalities related?• What does the equal sign mean?

Variation: This may be a whole-class activity or students may be paired and given an envelope with equations or inequalities . Pairs may sort their equations and inequalities into groups of true and false and compare their sorts with another pair .

Use this routine: • To emphasize the meaning of equality .• To emphasize relationships between and among numbers .• To solidify mental math strategies .• To support understanding of properties of operations .

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Optional models and manipulatives:• Number lines• Open number lines• Two-sided counters

Ways to Make a Number

Materials: whiteboards and markers, or copy paper and pencils

Steps

1 . Pair students and assign students a number . Distribute whiteboards and markers or copy paper and pencils to students . Pairs may all receive the same number, or you may differentiate the number based on student needs .

2 . Pairs should find every possible way they can think of to make the number . They may use expressions, equations, visual representations, etc .

3 . Have students share and compare their ways to make a number .

4 . After completing the Ways to Make a Number routine, have students discuss:• How did you find ways to make your number? • What ways of making the number did you start with? Why? • Were you surprised by other students’ ways of making the number?

Variation: You may complete the Ways to Make a Number routine as a class .

Use this routine: • As students think flexibly about numbers .• As students master arithmetic facts .• As students master the base-10 and rational number systems .

Optional models and manipulatives:• Number lines • Open number lines• Base-10 blocks• Place value charts• Number bonds• 10-frames• Counters• Addition chart• Multiplication table

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15©2021 Levels 3–5 Discourse Routines

Discourse Routines Levels 3–5

Math discourse is essential to the development of deep, fluent, and flexible math thinking and problem-solving . Students who engage in structured discussions about math become more motivated and empowered math practitioners . As students present their thinking and receive affirmation, they become more confident and increasingly eager to take risks, explore new concepts, and tackle new problems . Math ideas often gain credibility with students as their peers outline the connections and discoveries they’ve made, and a student’s logic can register with their peers more deeply than their teacher’s explanations . Students also learn important skills such as taking turns, collaborating, summarizing, justifying, extrapolating, and constructive disagreement .

The AchieveMath program provides discourse routines that foster student thinking and discussion . Discourse routines are included throughout the Focus and Reteach lessons as students explore math concepts, demonstrate their knowledge and abilities, develop their math vocabulary, and become increasingly fluent and reflective math practitioners . You should feel empowered to choose the routines that will best encourage your students to feel enthusiastic about sharing their ideas . Many of the routines include variations you might use to meet the needs of students who struggle with writing, organizing their thoughts, or feeling comfortable participating in a discussion .

Contents Discussion Routines

Ask One Question . . . . . . . . . . . . . . . . . . 16Find Someone Who . . . . . . . . . . . . . . . . . 16Gallery Walk . . . . . . . . . . . . . . . . . . . . . . . 16My Favorite Mistake . . . . . . . . . . . . . . . . . 17On Your Mind . . . . . . . . . . . . . . . . . . . . . . 17Q-ADE . . . . . . . . . . . . . . . . . . . . . . . . . . . 18Show My Thinking . . . . . . . . . . . . . . . . . . 19Talking Heads Together . . . . . . . . . . . . . . . 19Think-Pair-Share . . . . . . . . . . . . . . . . . . . . 19Think-Pair-Square . . . . . . . . . . . . . . . . . . . 20Write-Pair-Share . . . . . . . . . . . . . . . . . . . . 20

Journaling Routines Aha Moment . . . . . . . . . . . . . . . . . . . . . . 21How Today Went . . . . . . . . . . . . . . . . . . . . 21Posters . . . . . . . . . . . . . . . . . . . . . . . . . . . 22Solve Now . . . . . . . . . . . . . . . . . . . . . . . . 22The Going Got Tough . . . . . . . . . . . . . . . . 22Two Strengths and a Shrug . . . . . . . . . . . . 23What You Learned . . . . . . . . . . . . . . . . . . . 23Word Problems . . . . . . . . . . . . . . . . . . . . . 24

Vocabulary RoutinesFrayer Model . . . . . . . . . . . . . . . . . . . . . . . 24Labels . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24Vocabulary Snowman . . . . . . . . . . . . . . . . 25You Be the Artist . . . . . . . . . . . . . . . . . . . . 25

Check for Understanding RoutinesHelpful Hint . . . . . . . . . . . . . . . . . . . . . . . 26Slates . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26Sticky Notes . . . . . . . . . . . . . . . . . . . . . . . 26Thumbs Up, Down, or Sideways . . . . . . . 27Thumbs Up or Down . . . . . . . . . . . . . . . . 27

Motivation Routines and AwardsEponymous Strategies . . . . . . . . . . . . . . . 28You Be the Teacher . . . . . . . . . . . . . . . . . . 28Award Descriptions . . . . . . . . . . . . . . . . . 28

Award Badges and Certificates ReproduciblesConsistently Persistent Award . . . . . . . . . 32Conversation Starter Award . . . . . . . . . . . 34Featured Teacher Award . . . . . . . . . . . . . . 36Fluency Fanatic Award . . . . . . . . . . . . . . . 38I Like Your Math Award . . . . . . . . . . . . . . . 40Inventor Award . . . . . . . . . . . . . . . . . . . . . 42Real-World Award . . . . . . . . . . . . . . . . . . . 44Switcheroo Award . . . . . . . . . . . . . . . . . . 46

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16 Levels 3–5 Discourse Routines ©2021

Discussion Routines

Ask One Question

Materials: none required; optional: sticky notes

Steps

1 . Assign students a problem .

2 . Bring students’ focus to a particular way of solving the problem . You may choose a certain student’s representation or make up one of your own .

3 . Encourage students to ask one question about the way you solved the problem . You may refer students to the Question prompts on the Q-ADE anchor chart .

Variations: • Have students write their questions on sticky notes .• Have students think-pair about their questions before sharing with the whole class .

Use this routine:• To help students pay attention to a particular procedure .• To encourage students to think about alternative ways to solve a problem .• When emphasizing the different ways to represent a problem .

Find Someone Who


Steps

1 . Assign students a trait to look for in other students . This may be something visual (for example, wearing the same color shirt as you) or something math-related (for example, solved the problem in the same way or found a different answer) .

2 . Students pair up and discuss their work .

3 . Once students are in pairs, you may ask them to check their work or give them a prompt to discuss .

4 . You may want to engage in a full-class discussion after pairs have had a chance to talk .

Use this routine:• To get students out of their seats and finding different partners than they normally might choose .• To have students analyze some portion of their peers’ math .• To begin a discussion about math .

Gallery Walk

Materials: writing paper, copy paper, pencils, sticky notes

Steps

1 . Assign students a problem or prompt . Students may work individually or in pairs or small groups .

2 . Communicate to students that you expect a written product that shows their thinking and how they solved the problem .

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3 . As students finish, display their work so they can easily view their peers’ work .

4 . Give each student a sticky note and have them add comments or questions about their peers’ work .

5 . Bring students together and engage in a discussion of what they noticed about how their peers completed the problem or responded to the prompt .

Use this routine:• When students solve a problem or prompt that has multiple ways of being represented or solved .• When completing a culminating activity for a lesson or unit .

My Favorite Mistake


Steps

1 . As students complete their work during SAP in pairs or independently, monitor their work .

2 . If a student or pair shows an interesting mistake or misconception, bring it to the class’s attention . Explain what’s interesting about the mistake and why it doesn’t work .

3 . Compliment the student or pair for working hard, trying something new, and teaching everyone in the class about the skill or concept .

4 . Celebrate that none of you ever have to make that mistake again!

Variations: • During the TIP, you may make a common mistake to see if students catch it, or catch it yourself and

emphasize to students why it is incorrect .• Consider pairing this routine with the Switcheroo award for students who make an interesting

mistake and then correct their thinking .

Use this routine:• To instill a growth mindset in students . • To show students that mistakes are a way to learn something .• To show a common error or misconception in a procedure or concept and make sure students know

how to avoid it .

On Your Mind


Steps

1 . Give students a topic, concept, or problem to examine .

2 . Ask: What’s on your mind?

3 . Accept student answers that include opinions, ideas, facts, questions, or confusion .

4 . Use student responses to determine students’ level of comfort with the topic, concept, or problem and to launch into a larger conversation about the topic, as necessary .

Use this routine:• During the ARK, especially when beginning a new unit or topic or exploring new concepts . • As a check for understanding when completing work on a concept .

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Q-ADE

Materials: Q-ADE anchor chart

It can be challenging for students to carry on conversations . Help students feel more confident engaging with their peers by using the mnemonic Q-ADE, which stands for “question, agree, disagree, and elaborate .” Use the Q-ADE anchor chart or the table below to encourage students as they engage in small-group or whole-class interactions .

QUESTION• Why did you choose to solve it that way?• Why did you choose to represent the problem

that way?• How did you do that?• What is a different way to do it?• Where did you find that information?• Does your answer make sense? Why or why

not?• Would this way work too? How might it work?

AGREE• I got the same answer!• I represented it the same way .• I like the way you solved it .• I got the same answer, but I got it a different

way .• I think that answer is reasonable .• I’m going to use that way next time!• That makes so much sense!• That’s easier than my way .

DISAGREE• I got a different answer .• I tried it in a different way .• I don’t think that answer makes sense .• What if . . . • Have you thought of trying . . . • I think this way might be easier . . .

ELABORATE• I want to add . . .• I found some more information . . .• Yes, and . . .• I made a connection to . . .• I think it would also work if . . .• I was surprised that . . .• Could we try it this way . . . • Could we show it this way . . .

Use this routine:• When having a whole-class discussion . • When setting up students to discuss their work in pairs or small groups . • When students are struggling with how to discuss their work or their ideas .

Consider keeping the Q-ADE anchor chart posted in your classroom .

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Show My Thinking

Materials: chart paper and marker, whiteboards and markers, manipulatives as appropriate for the problem

Steps

1 . Assign students a problem .

2 . Choose one student to be the Explainer . That student will narrate their thinking about how to solve the problem .

3 . The other students in the class illustrate the Explainer’s thinking using manipulatives or visual representations . Encourage students to use math visuals you have covered in class .

4 . The Explainer monitors the representations and decides whether or not they represent their thinking . The Explainer may then use manipulatives or visual representations to represent their own thinking .

Use this routine:• When comparing different ways of thinking about a problem .• When emphasizing the different ways to represent a problem .• To help students pay attention to a particular procedure .

Talking Heads Together

Materials: as appropriate for the problem

Steps

1 . Put students into small groups of three or four, assigning each student in the group a number, 1–4 (i .e ., each group should have a 1, a 2, etc .) .

2 . Give students a prompt, question, or problem . Provide groups with the necessary materials or allow groups to choose their own materials .

3 . At the end of the work time, choose a number . The student assigned that number in each group will share the ideas and solutions found by their group .

Use this routine:• When students need to practice cooperation and interpersonal skills .• When you want to hold all students accountable for group work .

Think-Pair-Share

Materials: none required; optional: copy paper or sticky notes, pencils

Steps

1 . Give students a prompt, question, or problem .

2 . Give students time to silently think about the prompt, question, or problem .

3 . Direct pairs to sit facing each other . Say: Knees facing, eyes facing.

4 . Partners take turns sharing their thoughts .

5 . Select some students to share their ideas with the whole class .

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Variations: • Have students share their partner’s thoughts .• Have students write ideas from their discussion on copy paper or sticky notes, then gather their

ideas to stimulate whole-class discussion .

Use this routine:• To begin a discussion .• To check for understanding .• To make sure that all students are engaged .• To allow all students to contribute .

Think-Pair-Square

Materials: none required; optional: writing paper, copy paper, pencils

Steps


2 . Give students time to silently think about the prompt, question, or problem .

3 . Direct pairs to sit facing each other . Say: Knees facing, eyes facing .

4 . Students take turns sharing their thoughts with each other .

5 . Pairs join with another pair and share their thoughts . These groups may create a poster that expresses their thoughts, when appropriate .

Variation: You may choose to perform this as a Write-Pair-Square .

Use this routine:• When you want students to share their thoughts but do not want to engage in a whole-class

discussion . • To check for understanding . • To allow all students to contribute .

Write-Pair-Share


Steps


2 . Give students time to silently write about the prompt, question, or problem .

3 . Direct pairs to sit facing each other . Say: Knees facing, eyes facing.

4 . Students take turns sharing their writing, either by switching papers or by reading them aloud to each other . Students may use sticky notes to add thoughts to their peers’ writing .

5 . Select some pairs to share their ideas with the whole class .

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Variations: • Complete the routine as a Draw-Pair-Share . Have students draw math representations and other

pictures to respond to the prompt, question, or problem .• Have students share their partner’s thoughts .• Have students write ideas from their discussion on copy paper or sticky notes, then gather their

ideas to stimulate whole-class discussion .

Use this routine:• To hold all students accountable for coming up with a written answer .• To check for understanding .• To begin a discussion about different ways of solving a problem or to explore different

perspectives on a mathematical idea .

Journaling Routines

Aha Moment

Materials: writing paper, copy paper, pencils

Steps

1 . Have students write about when something they were struggling to understand finally made sense to them . Have students share their new understanding, what helped them to understand, and how it made them feel to finally understand it .

2 . Students may use drawings, equations, or math representations to accompany their response .

3 . Students may share their responses in pairs, in small groups, or with the whole class .

Use this routine:• When some part of a concept or procedure seems to click into place for a student or a group .• As a check for understanding .• As the beginning of a larger discussion .

How Today Went


Steps

1 . Ask students to write about how they feel they did in class today . Tell students that this is about their opinions about their own level of understanding and feelings about the class, not about what they learned (although they may go into that if they wish) .

2 . Tell students they may keep their answers anonymous .

3 . Collect student responses to use as a formative assessment about how students are feeling about a skill or concept .

Use this routine:• After teaching a difficult procedure or concept .• To validate students’ emotions about learning .• As a self-assessment and check for understanding .

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Posters

Materials: chart paper, copy paper, pencils, crayons or markers

Steps

1 . Assign students a prompt, such as “Explain how you solved the problem .”

2 . Distribute materials .

3 . Have students create a poster to illustrate their ideas about the given prompt .

4 . You may display students’ work to recognize their hard work and expertise .

Use this routine:• When a student discovers, creates, or understands a new strategy .• As a motivational technique to help students acknowledge their own expertise .• As a check for understanding .

Solve Now

Materials: whiteboards and markers, or copy paper and pencils

Steps

1 . Give students a model problem that exemplifies the concept or procedure you have been exploring .

2 . Encourage students to solve the problem using any visual representations or algorithms you have been exploring in class .

3 . Provide feedback on students’ work that can serve as a model for their future work with this concept or procedure .

Use this routine:• To provide students with a model of a concept or procedure .• As a check for understanding .

The Going Got Tough


Steps

1 . Ask students to think about what they did during the class and identify something that was hard for them .

2 . Have students use drawings and math representations to describe how they responded to the problem .

3 . Invite students to share with the class how they got through the problem .

4 . Celebrate students’ perseverance .

Variation: Have students solve a difficult or effort-intensive problem to the point of frustration and circle where they got stuck .

Use this routine:• On days when students work especially hard .• On days when you are introducing difficult concepts or procedures .• As a formative assessment to show where student understanding is breaking down when using a

procedure .

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Two Strengths and a Shrug


Steps

1 . Ask students to reflect on the topic you are learning about in class .

2 . Students write about two parts of that topic that they feel are easy or going well or that they feel they have mastered (strengths) .

3 . Have students write about one part of that topic that they still have questions about or still find difficult (shrug) .

4 . Students may keep their responses anonymous or share them with a partner, small group, or the whole class .

Use this routine:• To assess students’ comfort with a topic .• To begin a discussion about a topic .• As a check for understanding .

What You Learned


Steps

1 . Ask students to write about what they learned during the class .

2 . Set parameters for how students should respond . Do they need to use complete sentences? Is it okay to use math representations? Can they solve a model problem to show what they learned? How much writing are they expected to provide? (Instead of a blank page, you may want to provide a box or a limited number of lines .)

Variations: • Students may present their responses orally . • Have students share their writing using the Write-Pair-Share routine .• Collect student journal entries to use for formative assessment .• Ask students to write about how they will use their learning in the future .• Ask students to connect their learning to other mathematics concepts .

Use this routine: • To hold all students accountable for their learning .• To allow students to explore their learning without limiting their focus .• As a check for understanding .

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Word Problems


Steps

1 . Display a word problem structure, such as part-part-whole or a comparison tape diagram .

2 . Students write a word problem that follows that structure .

3 . Students trade problems with a partner and use the word problem structure to solve their partner’s problem .

4 . Collect students’ word problems and solutions to display .

Use this routine:• During units on word problem structures • As a review of the problem structures students used previously .

Vocabulary Routines

Frayer Model

Materials: Frayer Template, pencils

Steps

1 . Distribute Frayer Templates .

2 . Guide students through filling out the template . Students should include definitions, facts/characteristics, examples, and non-examples .

3 . Have students keep their Frayer diagrams in a safe place for use or display during relevant lessons .

Use this routine:• When introducing new vocabulary .

Labels


Steps

1 . Show students a problem or a math representation that is already completed . Have students copy the problem or representation on a sheet of paper, or you can provide a photocopy to each student .

2 . Have students label all the parts of the problem or representation with relevant vocabulary . You may want to include a word box to make sure students label all relevant parts .

3 . Have students keep their labeled papers in a safe place for use or display during relevant lessons .


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Vocabulary Snowman

Materials: copy paper, pencils

Steps

1 . Choose a vocabulary word . Indicate the number of letters in the word using blank spaces .

2 . Distribute copy paper and pencils to students .

3 . Have students guess letters for the vocabulary word . If they guess a letter that is in the word, write that letter on the correct blank . If the letter is not in the word, write it below the word so students do not guess it again . If you choose, you can draw a part of a snowman when students make an incorrect guess . The game is over when the snowman is drawn completely .

4 . If a student thinks he or she knows the answer, the student should draw a visual representation of the vocabulary word and hold it up . Allow the student to explain the representation and what word it represents . If the student is correct, you may display the visual representation .

Variations: • Students may play this game in pairs . • The student who guesses the word and provides a visual representation gets to choose the next

vocabulary word .

Use this routine:• To reinforce vocabulary knowledge .• When introducing new vocabulary .

You Be the Artist

Materials: copy paper, pencils, crayons or markers

Steps

1 . Have students design a picture or math representation to accompany a math word .

2 . Display student drawings during relevant lessons .


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Check for Understanding Routines

Helpful Hint

Materials: sticky notes, pencils

Steps

1 . Distribute sticky notes to students .

2 . Ask them to provide a “helpful hint” to other students who are learning the procedure or concept they have been studying . The hint can be about what they should do, a useful visual representation, an idea about what to do when the problem is difficult, or words of encouragement .

3 . Display students’ helpful hints .

Use this routine:• To assess if students understand the concept or procedure .• To help students feel ownership and mastery over a concept or procedure .

Slates

Materials: whiteboards, markers

Steps

1 . Distribute whiteboards and markers to students .

2 . Give students a problem to complete independently or in pairs .

3 . After a specified amount of time, have students display their work .

4 . Make decisions about your teaching based on student responses .

Use this routine:• To assess if students understand a procedure .• To assess if students can use math representations effectively .

Sticky Notes

Materials: sticky notes, pencils

Steps

1 . Assign students a prompt or a problem or ask them a question . The prompt, problem, or question must be relatively simple to answer .

2 . Have students complete the problem or answer the question on a sticky note .

3 . Collect the sticky notes for analysis .

Variations: • Have students post the sticky notes and then examine each other’s work to provide different

perspectives on a problem, concept, or idea .• Assign students to use the sticky notes to comment on or ask questions about each other’s work .

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Use this routine: • To assess if students can quickly solve a simple problem .• To gather student opinions or ideas about a topic .• For students to analyze and comment on each other’s work .

Thumbs Up, Down, or Sideways


Steps

1 . Ask students a question that has three answer choices, such as understand/getting there/don’t understand .

2 . Have students give a thumbs-up for understand, a thumbs-sideways for getting there, and a thumbs-down for don’t understand .


Use this routine:• To add more subtlety than the Thumbs Up or Down routine allows . • When students are choosing one of three answers .

Thumbs Up or Down


Steps

1 . Ask students a question that has two answer choices, such as yes/no, true/false, or understand/not there yet .

2 . Have students give a thumbs-up for one response and a thumbs-down for the other .


Variation: Have students close their eyes before they give their responses .

Use this routine:• To determine whether students understand the instructions .• When students are choosing between one of two answers .

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Motivation Routines and Awards

Eponymous Strategies

Materials: chart paper, pencils, crayons or markers

Steps

1 . Praise the student for their ingenuity and name the strategy after the student . (For example, Tony uses counting up as a strategy to subtract . Tell the class that from now on, the class will refer to counting up to solve a subtraction problem as “The Tony Strategy for Subtraction .”)

2 . Invite the student to share their strategy with the class or use the Posters routine to illustrate the procedure or strategy .

3 . Consider giving the Inventor award to any student who creates a new procedure or strategy .

Use this routine:• When a student comes up with a unique or interesting way to solve a problem .

You Be the Teacher

Materials: optional: Featured Teacher badge/certificate (Teacher Resource Book, page 36)

Steps

1 . Give students a problem . Monitor student performance .

2 . If a student seems to have mastered the procedure you have taught or has used a strategy that you would like to highlight, invite the student to be the teacher and explain how to solve the problem . Be sure to only use this routine when the student has already gotten the correct answer and all their work is correct.

3 . Consider awarding the Featured Teacher award to any students who teach others .

Use this routine:• To highlight an interesting strategy or routine .• To show other students how to solve a problem through their peer’s work .• To highlight students’ own expertise .

Award Descriptions

You may provide students with badges or certificates to celebrate their receipt of the awards below .

Consistently PersistentGive this award to students on days when they work through especially hard problems and refuse to give up . You might pair this award with the journaling routine The Going Got Tough . Make sure to specifically acknowledge that recipients completed something challenging and that they worked very hard .

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Conversation StarterGive this award to students who are willing to be a part of the discussion . This award is for when students do an especially good job explaining their thinking, commenting on other’s thinking, asking questions, making compelling observations, or otherwise engaging in math discourse . Make sure to acknowledge the specific way in which the recipient helped others to be part of the conversation or enhanced other students’ understanding of math .

Featured TeacherGive this award to students who help others understand a concept or procedure . This award may be paired with the motivational routine You Be the Teacher, but you may also give it to students who share something interesting with the class during the ISS or who teach a partner something during Guided Practice . Make sure to acknowledge the specific skill, concept, or procedure the recipients taught to others and to highlight their expertise in this area .

Fluency FanaticGive this award to students who work especially hard during the Fluency section of the lesson or who master a difficult piece of arithmetic (for example, if a student memorized all the multiplication tables) . Make sure to acknowledge what the recipients learned, their interesting way of thinking about something, or the hard work they put into mastering this essential piece of mathematics .

I Like Your MathGive this award to students who completed a problem in an interesting way or were especially careful and precise in how they solved a problem . Make sure to specifically acknowledge the parts of the students’ math that you found elegant or unique .

Inventor Give this award to students who invent a new way of doing a problem or who try something new in class . This award can be paired with Eponymous Strategies . Make sure to specifically acknowledge that the recipients came up with something new or applied other math understanding to a new procedure .

Real-WorldGive this award to students who make a real-world connection to a math concept or representation . Emphasize that students who can make a deep and relevant connection between math and the real world must really understand the math under discussion .

SwitcherooGive this award to students who start out using one strategy, manipulative, drawing, or procedure and then switch to something new when what they started with didn’t work . Make sure to specifically acknowledge how hard the students worked and elicit what drove them to make the switch .

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Badges and Certificates

The following badges and certificates are included as an optional way to celebrate your students’ hard work and to serve as a motivational tool to inspire students to try hard, persevere, and explain their thinking . Some teachers hand these out formally during a brief ceremony, and they may be accompanied by a small reward or stickers . Students should be encouraged to take the awards home and share them with their families . As you hand out the awards, narrate the specific behaviors that led to the student receiving the award .

Each AchieveMath lesson suggests one or more awards you might want to give to students in specific situations, but you can give out an award to a student who shows the desired behavior at any time . Consider making multiple copies of each certificate and badge so that you are ready to award them to students during your lessons . You don’t need to give out an award every class—in fact, they should be rare enough that students feel special when they receive them . You may give an award to all students in your class or to one student who worked especially hard .

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32 Levels 3–5 Awards ©2021

has earned the

has earned the

has earned the

has earned the

Consistently Persistent

Award


Award


Award


Award

This certificate is awarded to

____________________________________________

In recognition of

____________________________________________

____________________________________________

____________________________ __________________ Signature Date

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Consistently PersistentConsistently PersistentAwardAward


has earned the

has earned the

has earned the

has earned the

Conversation Starter A

war

dConversation Starter A

war

dConversation Starte

r Aw

ardConversation Starte

r Aw

ard


____________________________________________

In recognition of

____________________________________________

____________________________________________

____________________________ __________________ Signature Date

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Conversation StarterConversation Starter AwardAward


has earned the

has earned the

has earned the

has earned the

Featured Teacher Aw

ard

Featured Teacher Aw

ard

Featured Teacher Aw

ard

Featured Teacher Aw

ard


____________________________________________

In recognition of

____________________________________________

____________________________________________

____________________________ __________________ Signature Date

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Featured TeacherFeatured Teacher AwardAward


has earned the

has earned the

has earned the

has earned theFluency Fanatic Awar

d Fluency Fanatic Award

Fluency Fanatic Award Fluency Fanatic Award


____________________________________________

In recognition of

____________________________________________

____________________________________________

____________________________ __________________ Signature Date

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Fluency FanaticFluency Fanatic AwardAward


has earned the

has earned the

has earned the

has earned theI Like Your Math Aw

ard I Like Your Math Aw

ard

I Like Your Math Aw

ard I Like Your Math Aw

ard


____________________________________________

In recognition of

____________________________________________

____________________________________________

____________________________ __________________ Signature Date

©2021

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I Like Your MathI Like Your Math AwardAward


has earned the

has earned the

has earned the

has earned the

Inventor AwardInventor Award

Inventor AwardInventor Award


____________________________________________

In recognition of

____________________________________________

____________________________________________

____________________________ __________________ Signature Date

©2021

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Inventor Inventor AwardAward


has earned the

has earned the

has earned the

has earned the

Real-World AwardReal-World Award

Real-World AwardReal-World Award


____________________________________________

In recognition of

____________________________________________

____________________________________________

____________________________ __________________ Signature Date

©2021

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Real-WorldReal-World AwardAward


has earned the

has earned the

has earned the

has earned the

Switcheroo AwardSwitcheroo Award

Switcheroo AwardSwitcheroo Award


____________________________________________

In recognition of

____________________________________________

____________________________________________

____________________________ __________________ Signature Date

©2021

47

SwitcherooSwitcheroo AwardAward


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49©2021 Levels 3–5 Resources

Resources Levels 3–5

Contents Addition Chart (10 x 10) . . . . . . . . . . . . . . . . 50

Addition Chart (20 x 20) . . . . . . . . . . . . . . . . 51

Hundred Chart . . . . . . . . . . . . . . . . . . . . . . . 52

Multiplication Table . . . . . . . . . . . . . . . . . . . 53

Coordinate Planes (First Quadrant) . . . . . . . 54

Digit Cards (0–9) . . . . . . . . . . . . . . . . . . . . . 55

Frayer Template . . . . . . . . . . . . . . . . . . . . . . 57

Number Bonds . . . . . . . . . . . . . . . . . . . . . . 58

Number Triangles . . . . . . . . . . . . . . . . . . . . . 59

Open Number Lines . . . . . . . . . . . . . . . . . . 60

Number Lines (0–20) . . . . . . . . . . . . . . . . . . 61

Fraction Number Lines . . . . . . . . . . . . . . . . 62

Double Number Lines . . . . . . . . . . . . . . . . . 63

Place Value Charts (Hundreds) . . . . . . . . . . . 64

Place Value Charts (Thousands) . . . . . . . . . . 65

Place Value Charts (Millions) . . . . . . . . . . . . 66

Decimal Place Value Charts (Hundredths) . . 67

Decimal Place Value Charts (Thousandths) . 68

Place Value Mat (Hundreds) . . . . . . . . . . . . . 69

Place Value Mat (Thousands) . . . . . . . . . . . . 70

Place Value Mat (Millions) . . . . . . . . . . . . . . 71

Decimal Place Value Mat (Hundredths) . . 72

Decimal Place Value Mat (Thousandths) . . 73

10-Frames . . . . . . . . . . . . . . . . . . . . . . . . . 74

Tape Diagrams . . . . . . . . . . . . . . . . . . . . . 75

Part-Part-Whole Tape Diagrams . . . . . . . . 76

Comparison Tape Diagrams . . . . . . . . . . . 77

Fraction Strips . . . . . . . . . . . . . . . . . . . . . . 78

Ratio Tables . . . . . . . . . . . . . . . . . . . . . . . . 79

1-Dot Dominoes . . . . . . . . . . . . . . . . . . . . 80

2-Dot Dominoes . . . . . . . . . . . . . . . . . . . . 81

3-Dot Dominoes . . . . . . . . . . . . . . . . . . . . 82

4-Dot Dominoes . . . . . . . . . . . . . . . . . . . . 83

5-Dot Dominoes . . . . . . . . . . . . . . . . . . . . 84

6-Dot Dominoes . . . . . . . . . . . . . . . . . . . . 85

7-Dot Dominoes . . . . . . . . . . . . . . . . . . . . 86

8-Dot Dominoes . . . . . . . . . . . . . . . . . . . . 87

9-Dot Dominoes . . . . . . . . . . . . . . . . . . . . 88

10-Dot Dominoes . . . . . . . . . . . . . . . . . . . 89

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Addition Chart (10 x 10)

+ 1 2 3 4 5 6 7 8 9 10

1 2 3 4 5 6 7 8 9 10 11

2 3 4 5 6 7 8 9 10 11 12

3 4 5 6 7 8 9 10 11 12 13

4 5 6 7 8 9 10 11 12 13 14

5 6 7 8 9 10 11 12 13 14 15

6 7 8 9 10 11 12 13 14 15 16

7 8 9 10 11 12 13 14 15 16 17

8 9 10 11 12 13 14 15 16 17 18

9 10 11 12 13 14 15 16 17 18 19

10 11 12 13 14 15 16 17 18 19 20

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Addition Chart (20 x 20)+ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34

15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35

16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37

18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38

19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39

20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

52 Levels 3–5 Resources ©2021

Hundred Chart

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100

53©

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Multiplication Table

× 1 2 3 4 5 6 7 8 9 10 11 12

1 1 2 3 4 5 6 7 8 9 10 11 12

2 2 4 6 8 10 12 14 16 18 20 22 24

3 3 6 9 12 15 18 21 24 27 30 33 36

4 4 8 12 16 20 24 28 32 36 40 44 48

5 5 10 15 20 25 30 35 40 45 50 55 60

6 6 12 18 24 30 36 42 48 54 60 66 72

7 7 14 21 28 35 42 49 56 63 70 77 84

8 8 16 24 32 40 48 56 64 72 80 88 96

9 9 18 27 36 45 54 63 72 81 90 99 108

10 10 20 30 40 50 60 70 80 90 100 110 120

11 11 22 33 44 55 66 77 88 99 110 121 132

12 12 24 36 48 60 72 84 96 108 120 132 144

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Coordinate Planes (First Quadrant)

y

x

y

x


Digit Cards (0–5)

0 1 2

3 4 5


Digit Cards (6–9)

6 7

8 9

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Frayer TemplateDefinition Facts/Characteristics

Examples Non-examples


Number Bonds


Number Triangles

÷ ÷

×

÷ ÷

×

÷ ÷

×

÷ ÷

×

÷ ÷

×

÷ ÷

×

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Open Number Lines

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Number Lines (0–20)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

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0 1

Fraction Number Lines

0 1


Double Number Lines

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Place Value Charts (Hundreds)

Hundreds Tens Ones

Hundreds Tens Ones

Hundreds Tens Ones

Hundreds Tens Ones


Place Value Charts (Thousands)Thousands Ones

Hundred Thousands

Ten Thousands Thousands Hundreds Tens Ones

Thousands OnesHundred

ThousandsTen

Thousands Thousands Hundreds Tens Ones

Thousands OnesHundred

ThousandsTen


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Place Value Charts (Millions)

Millions Thousands OnesHundred Millions

Ten Millions Millions Hundred

ThousandsTen


Millions Thousands OnesHundred Millions


ThousandsTen



Decimal Place Value Charts (Hundredths)

Tens Ones Tenths Hundredths

.

.


.

.


.

.


Decimal Place Value Charts (Thousandths)

Ones Tenths Hundredths Thousandths

.

.


.

.


.

.

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Place Value Mat (Hundreds)

Hundreds Tens Ones

70Le

vels

3–5

Res

ourc

es

©20

21

Place Value Mat (Thousands)Thousands Ones

Hundred Thousands Ten Thousands Thousands Hundreds Tens Ones

71©

2021 Levels 3–5 R

esources

Place Value Mat (Millions)Millions Thousands Ones

Hundred Millions


ThousandsTen


72Le

vels

3–5

Res

ourc

es

©20

21

Decimal Place Value Mat (Hundredths)Tens Ones Tenths Hundredths

.

.

73©

2021 Levels 3–5 R

esources

Decimal Place Value Mat (Thousandths)Ones Tenths Hundredths Thousandths

.

.


10-Frames


Tape Diagrams


Part-Part-Whole Tape Diagrams


Comparison Tape Diagrams


Fraction Strips

18

18

18

18

18

18

18

18

14

14

14

14

17

17

17

17

17

17

17

13

13

13

110

110

110

110

110

110

110

110

110

110

111

111

111

111

111

111

111

111

111

111

111

112

112

112

112

112

112

112

112

112

112

112

112

16

16

16

16

16

16

12

12

19

19

19

19

19

19

19

19

19

15

15

15

15

15

1


(x) (y)

(x) (y)

(x) (y)

(x) (y)

Ratio Tables


1-Dot Dominoes


2-Dot Dominoes


3-Dot Dominoes


4-Dot Dominoes


5-Dot Dominoes


6-Dot Dominoes


7-Dot Dominoes


8-Dot Dominoes


9-Dot Dominoes


10-Dot Dominoes

Date post:	12-Dec-2021
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