[ Classroom playbook ]

The Middle School
Classroom Playbook.

Practical routines for the moments that matter: starting a lesson, getting students talking, investigating an idea, and checking what they understand.

Find a routine
40 adaptable activities5–30 minutesMath · Science · Any subject
NEW TO THE CLASSROOM / START HERE

A simple first-week path

Try one routine at a time. Practice the directions, notice what students do, and reuse the routines that help your class think.

DAY 01 · START

Notice & Wonder

Show 0.25 × 48. Give quiet thinking time, then collect two ways to reason about it.

DAY 02 · TALK

Partner Teach

Model a 30-second explanation, then let both partners practice speaking and listening.

DAY 03 · EXPLORE

Notice, Wonder, Explain

Show a plant leaning toward a window. Separate observations from possible explanations.

DAY 04 · CHECK

One-Minute Exit Check

Ask one question tied to your lesson. Sort responses to plan the next opening.

Day 5: Repeat the routine that gave you the clearest evidence of student thinking. Keep the directions familiar and change only the lesson prompt.

GRADE 7 · MONDAY / WEDNESDAY / FRIDAY

Build number sense, one routine at a time.

19 low-prep routines with dice, dominoes, and playing cards. Help students connect fractions, decimals, percents, and number relationships through prediction, partner play, and explanation.

02minutes to model
08minutes to explore
03minutes to discuss
02minutes to reflect
Plan your Monday / Wednesday / Friday routines

Use these suggested day groupings flexibly. Repeat a routine with a new target or select by skill; this is a routine bank, not a fixed calendar.

Monday

Wednesday

Friday

Materials, teacher moves, and skill guide

Prepare: 2–3 standard dice per pair; 8–15 dominoes per pair; or playing cards with face cards and jokers removed, Ace = 1. Follow each guide’s rules for zero tiles, doubles, and repeated card values.

Core habit: Predict or estimate first, explain the reasoning, then calculate or convert. Use calculators to verify after estimation.

  • Keep 1/4 = 25%, 1/2 = 50%, 3/4 = 75%, and 1 = 100% visible early in the year.
  • Ask “How do you know?” before accepting an answer. Welcome multiple mathematically valid strategies.
  • Keep recording brief: one or two worked rounds and a reflection.
Fractions & equivalence

Fraction Flip • Domino Match-Up • Make My Match • Which One Doesn’t Belong? • Capture the Whole

Decimal place value & magnitude

Domino Decimal Build • Domino Number Line Race • Between Two

Percent benchmarks & conversions

Percent Dice Challenge • Target 1 • Beat the Dealer • Roll & Scale

Percent of a quantity

Percent of a Roll • Dice Discount Dash

Percent change

Domino Percent Change

Ordering & distance

Fraction War: Closest Pair • Domino Ratio Ladder • Between Two

Additive complements & totals

Fraction Blackjack • Capture the Whole

Flexible construction & reasoning

Roll, Build, Prove • Make My Match • Which One Doesn’t Belong?

Reusable student reflection prompts

Record the routine and date, then select a prompt for a quick exit reflection.

1. What number relationship did you notice today?

2. Which strategy was most efficient for you? Why?

3. What did you estimate or predict before calculating?

4. Write one fraction, decimal, and percent that represent the same quantity.

5. What is one mistake you corrected or one idea that became clearer today?

THE ACTIVITY LIBRARY

Find your next activity

Browse by purpose, or narrow the list to fit your lesson.

40 activities
Need a routine for today?

Try a quick starting point, then open a guide for steps, materials, and a ready-to-say prompt.

Choose a pathway, not just an activity

Use these shortcuts when you know the classroom problem you are trying to solve but do not want to sort through forty routines.

REFINE THE COLLECTION
NUMBER SENSE · MONDAY22

Fraction Flip

Build, convert, and compare fractions with playing cards.

10-12 minCardsGrade 7
NUMBER SENSE · WEDNESDAY23

Domino Decimal Build

Use domino digits to build and reason about decimal place value.

10-15 minDominoesGrade 7
NUMBER SENSE · FRIDAY24

Percent Dice Challenge

Roll fractions, convert them, and classify them by benchmark size.

12-15 minDiceGrade 7
NUMBER SENSE · MONDAY25

Target 1

Choose two of three dice to build a fraction closest to a percent target.

12-15 minDiceGrade 7
NUMBER SENSE · MONDAY26

Fraction Blackjack

Add tenths and decide when to hold before exceeding one whole.

12-15 minCardsGrade 7
NUMBER SENSE · WEDNESDAY27

Domino Number Line Race

Place domino fractions on a benchmark number line and defend the position.

12-15 minDominoesGrade 7
NUMBER SENSE · FRIDAY28

Domino Match-Up

Find equivalent domino fractions and build value families.

12-15 minDominoesGrade 7
NUMBER SENSE · MONDAY29

Roll, Build, Prove

Use three dice to construct a fraction inside a target percent range.

12-15 minDiceGrade 7
NUMBER SENSE · WEDNESDAY30

Make My Match

Start from a percent target and build a matching fraction with cards.

12-15 minCardsGrade 7
NUMBER SENSE · FRIDAY31

Fraction War: Closest Pair

Arrange four cards into two fractions whose values are as close as possible.

12-15 minCardsGrade 7
NUMBER SENSE · MONDAY32

Beat the Dealer

Use dice to build a fraction that beats a dealer decimal.

12-15 minDiceGrade 7
NUMBER SENSE · WEDNESDAY33

Percent of a Roll

Use benchmark percents to find a part of a rolled quantity.

12-15 minDiceGrade 7
NUMBER SENSE · FRIDAY34

Domino Percent Change

Treat the two sides of a domino as original and new values.

12-15 minDominoesGrade 7
NUMBER SENSE · MONDAY35

Dice Discount Dash

Use benchmark percents to find discounts and sale prices.

12-15 minDiceGrade 7
NUMBER SENSE · WEDNESDAY36

Roll & Scale

Scale one quantity and watch fraction, decimal, and percent forms change together.

12-15 minDiceGrade 7
NUMBER SENSE · FRIDAY37

Between Two

Use playing cards to create rational numbers inside a given interval.

12-15 minCardsGrade 7
NUMBER SENSE · MONDAY38

Which One Doesn’t Belong? — Number Sense

Analyze four representations and defend a mathematical classification.

12-15 minDiceGrade 7
NUMBER SENSE · WEDNESDAY39

Domino Ratio Ladder

Build a growing least-to-greatest ladder from domino fractions.

12-15 minDominoesGrade 7
NUMBER SENSE · FRIDAY40

Capture the Whole

Find the missing complement needed to reach 1, 1.00, or 100%.

12-15 minCardsGrade 7
HANDS-ON MATH01

Think, Talk, Rotate, Record

Make group thinking visible while students compare and improve strategies.

25 MINMathLow prep
START CLASS02

Number Talk: Notice & Wonder

Invite multiple mental strategies before formal instruction.

10 MINMathNo prep
HANDS-ON MATH03

Dice: Fraction, Decimal, Percent

Build flexible connections among equivalent forms.

12 MINMathLow prep
HANDS-ON MATH04

Domino Target Number

Use operations and number sense to reach a shared target.

12 MINMathLow prep
HANDS-ON MATH05

Integer Card Challenge

Practice signed-number reasoning with quick comparisons.

12 MINMathLow prep
START CLASS06

Which One Doesn’t Belong?

Open a lesson with classification and more than one defensible answer.

8 MINAny subjectLow prep
CHECK UNDERSTANDING07

Error Detective

Turn a common mistake into a precise explanation.

15 MINMathLow prep
SCIENCE INQUIRY08

Phenomenon: Notice, Wonder, Explain

Launch an investigation from observation rather than a definition.

12 MINScienceLow prep
SCIENCE INQUIRY09

Variable Sort

Practice identifying what changes, what is measured, and what stays constant.

15 MINScienceLow prep
SCIENCE INQUIRY10

Observation Stations

Slow down looking and gather precise evidence.

20 MINScienceSome prep
CHECK UNDERSTANDING11

Claim–Evidence–Reasoning Quickwrite

Help students connect an answer to evidence and a clear explanation.

12 MINAny subjectNo prep
SCIENCE INQUIRY12

Build, Revise, Share a Model

Make student thinking visible and revisable.

25 MINScienceLow prep
START CLASS13

Vocabulary: Sketch & Explain

Move beyond memorizing a definition.

10 MINAny subjectNo prep
DISCUSSION14

30-Second Partner Teach

Give every student a low-stakes chance to explain an idea aloud.

8 MINAny subjectNo prep
DISCUSSION15

Four Corners with Evidence

Turn a choice into an evidence-based conversation.

15 MINAny subjectLow prep
DISCUSSION16

Question Carousel

Collect ideas across groups without repeating a whole-class share-out.

15 MINAny subjectSome prep
CHECK UNDERSTANDING17

One-Minute Exit Check

Get a quick signal for the next lesson.

5 MINAny subjectNo prep
CHECK UNDERSTANDING18

Confidence Sort & Next Step

Pair self-assessment with evidence from actual work.

8 MINAny subjectNo prep
CHECK UNDERSTANDING19

Two Strengths, One Next Step

Make peer feedback specific enough to use.

10 MINAny subjectNo prep
CREATE & SHARE20

Student Video Storyboard

Plan a short explanation before anyone starts recording.

30 MINAny subjectLow prep
CREATE & SHARE21

Source Check in Pairs

Practice comparing evidence and source context before sharing a claim.

15 MINAny subjectLow prep

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Keep building your classroom system

The playbook works best when routines connect to the other tools you already use for grouping, English learner support, and independent technology practice.

English Learner SupportScaffolds, language supports, and proven EL strategies.Technology & Learning ResourcesFind student-independent and teacher-setup digital tools.Teacher ResourcesReturn to the full collection of classroom tools and resources.

Adapt the prompts, timing, materials, and safety practices to the needs of your own class. Icons are CC0 via SVG Repo.

NUMBER SENSE · MONDAY · ACTIVITY 22

Fraction Flip

TEACHER GUIDE

Build, convert, and compare fractions with playing cards.

SAY TO STUDENTS

Each player flips two cards and builds a fraction. Convert the fraction to a decimal and percent. Compare both values; the greater value earns 1 point. Play 5-8 rounds and explain at least one comparison without relying only on decimal conversion.

BEFORE YOU PLAY

Use exact fractions to compare when possible. Mark rounded decimals and percents as approximations. Agree on tie and scoring rules before play.

OBJECTIVE

I can create fractions and compare their values using fraction, decimal, and percent forms.

Setup

  • Remove face cards and jokers; Ace = 1.
  • Each pair gets 20-30 number cards.
  • The first card is the numerator and the second is the denominator.

Teacher Directions

  1. Model a draw of 3 and 4: 3/4 = 0.75 = 75%.
  2. Show how two students compare their fractions and justify which is greater.
  3. Keep improper fractions when they occur so students see values above 1 and 100%.
  4. After several rounds, ask students to find how much greater the winning value is.

Student Directions

  1. Each player flips two cards and builds a fraction.
  2. Convert the fraction to a decimal and percent.
  3. Compare both values; the greater value earns 1 point.
  4. Play 5-8 rounds and explain at least one comparison without relying only on decimal conversion.

Worked Example

EXAMPLE: 2/5 vs. 3/4

2/5 = 0.40 = 40%. 3/4 = 0.75 = 75%. The second fraction is greater. The difference is 35 percentage points.

Teacher Questions

  • How can you tell which fraction is larger without converting?
  • What happens to the value when the denominator changes but the numerator stays fixed?
  • Can a percent be greater than 100%? Give an example.

Support & Challenge Options

SUPPORT

Provide a benchmark card with 1/4 = 25%, 1/2 = 50%, 3/4 = 75%, and 1 = 100%. Let students compare to a benchmark before converting.

CHALLENGE

Require students to state the difference between the two values in percentage points and explain whether their estimate was reasonable.

EXTENSION

Allow improper fractions and ask students to order three generated values from least to greatest before converting.

Suggested Timing

MinutesWhat Happens
2Model one round
7Partner play
2Discuss strategies
1Reflection

Student Reflection

  1. Which form was easiest for you to compare: fraction, decimal, or percent? Why?
  2. What strategy helped you decide which value was larger?
  3. What connection did you notice between fractions, decimals, and percents?
NUMBER SENSE · WEDNESDAY · ACTIVITY 23

Domino Decimal Build

TEACHER GUIDE

Use domino digits to build and reason about decimal place value.

SAY TO STUDENTS

Draw two dominoes and record the four digits. Build the greatest possible decimal under 10. Build the smallest possible decimal under 10. Use the same digits to make a number as close as possible to a teacher-given target. Explain which place value mattered most.

BEFORE YOU PLAY

Use exact fractions to compare when possible. Mark rounded decimals and percents as approximations. Agree on tie and scoring rules before play.

OBJECTIVE

I can use digits to create decimals and explain the value of each digit.

Setup

  • Give each pair several dominoes.
  • Students draw two dominoes and use the four visible digits to build decimals.
  • Use a consistent format such as one digit before the decimal and three after it.

Teacher Directions

  1. Model digits 6, 2, 4, 5 and build the greatest decimal less than 10: 6.542.
  2. Ask students to justify why each digit belongs in its place.
  3. Repeat with the smallest decimal and then a target-number challenge.
  4. Connect the tenths digit to a fraction over 10 and to a percent.

Student Directions

  1. Draw two dominoes and record the four digits.
  2. Build the greatest possible decimal under 10.
  3. Build the smallest possible decimal under 10.
  4. Use the same digits to make a number as close as possible to a teacher-given target.
  5. Explain which place value mattered most.

Worked Example

EXAMPLE: Digits 6, 2, 4, 5

Greatest: 6.542. Smallest: 2.456. For target 5, 5.246 is 0.246 away. The 2 in the tenths place represents 2/10 = 0.2 = 20%, but the entire number 5.246 is not 20%.

Teacher Questions

  • Which place value matters most when comparing decimals?
  • Why does changing the tenths digit usually matter more than changing the thousandths digit?
  • How can you tell which decimal is larger without reading every digit?

Support & Challenge Options

SUPPORT

Use only three digits at first and provide a place-value chart labeled ones, tenths, hundredths, and thousandths.

CHALLENGE

Give interval constraints such as “between 3.5 and 4” or “greater than 6.2 but less than 6.5.”

EXTENSION

Require students to build two decimals whose difference is less than 0.1 and prove the difference.

Suggested Timing

MinutesWhat Happens
2Model place-value reasoning
7Build and compare
3Target challenge
2Reflection

Student Reflection

  1. Which digit had the greatest effect on your number? Explain.
  2. What strategy did you use to get close to the target number?
  3. What did today’s activity help you understand about decimal place value?
NUMBER SENSE · FRIDAY · ACTIVITY 24

Percent Dice Challenge

TEACHER GUIDE

Roll fractions, convert them, and classify them by benchmark size.

SAY TO STUDENTS

Roll two dice and build a fraction. Convert to decimal and percent. Place the value in a benchmark category and justify the choice. Compare with your partner and score for correct representations and reasoning.

BEFORE YOU PLAY

Equal dice make 1 = 100%. The categories use exact boundaries; round only for reporting, not to decide a category. Agree how reasoning earns points before starting.

OBJECTIVE

I can represent the same number as a fraction, decimal, and percent and estimate its size using benchmarks.

Setup

  • Each pair gets two dice.
  • Use the smaller roll as numerator and larger roll as denominator.
  • Post benchmark regions: near 0, near 1/2, near 1.
CategoryRange
Near 00% ≤ value < 25%
Near 1/225% ≤ value < 75%
Near 175% ≤ value ≤ 100%

Teacher Directions

  1. Model a roll of 3 and 6: 3/6 = 1/2 = 0.5 = 50%.
  2. Classify the value by benchmark and explain the reasoning.
  3. Have students compare who is closer to 50% or 100% in later rounds.

Student Directions

  1. Roll two dice and build a fraction.
  2. Convert to decimal and percent.
  3. Place the value in a benchmark category and justify the choice.
  4. Compare with your partner and score for correct representations and reasoning.

Worked Example

EXAMPLE: 4 and 5

4/5 = 0.8 = 80%, so it is near 1. A student can justify this because 80% is only 20 percentage points from 100%.

Teacher Questions

  • What fractions immediately make you think of 50%?
  • How can you estimate a percent without calculating it exactly?
  • What happens when the numerator is close to the denominator?

Support & Challenge Options

SUPPORT

Keep a visible chart of 1/4, 1/2, 3/4, and 1 in all three forms.

CHALLENGE

Instead of simply comparing values, award the point to the fraction closest to a target benchmark.

EXTENSION

Ask students to justify a comparison before converting and then verify with calculations.

Suggested Timing

MinutesWhat Happens
2Model benchmark classification
8Partner rounds
3Target comparison
2Reflection

Student Reflection

  1. Name one fraction you now recognize quickly as a percent.
  2. How can 0%, 50%, and 100% help you estimate?
  3. Which conversion is hardest for you and why?
NUMBER SENSE · MONDAY · ACTIVITY 25

Target 1

TEACHER GUIDE

Choose two of three dice to build a fraction closest to a percent target.

SAY TO STUDENTS

Roll three dice. Choose two dice and build a fraction closest to the announced target. Convert the fraction to a decimal and percent. Find how many percentage points away it is from the target. Compare with your partner; closest value earns the point.

BEFORE YOU PLAY

Use exact fractions to compare when possible. Mark rounded decimals and percents as approximations. Agree on tie and scoring rules before play.

OBJECTIVE

I can build a fraction close to a target and use fractions, decimals, and percents to justify how close it is.

Setup

  • Post targets 25%, 50%, and 75%.
  • Students roll three dice and choose any two to form a fraction.
  • They may choose which number is numerator and denominator.

Teacher Directions

  1. Model a roll of 2, 3, 5 for a 50% target.
  2. Compare 2/5 = 40%, 3/5 = 60%, and 2/3 ≈ 66.7%.
  3. Show that more than one choice can be equally close to the target.
  4. Require a prediction before calculation.

Student Directions

  1. Roll three dice.
  2. Choose two dice and build a fraction closest to the announced target.
  3. Convert the fraction to a decimal and percent.
  4. Find how many percentage points away it is from the target.
  5. Compare with your partner; closest value earns the point.

Worked Example

EXAMPLE: Target 75%; dice 2, 4, 5

4/5 = 0.80 = 80%, only 5 percentage points from 75%. 2/4 = 50%, which is 25 points away. 4/5 is the better choice.

Teacher Questions

  • Before calculating, which fraction looks closest?
  • If the numerator is about half the denominator, what percent should you expect?
  • Can two different fractions be equally close to a target?

Support & Challenge Options

SUPPORT

Provide benchmark cards for 25%, 50%, and 75% and sentence frames for predictions.

CHALLENGE

Add a 60% target, where students may find exact hits such as 3/5.

EXTENSION

Require students to prove that no other fraction from the same roll is closer.

Suggested Timing

MinutesWhat Happens
2Model one roll
8Partner target rounds
360% challenge
2Reflection

Student Reflection

  1. What did you look at first when choosing numerator and denominator?
  2. How did benchmark fractions help you today?
  3. What relationship did you notice among fractions, decimals, and percents?
NUMBER SENSE · MONDAY · ACTIVITY 26

Fraction Blackjack

TEACHER GUIDE

Add tenths and decide when to hold before exceeding one whole.

SAY TO STUDENTS

Draw two cards and add their tenths values. Record the total as a fraction, decimal, and percent. Choose HOLD or DRAW. Continue until you hold or exceed the target. Closest total without going over wins.

BEFORE YOU PLAY

If the opening two cards already exceed the target, that hand busts. If all players bust, start a new hand. Tied winning totals share the win.

OBJECTIVE

I can compare and combine fractions, decimals, and percents to get as close as possible to a target value without going over.

Setup

  • Remove face cards and jokers; Ace = 1.
  • Each card represents tenths: 3 means 3/10 = 0.30 = 30%.
  • Target is 1 whole = 1.00 = 100%.

Teacher Directions

  1. Deal two cards and model the starting total.
  2. Students choose HOLD or DRAW.
  3. If a new card pushes the total above 100%, the player busts.
  4. After the basic game, change the target to 150%.

Student Directions

  1. Draw two cards and add their tenths values.
  2. Record the total as a fraction, decimal, and percent.
  3. Choose HOLD or DRAW.
  4. Continue until you hold or exceed the target.
  5. Closest total without going over wins.

Worked Example

EXAMPLE: 3 + 4 + 2

3/10 + 4/10 = 7/10 = 70%. Drawing a 2 gives 9/10 = 90%. Drawing a 5 instead would make 12/10 = 120%, which busts a 100% target.

Teacher Questions

  • Should you draw another card? Why?
  • What cards are safe when you are already at 80%?
  • How does the strategy change when the target becomes 150%?

Support & Challenge Options

SUPPORT

Use a visible tenths chart from 1/10 through 10/10.

CHALLENGE

Require students to identify all safe draw values before deciding whether to draw.

EXTENSION

Use twentieths instead of tenths or a 125% target.

Suggested Timing

MinutesWhat Happens
2Model
2Whole-class practice
7Partner play
2150% round
2Reflection

Student Reflection

  1. When did you decide it was better to hold? Explain.
  2. Show one fraction-decimal-percent relationship from your game.
  3. If you are at 70%, which cards are safe when the target is 100%?
NUMBER SENSE · WEDNESDAY · ACTIVITY 27

Domino Number Line Race

TEACHER GUIDE

Place domino fractions on a benchmark number line and defend the position.

SAY TO STUDENTS

Draw one domino and create a proper fraction. Estimate which benchmark interval contains it. Convert to decimal and percent. Place the value on a number line. Compare with your partner and justify which is greater or closer to a target benchmark.

BEFORE YOU PLAY

Set aside doubles in proper-fraction rounds: a nonzero double equals 1, which is not a proper fraction. Keep zero tiles aside for these rounds.

OBJECTIVE

I can represent a fraction as a decimal and percent and use benchmark numbers to determine where it belongs on a number line.

Setup

  • Each domino becomes a proper fraction using smaller number over larger number.
  • Set aside dominoes with zero for the regular rounds.
  • Display a 0%-25%-50%-75% ≤ value ≤ 100% number line.

Teacher Directions

  1. Model 2/5 and estimate its location before calculating.
  2. Convert to 0.40 = 40% and place it between 25% and 50%.
  3. Have students compare partner values and later play closest-to-benchmark rounds.

Student Directions

  1. Draw one domino and create a proper fraction.
  2. Estimate which benchmark interval contains it.
  3. Convert to decimal and percent.
  4. Place the value on a number line.
  5. Compare with your partner and justify which is greater or closer to a target benchmark.

Worked Example

EXAMPLE: 2/3 vs. 3/5

2/3 ≈ 66.7%; 3/5 = 60%. Both lie between 50% and 75%, but 2/3 is greater.

Teacher Questions

  • What benchmark helped you most?
  • How can you tell whether a fraction is above or below 50% without dividing?
  • Why can improper fractions lie beyond 100%?

Support & Challenge Options

SUPPORT

Use benchmark cards and sentence frames such as “My fraction is between ___ and ___ because…”.

CHALLENGE

Allow students to rotate dominoes and include improper fractions on a 0%-200% number line.

EXTENSION

Draw three dominoes and order them least to greatest before calculating decimals.

Suggested Timing

MinutesWhat Happens
2Model 2/5
6Number-line race
3Closest-to-benchmark
2Three-domino challenge
2Reflection

Student Reflection

  1. How did 25%, 50%, 75%, and 100% help you place an unfamiliar fraction?
  2. How can you tell if a fraction is above or below 50%?
  3. Show one fraction, decimal, and percent from today.
NUMBER SENSE · FRIDAY · ACTIVITY 28

Domino Match-Up

TEACHER GUIDE

Find equivalent domino fractions and build value families.

SAY TO STUDENTS

Draw four dominoes each. Write the fraction represented by each. Simplify when possible. Find equivalent pairs or families. Prove each match with fraction, decimal, and percent reasoning.

BEFORE YOU PLAY

Remove the 0|0 tile. Zero may be the numerator, never the denominator; all 0/n values with n > 0 equal zero. Nonzero doubles equal 1.

OBJECTIVE

I can identify equivalent fractions and explain how different fractions, decimals, and percents can represent the same quantity.

Setup

  • Each pair draws several dominoes face up.
  • Use smaller number over larger number.
  • Look for different dominoes that represent equal quantities.

Teacher Directions

  1. Model 1/2 and 2/4 as an equivalent pair.
  2. Contrast with a non-match such as 2/3 and 3/4.
  3. Require students to prove matches by simplifying or converting.
  4. Extend to equivalent “families” of more than two representations.

Student Directions

  1. Draw four dominoes each.
  2. Write the fraction represented by each.
  3. Simplify when possible.
  4. Find equivalent pairs or families.
  5. Prove each match with fraction, decimal, and percent reasoning.

Worked Example

EXAMPLE: 1/2, 2/4, 3/6

1/2 = 2/4 = 3/6 = 0.50 = 50%. Different fractions can occupy the same location because they represent the same quantity.

Teacher Questions

  • How can two fractions with different numbers represent the same amount?
  • What is the fastest way to test equivalence?
  • How do equivalent fractions appear as decimals and percents?

Support & Challenge Options

SUPPORT

Use benchmark families such as 25%, 50%, 75%, and 100%.

CHALLENGE

No division: students must prove equivalence by simplifying or using common factors.

EXTENSION

Create a “three matches and one impostor” puzzle for another pair.

Suggested Timing

MinutesWhat Happens
2Model equivalence
6Partner match-up
3Build a family
2Impostor challenge
2Reflection

Student Reflection

  1. How can two different fractions still represent the same quantity?
  2. Give three representations of one value.
  3. Which strategy helped you find equivalents fastest?
NUMBER SENSE · MONDAY · ACTIVITY 29

Roll, Build, Prove

TEACHER GUIDE

Use three dice to construct a fraction inside a target percent range.

SAY TO STUDENTS

Roll three dice. Listen for the target range. Choose two dice and build a fraction. Predict whether it fits the range. Convert to decimal and percent to prove it. Find a second valid fraction for a bonus point.

BEFORE YOU PLAY

Use two distinct dice, even if they show the same number. If no fraction fits, show why and reroll. State allowed operations for the all-three-dice challenge.

OBJECTIVE

I can use number relationships to create equivalent fractions, decimals, and percents and explain why they represent the same quantity.

Setup

  • Post nonoverlapping target ranges: below 25%; at least 25% but below 50%; at least 50% but below 75%; and 75% or greater. State any additional upper boundary before play.
  • Students roll three dice and choose two to form a fraction.
  • Not all dice must be used in the basic round.

Teacher Directions

  1. Model 2, 3, 5 with a 50%-75% target.
  2. Show that both 2/3 and 3/5 fit.
  3. Require prediction before calculation.
  4. Discuss why multiple answers may be correct.

Student Directions

  1. Roll three dice.
  2. Listen for the target range.
  3. Choose two dice and build a fraction.
  4. Predict whether it fits the range.
  5. Convert to decimal and percent to prove it.
  6. Find a second valid fraction for a bonus point.

Worked Example

EXAMPLE: Dice 1, 4, 5; target 75%-100%

4/5 = 0.80 = 80%, so it fits. 1/4 = 25% and 1/5 = 20% do not.

Teacher Questions

  • What did you notice first about numerator and denominator?
  • How can you estimate whether a fraction is above 50%?
  • Can one roll produce multiple correct answers?

Support & Challenge Options

SUPPORT

Use visible benchmark cards and sentence frames.

CHALLENGE

Require all three dice to be used exactly once with operations to get as close as possible to a target.

EXTENSION

Ask students to create the largest possible fraction below 100% and prove it is best.

Suggested Timing

MinutesWhat Happens
2Model
6Four partner rounds
3All-three-dice challenge
2Mystery target
2Reflection

Student Reflection

  1. What did you look at first when choosing numerator and denominator?
  2. How can you tell whether a fraction is above or below 50% without dividing?
  3. Show one complete fraction-decimal-percent relationship.
NUMBER SENSE · WEDNESDAY · ACTIVITY 30

Make My Match

TEACHER GUIDE

Start from a percent target and build a matching fraction with cards.

SAY TO STUDENTS

Read the percent target. Draw five cards. Choose two cards to build a fraction equal or closest to the target. Prove the relationship using fraction, decimal, and percent forms. Reset and play the next target.

BEFORE YOU PLAY

Use exact fractions to compare when possible. Mark rounded decimals and percents as approximations. Agree on tie and scoring rules before play.

OBJECTIVE

I can use fraction, decimal, and percent relationships to construct a fraction equivalent to a given percent.

Setup

  • Remove face cards and jokers; Ace = 1.
  • Post targets such as 20%, 25%, 40%, 50%, 60%, 75%, and 80%.
  • Pairs draw five cards and use two to build a matching fraction.

Teacher Directions

  1. Model target 60% with cards 2, 3, 5, 8, 9 and identify 3/5.
  2. Show 60% = 60/100 = 3/5.
  3. If no exact match exists, students find the closest available fraction.

Student Directions

  1. Read the percent target.
  2. Draw five cards.
  3. Choose two cards to build a fraction equal or closest to the target.
  4. Prove the relationship using fraction, decimal, and percent forms.
  5. Reset and play the next target.

Worked Example

EXAMPLE: Target 40%; cards 2, 3, 5, 7, 8

2/5 = 0.40 = 40%, an exact match.

NO EXACT MATCH

Target 75%; cards 1, 2, 5, 6, 9. 5/6 ≈ 83.3% and 6/9 = 2/3 ≈ 66.7%; both are about 8.3 percentage points from the target.

Teacher Questions

  • Which percent-fraction pairs do you recognize immediately?
  • How can simplifying a fraction over 100 help?
  • When there is no exact match, how do you decide what is closest?

Support & Challenge Options

SUPPORT

Provide a benchmark chart for 20%, 25%, 40%, 50%, 60%, 75%, and 80%.

CHALLENGE

No division: students must simplify target percent as a fraction over 100 first.

EXTENSION

Draw seven cards and find two different fractions equivalent to the same target.

Suggested Timing

MinutesWhat Happens
2Model 60%
6Four target rounds
3Steal or alternate match
2Multiple-representation challenge
2Reflection

Student Reflection

  1. Which percent was easiest to turn into a fraction? Why?
  2. How can simplifying a fraction over 100 help you find an equivalent fraction?
  3. Write one percent = fraction over 100 = simplified fraction = decimal relationship.
NUMBER SENSE · FRIDAY · ACTIVITY 31

Fraction War: Closest Pair

TEACHER GUIDE

Arrange four cards into two fractions whose values are as close as possible.

SAY TO STUDENTS

Draw four cards. Arrange them into two proper fractions. Predict whether the values are close. Convert and find the difference in percentage points. Compare with your partner; smaller distance wins.

BEFORE YOU PLAY

Each physical card is used exactly once. Redraw if repeated card values make two proper fractions impossible. Tied distances earn a point for both players.

OBJECTIVE

I can compare two fractions by representing them as decimals and percents and determine the distance between their values.

Setup

  • Remove face cards and jokers; Ace = 1.
  • Each player draws four cards.
  • Use each card exactly once to build two proper fractions.

Teacher Directions

  1. Model cards 2, 3, 4, 5.
  2. Compare 2/3 and 4/5 (about 13.3 points apart) with 2/4 and 3/5 (10 points apart).
  3. Show that students can rearrange the same cards to reduce the distance.

Student Directions

  1. Draw four cards.
  2. Arrange them into two proper fractions.
  3. Predict whether the values are close.
  4. Convert and find the difference in percentage points.
  5. Compare with your partner; smaller distance wins.

Worked Example

EXAMPLE: Cards 1, 2, 3, 6

1/2 and 3/6 are both 50%, so their distance is 0. Another exact pair is 1/3 and 2/6, both about 33.3%.

Teacher Questions

  • What arrangement tends to make two fractions close?
  • Which representation makes distance easiest to see?
  • Can the same four cards make more than one equivalent pair?

Support & Challenge Options

SUPPORT

Use benchmark fractions and permit a comparison to 1/2 before converting.

CHALLENGE

Reverse the goal and make the two fractions as far apart as possible.

EXTENSION

Require students to prove their arrangement is the closest possible among all reasonable arrangements.

Suggested Timing

MinutesWhat Happens
2Model
6Closest-pair rounds
2Exact-match hunt
3Farthest-pair challenge
2Reflection

Student Reflection

  1. What strategy helped you make your two fractions close?
  2. Which representation helped you compare most easily? Why?
  3. Show two values from today and their distance in percentage points.
NUMBER SENSE · MONDAY · ACTIVITY 32

Beat the Dealer

TEACHER GUIDE

Use dice to build a fraction that beats a dealer decimal.

SAY TO STUDENTS

Read the dealer value. Roll two dice and build a proper fraction. Predict BEAT or DEALER before calculating. Convert your fraction and compare. Score for prediction, conversion, and explanation.

BEFORE YOU PLAY

Reroll equal dice in the proper-fraction rounds. Use the smaller number over the larger. Award one point each for a correct prediction, conversion, and explanation; equality with the dealer is a tie.

OBJECTIVE

I can compare fractions, decimals, and percents and use number relationships to justify which value is greater.

Setup

  • Post dealer decimals such as 0.35, 0.48, 0.60, 0.72, 0.85.
  • Students roll two dice and build the largest proper fraction.
  • They predict whether the fraction beats the dealer before calculating.

Teacher Directions

  1. Model dealer 0.60 and roll 4, 5: 4/5 = 80%, which beats 60%.
  2. Model a losing example such as 2/5 = 40%.
  3. Require students to explain the prediction using benchmarks before conversion.

Student Directions

  1. Read the dealer value.
  2. Roll two dice and build a proper fraction.
  3. Predict BEAT or DEALER before calculating.
  4. Convert your fraction and compare.
  5. Score for prediction, conversion, and explanation.

Worked Example

EXAMPLE: Dealer 0.48; roll 3 and 5

3/5 = 0.60 = 60%. Since 3 is more than half of 5, the fraction should be above 50%, so it reasonably beats 48%.

Teacher Questions

  • Is your fraction greater or less than 1/2?
  • Which benchmark helped you predict?
  • How far is your fraction from the dealer?

Support & Challenge Options

SUPPORT

Use a benchmark strip from 1/4 through 1.

CHALLENGE

Allow either die to be numerator, introducing improper fractions and dealer values above 100%.

EXTENSION

Beat the dealer by the smallest possible amount, emphasizing distance rather than merely greater-than.

Suggested Timing

MinutesWhat Happens
2Model
6Four dealer rounds
2Discuss prediction
3Stay-close challenge
2Reflection

Student Reflection

  1. What benchmark helped you make predictions today?
  2. How can you tell if a fraction is above 50% without dividing?
  3. Show one comparison and state the difference in percentage points.
NUMBER SENSE · WEDNESDAY · ACTIVITY 33

Percent of a Roll

TEACHER GUIDE

Use benchmark percents to find a part of a rolled quantity.

SAY TO STUDENTS

Roll three dice. Multiply the first two to create the whole. Use the third die to select the percent. Rewrite the percent as a useful fraction or decimal. Find that percent of the whole and explain your strategy.

BEFORE YOU PLAY

Use exact fractions to compare when possible. Mark rounded decimals and percents as approximations. Agree on tie and scoring rules before play.

OBJECTIVE

I can use benchmark fractions and percents to mentally find part of a quantity and explain the number relationships I used.

Setup

  • Two dice create the whole by multiplication.
  • The third die selects a percent target.
Third DieFind
110%
220%
325%
450%
575%
6Choose 10%, 25%, 50%, or 75%

Teacher Directions

  1. Model 3, 6, 4: whole = 18; target = 50%; 1/2 of 18 = 9.
  2. Emphasize choosing the most efficient representation.
  3. Have students solve mentally before formal multiplication whenever possible.

Student Directions

  1. Roll three dice.
  2. Multiply the first two to create the whole.
  3. Use the third die to select the percent.
  4. Rewrite the percent as a useful fraction or decimal.
  5. Find that percent of the whole and explain your strategy.

Worked Example

EXAMPLE: 4, 5, 3

Whole = 4 x 5 = 20. A third die of 3 means 25%. Since 25% = 1/4, 1/4 of 20 = 5.

ANOTHER PATH

75% of 30 can be found as 3/4 of 30 = 22.5, or as 50% + 25%: 15 + 7.5 = 22.5.

Teacher Questions

  • Which form makes this calculation easiest?
  • How can 10% help you build other percents?
  • If you know 25%, how could you find 75%?

Support & Challenge Options

SUPPORT

Use a benchmark card for 10%, 20%, 25%, 50%, and 75%.

CHALLENGE

Require two different strategies for the same percent-of problem.

EXTENSION

Use non-benchmark targets such as 35% by decomposing into 25% + 10%.

Suggested Timing

MinutesWhat Happens
2Model
6Partner rounds
3Two-strategy round
235% challenge
2Reflection

Student Reflection

  1. Which benchmark percent was easiest to use mentally? Why?
  2. How does knowing 25% = 1/4 help?
  3. Show one percent = decimal = fraction relationship and the quantity you found.
NUMBER SENSE · FRIDAY · ACTIVITY 34

Domino Percent Change

TEACHER GUIDE

Treat the two sides of a domino as original and new values.

SAY TO STUDENTS

Draw a domino. Identify increase or decrease. Find the absolute change. Compare the change with the original as a fraction. Convert to decimal and percent and state the percent change.

BEFORE YOU PLAY

An unchanged value has 0% change. Keep original values positive: percent change from zero is undefined. A later extension may include a new value of zero, a 100% decrease.

OBJECTIVE

I can describe how one quantity changes to another using fractions, decimals, and percents.

Setup

  • Left side = original amount; right side = new amount.
  • Set aside zero values in regular rounds.
  • Use change ÷ original to determine percent change.

Teacher Directions

  1. Model 4 → 6: change is 2; 2/4 = 1/2 = 50% increase.
  2. Reverse to 6 → 4: change is still 2, but 2/6 ≈ 33.3% decrease.
  3. Emphasize that the original amount determines the denominator.

Student Directions

  1. Draw a domino.
  2. Identify increase or decrease.
  3. Find the absolute change.
  4. Compare the change with the original as a fraction.
  5. Convert to decimal and percent and state the percent change.

Worked Example

EXAMPLE: 5 → 3

Change = 2. Relative change = 2/5 = 0.40 = 40%, so the quantity decreased by 40%.

REVERSE IT

4 → 6 is a 50% increase, but 6 → 4 is about a 33.3% decrease because the starting value is different.

Teacher Questions

  • What is the original amount?
  • Why is the change compared with the original?
  • Why can reversing the same two numbers produce different percentages?

Support & Challenge Options

SUPPORT

Use a recording frame: Original, New, Change, Change/Original, Decimal, Percent, Increase/Decrease.

CHALLENGE

Calculate both directions for the same domino and compare.

EXTENSION

Compare two changes with the same absolute difference and determine which has the greater percent change.

Suggested Timing

MinutesWhat Happens
3Model 4 → 6
5Partner rounds
3Reverse challenge
2Same-change comparison
2Reflection

Student Reflection

  1. Why do we compare the change with the original?
  2. Why are 4 → 6 and 6 → 4 not opposite percentages?
  3. Show one original/new/change relationship in fraction, decimal, and percent form.
NUMBER SENSE · MONDAY · ACTIVITY 35

Dice Discount Dash

TEACHER GUIDE

Use benchmark percents to find discounts and sale prices.

SAY TO STUDENTS

Read the original price. Roll two dice and use the key to find your discount. Rewrite the percent in a useful fraction or decimal form. Find the discount amount and sale price. Compare with your partner; lower correct sale price wins.

BEFORE YOU PLAY

Use exact fractions to compare when possible. Mark rounded decimals and percents as approximations. Agree on tie and scoring rules before play.

OBJECTIVE

I can use fraction, decimal, and percent relationships to mentally calculate discounts and sale prices.

Setup

  • Teacher provides an original price.
  • Students roll two dice; the sum determines the discount.
Dice TotalDiscount
2-310%
4-525%
6-850%
9-1075%
11-1220%

Teacher Directions

  1. Model $40 with a roll total of 7: 50% off.
  2. Find the discount amount, then subtract to get the sale price.
  3. Contrast “percent off” with “percent paid.”

Student Directions

  1. Read the original price.
  2. Roll two dice and use the key to find your discount.
  3. Rewrite the percent in a useful fraction or decimal form.
  4. Find the discount amount and sale price.
  5. Compare with your partner; lower correct sale price wins.

Worked Example

EXAMPLE: $60 at 25% off

25% = 1/4. One-fourth of $60 is $15. Discount = $15; sale price = $45.

75% OFF

75% off $80 means paying the remaining 25%. Since 25% = 1/4, the sale price is $20.

Teacher Questions

  • What fraction is equivalent to your discount?
  • What percent of the original price are you actually paying?
  • Could you solve by finding the remaining percent instead?

Support & Challenge Options

SUPPORT

Provide a chart connecting discount percent to fraction and percent paid.

CHALLENGE

Solve each discount two ways: discount-first and percent-paid-first.

EXTENSION

Apply two discounts successively and explain why 25% off then 50% off is not the same as 75% off.

Suggested Timing

MinutesWhat Happens
2Model
6Discount rounds
2Discuss percent paid
3Double-discount challenge
2Reflection

Student Reflection

  1. Which percent was easiest to calculate mentally and why?
  2. If an item is 25% off, why can you calculate 75% to get the sale price?
  3. If an item is 50% off and then another 50% off, is it free? Explain.
NUMBER SENSE · WEDNESDAY · ACTIVITY 36

Roll & Scale

TEACHER GUIDE

Scale one quantity and watch fraction, decimal, and percent forms change together.

SAY TO STUDENTS

Roll both dice. Identify the starting value and scale factor. Predict whether the new value will be larger or smaller. Scale fraction, decimal, and percent. Check that all three still represent the same quantity.

BEFORE YOU PLAY

Use exact fractions to compare when possible. Mark rounded decimals and percents as approximations. Agree on tie and scoring rules before play.

OBJECTIVE

I can use multiplication and division to scale a fraction, decimal, and percent while explaining how the representations are connected.

Setup

  • Die 1 chooses a starting benchmark value.
  • Die 2 chooses a scale factor.
Die 1Starting Value
11/10 = 0.10 = 10%
21/5 = 0.20 = 20%
31/4 = 0.25 = 25%
41/2 = 0.50 = 50%
53/4 = 0.75 = 75%
64/5 = 0.80 = 80%

Teacher Directions

  1. Use second-die rule: 1-2 means x2; 3-4 means x1/2; 5 means x3; 6 is student choice.
  2. Model 1/4 = 0.25 = 25%, scaled by 2 to 1/2 = 0.50 = 50%.
  3. Discuss why all representations must scale together.

Student Directions

  1. Roll both dice.
  2. Identify the starting value and scale factor.
  3. Predict whether the new value will be larger or smaller.
  4. Scale fraction, decimal, and percent.
  5. Check that all three still represent the same quantity.

Worked Example

EXAMPLE: Start 1/2; scale by 1/2

1/2 x 1/2 = 1/4; 0.50 x 1/2 = 0.25; 50% x 1/2 = 25%.

GREATER THAN 100%

3/4 x 2 = 3/2 = 1.50 = 150%. Percentages can validly exceed 100%.

Teacher Questions

  • Should your answer become larger or smaller? Why?
  • If the percent doubles, what happens to the decimal?
  • Can a percent exceed 100%?

Support & Challenge Options

SUPPORT

Use only x2 and x1/2 at first, with a START/SCALE/RESULT organizer.

CHALLENGE

Allow x3 and values above 100%.

EXTENSION

Reverse the scale: given the ending value and factor, determine the starting value.

Suggested Timing

MinutesWhat Happens
2Model
6Partner rounds
2Discuss >100%
3Reverse-scale challenge
2Reflection

Student Reflection

  1. What happens when you multiply a number by 1/2?
  2. If 25% doubles to 50%, what happens to its fraction and decimal forms?
  3. Show one complete scale relationship.
NUMBER SENSE · FRIDAY · ACTIVITY 37

Between Two

TEACHER GUIDE

Use playing cards to create rational numbers inside a given interval.

SAY TO STUDENTS

Draw five cards. Build proper fractions using two cards. Predict whether each fraction falls inside the interval. Convert to prove it. Find as many distinct values as possible before time expires.

BEFORE YOU PLAY

Use two different physical cards for each fraction; reuse the hand to explore other choices. If no fraction is strictly inside the interval, justify that conclusion and draw a new hand.

OBJECTIVE

I can create fractions, decimals, and percents that fall between two given values and justify their location using number relationships.

Setup

  • Remove face cards and jokers; Ace = 1.
  • Pairs draw five cards.
  • Teacher posts a percent interval such as 40% < ? < 70%.

Teacher Directions

  1. Model cards 2, 3, 4, 5, 8 and test 2/5 = 40% (not strictly between), 3/5 = 60%, and 2/3 ≈ 66.7%.
  2. Emphasize that several different values can fit the same interval.

Student Directions

  1. Draw five cards.
  2. Build proper fractions using two cards.
  3. Predict whether each fraction falls inside the interval.
  4. Convert to prove it.
  5. Find as many distinct values as possible before time expires.

Worked Example

EXAMPLE: 40% < ? < 70%

3/5 = 60% and 2/3 ≈ 66.7% both work. 2/5 = 40% does not because it equals the boundary.

Teacher Questions

  • Which benchmark helped you judge the interval?
  • What is the difference between a different fraction and a different value?
  • Why are there many numbers between 40% and 70%?

Support & Challenge Options

SUPPORT

Start with wide intervals such as 25%-75% and provide benchmark cards.

CHALLENGE

Use tight intervals such as 45%-55% and count equivalent fractions as only one location.

EXTENSION

Closest without crossing: find the value closest to the upper boundary while remaining inside the interval.

Suggested Timing

MinutesWhat Happens
2Model
5Three interval rounds
3Tight squeeze
3Closest-without-crossing
2Reflection

Student Reflection

  1. What benchmark helped you decide whether a number belonged in an interval?
  2. Why do equivalent fractions count as one location?
  3. Find and show a value between 60% and 70% in three forms.
NUMBER SENSE · MONDAY · ACTIVITY 38

Which One Doesn’t Belong? — Number Sense

TEACHER GUIDE

Analyze four representations and defend a mathematical classification.

SAY TO STUDENTS

Roll two dice and create a fraction. Find its equivalent decimal and percent. Create one impostor value. Challenge your partner to identify it and prove why. In later rounds, create sets where more than one “doesn’t belong” argument is defensible.

BEFORE YOU PLAY

Use exact fractions to compare when possible. Mark rounded decimals and percents as approximations. Agree on tie and scoring rules before play.

OBJECTIVE

I can analyze relationships among fractions, decimals, and percents and justify why a number does or does not belong in a group.

Setup

  • Pairs roll two dice to create a fraction.
  • They convert it to a decimal and percent.
  • They create a fourth “impostor” value for a partner to analyze.

Teacher Directions

  1. Start with 1/2, 0.50, 50%, 0.05.
  2. Model a second set such as 3/4, 75%, 0.75, 3/5.
  3. Explain that a response only counts when it includes a mathematical reason.

Student Directions

  1. Roll two dice and create a fraction.
  2. Find its equivalent decimal and percent.
  3. Create one impostor value.
  4. Challenge your partner to identify it and prove why.
  5. In later rounds, create sets where more than one “doesn’t belong” argument is defensible.

Worked Example

EXAMPLE: 3/4, 0.75, 75%, 0.075

0.075 does not belong because it equals 7.5%, while the other three all represent 75%.

MULTIPLE VALID ARGUMENTS

1/2, 2/4, 0.50, 50% are all equal, but 2/4 is the only unsimplified fraction, 0.50 the only decimal, and 50% the only percent.

Teacher Questions

  • What relationship connects the three equivalent values?
  • Can more than one answer be defensible?
  • What makes an explanation mathematically strong?

Support & Challenge Options

SUPPORT

Use a benchmark equivalence chart and a sentence frame for justification.

CHALLENGE

Create a sneaky impostor close to the correct value, such as 0.705 instead of 0.75.

EXTENSION

Create four correct values where at least three different “doesn’t belong” arguments can be defended.

Suggested Timing

MinutesWhat Happens
2Teacher model
5Partner-created rounds
3Sneaky impostor
3Multiple-answer challenge
2Reflection

Student Reflection

  1. How can you quickly check whether three representations are equivalent?
  2. Why do 0.5, 0.50, 50%, and 1/2 represent the same value?
  3. Create your own three-equivalent-one-impostor set and explain it.
NUMBER SENSE · WEDNESDAY · ACTIVITY 39

Domino Ratio Ladder

TEACHER GUIDE

Build a growing least-to-greatest ladder from domino fractions.

SAY TO STUDENTS

Draw three dominoes and orient them as proper fractions. Estimate whether each is below, near, or above 1/2. Order from least to greatest. On “ADD ONE,” draw another domino and insert it in the correct location. Prove at least one neighboring comparison.

BEFORE YOU PLAY

Set aside zero tiles and doubles for basic proper-fraction rounds. Place equivalent fractions at the same level of the ladder. In extensions, never use zero as a denominator.

OBJECTIVE

I can compare and order fractions by using benchmarks, decimals, and percents, and I can explain the relationships among the values.

Setup

  • Each pair gets 8-10 dominoes.
  • Students may rotate a domino to choose its orientation.
  • For basic rounds, use proper fractions only.

Teacher Directions

  1. Model 1/4, 1/2, 2/3, 3/4 and order them by benchmark knowledge.
  2. Show both percent conversion and common-denominator proof for neighboring values.
  3. Run “ADD ONE” rounds where students insert a new domino without rebuilding the entire ladder.

Student Directions

  1. Draw three dominoes and orient them as proper fractions.
  2. Estimate whether each is below, near, or above 1/2.
  3. Order from least to greatest.
  4. On “ADD ONE,” draw another domino and insert it in the correct location.
  5. Prove at least one neighboring comparison.

Worked Example

EXAMPLE LADDER

Fraction ladder: 1/3 < 2/5 < 1/2 < 2/3 < 3/4 < 4/5. Corresponding percents: approximately 33.3%, exactly 40%, exactly 50%, approximately 66.7%, exactly 75%, exactly 80%.

Teacher Questions

  • What strategy helped you insert a new fraction quickly?
  • Can you compare two fractions without decimals?
  • How does knowing 1/2 as a benchmark help?

Support & Challenge Options

SUPPORT

Use anchors 0%, 50%, and 100%, then sort each fraction below, equal to, or above 50% before ordering.

CHALLENGE

No decimals allowed; use benchmarks, equivalent fractions, or common denominators.

EXTENSION

Allow improper fractions and extend the ladder past 100% to 200%.

Suggested Timing

MinutesWhat Happens
2Model
2Build initial ladder
5ADD ONE rounds
3Improper-fraction challenge
3Proof and reflection

Student Reflection

  1. What strategy helped you place a new fraction without converting everything?
  2. How does knowing whether a fraction is above or below 1/2 help?
  3. Show three values from your ladder in fraction, decimal, and percent form.
NUMBER SENSE · FRIDAY · ACTIVITY 40

Capture the Whole

TEACHER GUIDE

Find the missing complement needed to reach 1, 1.00, or 100%.

SAY TO STUDENTS

Draw two cards and form a proper fraction. Predict whether the missing amount is above or below 50%. Find the missing fraction needed to make one whole. Convert starting and missing amounts to decimals and percents. Check that the percents total 100%.

BEFORE YOU PLAY

Put the smaller card over the larger. Redraw equal cards for proper-fraction rounds, or explicitly allow a whole of 1 and a complement of 0.

OBJECTIVE

I can use fraction, decimal, and percent relationships to determine how much more is needed to make one whole.

Setup

  • Remove face cards and jokers; Ace = 1.
  • Draw two cards and form a proper fraction.
  • Find the complement needed to reach one whole.

Teacher Directions

  1. Model 3/5 and ask what must be added to make 1.
  2. Show 3/5 + 2/5 = 1, 0.60 + 0.40 = 1.00, and 60% + 40% = 100%.
  3. Emphasize finding the fraction complement before doing division when possible.

Student Directions

  1. Draw two cards and form a proper fraction.
  2. Predict whether the missing amount is above or below 50%.
  3. Find the missing fraction needed to make one whole.
  4. Convert starting and missing amounts to decimals and percents.
  5. Check that the percents total 100%.

Worked Example

EXAMPLE: 5/8

5/8 + 3/8 = 1. Then 5/8 = 0.625 = 62.5% and 3/8 = 0.375 = 37.5%. Together they make 100%.

Teacher Questions

  • Can you find the missing fraction without dividing?
  • If the starting amount is above 50%, what must be true of the complement?
  • What should the two percents always total?

Support & Challenge Options

SUPPORT

Provide common complement pairs such as 1/4 + 3/4, 2/5 + 3/5, and 1/2 + 1/2.

CHALLENGE

No conversion until the fraction complement is found.

EXTENSION

Change the target whole to 200% and find how much more is needed.

Suggested Timing

MinutesWhat Happens
2Model
5Partner rounds
3Less-familiar fractions
3Capture 200%
2Reflection

Student Reflection

  1. If a fraction is greater than 1/2, what do you know about its complement?
  2. How can you find the missing amount when something is 65% complete?
  3. Show one starting amount and complement in fraction, decimal, and percent form.
HANDS-ON MATH · ACTIVITY 01

Think, Talk, Rotate, Record

TEACHER GUIDE

Run the routine

  1. Pose one open problem and give everyone two quiet minutes to form an idea.
  2. Groups solve on a vertical surface with one marker; the writer explains each move.
  3. Pause, rotate groups to another board, and ask them to add a question or new strategy.
  4. Return to the original board to revise and record a final explanation.
SAY TO STUDENTS

Show a way to solve it. What do you notice in another group’s approach?

EXAMPLE TO USE

For 120 students riding full cars of 4 and vans of 6, find possible combinations that use both kinds of vehicle.

LOOK FOR

Students justify why a combination fits every condition, not just the total.

WHAT STUDENT WORK COULD LOOK LIKE

Example student output: 6 cars and 16 vans carry 24 + 96 = 120 students. Another solution is 9 cars and 14 vans. Both use full vehicles and both types. Ask groups how they know they have found every possibility.

IF THIS HAPPENS

If groups stall, suggest trying even numbers of vans and recording the matching number of cars in a table. Give a new question at the rotation rather than letting visitors erase another group’s work.

START CLASS · ACTIVITY 02

Number Talk: Notice & Wonder

TEACHER GUIDE

Run the routine

  1. Display a short prompt without teaching a method first.
  2. Ask students to think silently and signal when they have one strategy.
  3. Invite two or three different explanations; record them faithfully.
  4. Ask which ideas connect and what needs to be checked.
SAY TO STUDENTS

What do you notice? What do you wonder? How could you find out?

EXAMPLE TO USE

Display 0.25 × 48 and ask for more than one mental method.

LOOK FOR

Students explain why their method works and respond to another strategy.

WHAT STUDENT WORK COULD LOOK LIKE

Example student output: “One quarter of 48 is 12, so 0.25 × 48 = 12.” A second route is 48 ÷ 4 = 12.

IF THIS HAPPENS

If only one student speaks, ask everyone to rehearse an explanation with a partner before taking another strategy.

HANDS-ON MATH · ACTIVITY 03

Dice: Fraction, Decimal, Percent

TEACHER GUIDE

Run the routine

  1. Partners roll two dice; the smaller number becomes the numerator and the larger the denominator.
  2. Each student writes the fraction, decimal, and percent.
  3. Partners compare their conversions and explain any disagreement.
  4. Repeat for several rounds, choosing one tricky result to discuss as a class.
SAY TO STUDENTS

Which form is easiest to calculate from your roll, and why?

EXAMPLE TO USE

A 3 and 4 make 3/4, 0.75, and 75%.

LOOK FOR

Conversions are equivalent and students can explain the relationship.

WHAT STUDENT WORK COULD LOOK LIKE

Example student output: 1/3 = 0.333… = 33⅓%. Accept a repeating decimal or an appropriate approximation labeled as such.

IF THIS HAPPENS

If students treat 1/3 as exactly 0.33, compare the repeating decimal with a rounded value.

HANDS-ON MATH · ACTIVITY 04

Domino Target Number

TEACHER GUIDE

Run the routine

  1. Set a target and allowed operations before play.
  2. Partners draw one domino and use its two numbers to make an expression.
  3. Award a point for reaching the target exactly, or for the closest justified result.
  4. Discuss two different expressions after several rounds.
SAY TO STUDENTS

How close can you get to the target using both numbers exactly once?

EXAMPLE TO USE

Target 10: a 2|5 domino gives 2 × 5 = 10.

LOOK FOR

Students follow the operation rules and explain their expressions.

WHAT STUDENT WORK COULD LOOK LIKE

Example student output: With target 10 and a 2|5 domino, 2 × 5 = 10. Post allowed operations and whether reversing order is permitted.

IF THIS HAPPENS

If a draw cannot hit the target, ask for the closest value with a written expression.

HANDS-ON MATH · ACTIVITY 05

Integer Card Challenge

TEACHER GUIDE

Run the routine

  1. Remove face cards; make red cards negative and black cards positive.
  2. Each partner draws two cards and adds their values.
  3. The greater sum wins the round; partners must explain the comparison.
  4. After five rounds, ask for a rule that helps with opposite signs.
SAY TO STUDENTS

Which sum is greater? Explain without a calculator.

EXAMPLE TO USE

A red 7 and black 3 make −4; a black 2 and black 4 make 6.

LOOK FOR

Students use signs correctly rather than comparing absolute values only.

WHAT STUDENT WORK COULD LOOK LIKE

Example student output: red 7 and black 3 give −7 + 3 = −4; black 2 and black 4 give 2 + 4 = 6, so 6 is greater. Decide whether aces count as 1 before play.

IF THIS HAPPENS

If signs cause confusion, place both sums on a number line before scoring.

START CLASS · ACTIVITY 06

Which One Doesn’t Belong?

TEACHER GUIDE

Run the routine

  1. Show four examples and allow one minute of private thinking.
  2. Partners choose one example and prepare a reason.
  3. Invite different choices, then ask students to defend a second choice.
  4. Name the feature or concept that emerged for today’s lesson.
SAY TO STUDENTS

Which one doesn’t belong? Give a reason someone could check.

EXAMPLE TO USE

Show four graphs: one nonlinear, one decreasing, one without the origin, and one with a fractional slope.

LOOK FOR

Reasons refer to observable features; more than one choice can work.

WHAT STUDENT WORK COULD LOOK LIKE

Ready-to-display set: A = 2, B = 3, C = 4, D = 9. Ask: “Which one doesn’t belong? Give a reason that could be checked.” Sample: 2 is the only even prime; 3 is the only multiple of 3 that is prime; 4 is the only perfect square that is even; 9 is the only odd perfect square. Multiple answers are welcome.

IF THIS HAPPENS

If students think there is one answer, model two valid reasons for different choices before asking pairs to create a third.

CHECK UNDERSTANDING · ACTIVITY 07

Error Detective

TEACHER GUIDE

Run the routine

  1. Display a solution with one meaningful mistake, but do not identify it.
  2. Partners annotate the first step that stops being valid.
  3. Have students correct the solution and write a helpful response to its author.
  4. Compare explanations before revealing the intended error.
SAY TO STUDENTS

Where does the reasoning first go wrong? What would you say to help?

EXAMPLE TO USE

A student writes −3 × −4 = −12 when solving a multistep expression.

LOOK FOR

Students identify the first error and justify the correction.

WHAT STUDENT WORK COULD LOOK LIKE

Ready-to-display work: “−3 × (−4) = −12 because 3 × 4 = 12.” Ask students to identify the first incorrect step, correct it, and explain why. Sample correction: −3 × (−4) = 12 because a negative times a negative is positive.

IF THIS HAPPENS

If students only give 12, ask them to write a supportive sentence explaining the sign rule.

SCIENCE INQUIRY · ACTIVITY 08

Phenomenon: Notice, Wonder, Explain

TEACHER GUIDE

Run the routine

  1. Show the phenomenon once without commentary.
  2. Students record two observations and one testable question.
  3. Partners separate what they saw from what they infer.
  4. Collect possible explanations and identify what evidence could distinguish them.
SAY TO STUDENTS

What did you observe? What evidence would help explain it?

EXAMPLE TO USE

Show a plant leaning toward a window and ask what might cause the direction of growth.

LOOK FOR

Students distinguish observations from explanations.

WHAT STUDENT WORK COULD LOOK LIKE

Example student output: “The stem bends toward the window” is an observation. “Light may influence the direction of growth” is a possible explanation to investigate.

IF THIS HAPPENS

If guesses are presented as observations, ask “Could we see or measure that directly in the image?”

SCIENCE INQUIRY · ACTIVITY 09

Variable Sort

TEACHER GUIDE

Run the routine

  1. Give each group one experiment scenario.
  2. Ask groups to label the changed factor, measured outcome, and controlled conditions.
  3. Groups trade scenarios and critique one another’s labels.
  4. Revise labels together and discuss one possible source of unfairness.
SAY TO STUDENTS

What would you change? What would you measure? What must stay the same?

EXAMPLE TO USE

Compare paper towel brands by measuring how much water each sheet absorbs.

LOOK FOR

The measured outcome is observable and the controls make the comparison fair.

WHAT STUDENT WORK COULD LOOK LIKE

Ready-to-use scenario: “Test whether paper towel brand affects how much water one sheet absorbs.” Change: brand. Measure: milliliters absorbed before dripping. Keep constant: sheet size, water source, and test procedure.

IF THIS HAPPENS

If groups identify “amount of water” as the changed factor, ask what the investigator deliberately chooses and what result they record.

SCIENCE INQUIRY · ACTIVITY 10

Observation Stations

TEACHER GUIDE

Run the routine

  1. Set up three stations with a common question.
  2. At each station, students sketch and record measurable or descriptive observations.
  3. Groups rotate, reading earlier notes without copying guesses.
  4. Finish by asking which observations best support an explanation.
SAY TO STUDENTS

Record what you can directly observe before you explain it.

EXAMPLE TO USE

Compare three leaf samples for shape, texture, veins, and evidence of damage.

LOOK FOR

Notes contain specific observations rather than only labels or guesses.

WHAT STUDENT WORK COULD LOOK LIKE

Example student output: “Leaf B has five visible veins branching from the midrib and two holes near its edge.”

IF THIS HAPPENS

If students write only “green leaf,” ask for a count, measurement, location, or comparison.

CHECK UNDERSTANDING · ACTIVITY 11

Claim–Evidence–Reasoning Quickwrite

TEACHER GUIDE

Run the routine

  1. Ask a question with more than a one-word answer.
  2. Students write a claim, cite one specific piece of evidence, and explain its connection.
  3. Partners underline the evidence and circle the reasoning.
  4. Allow two minutes to revise missing or unclear reasoning.
SAY TO STUDENTS

What is your claim? Which evidence supports it? Why does that evidence matter?

EXAMPLE TO USE

Claim: the plant received uneven light. Evidence: its stem grew toward the window. Reasoning: growth toward light supports that explanation.

LOOK FOR

The reasoning explains the link between evidence and claim.

WHAT STUDENT WORK COULD LOOK LIKE

Example student output: “The plant may have received light mainly from one side (claim). Its stem leaned toward the window (evidence). Growth toward the light is consistent with that explanation (reasoning).”

IF THIS HAPPENS

If reasoning repeats the evidence, ask “Why would that observation support this claim?”

SCIENCE INQUIRY · ACTIVITY 12

Build, Revise, Share a Model

TEACHER GUIDE

Run the routine

  1. Ask groups to draw an initial model of a process or phenomenon.
  2. Provide new evidence, a short reading, or a peer question.
  3. Groups revise using a different color and annotate what changed.
  4. Invite a brief explanation of what the new evidence improved.
SAY TO STUDENTS

How does your model explain what happened? What did you change after seeing evidence?

EXAMPLE TO USE

Model how water moves through a plant, then revise after examining a stem cross-section.

LOOK FOR

Revisions respond to evidence instead of adding decoration.

WHAT STUDENT WORK COULD LOOK LIKE

Example student output: An initial drawing shows water entering roots. A revised model adds a route up the stem to leaves and an arrow labeled with the evidence that prompted the change.

IF THIS HAPPENS

If revisions are only decorative, have groups circle the new evidence and annotate the specific change it caused.

START CLASS · ACTIVITY 13

Vocabulary: Sketch & Explain

TEACHER GUIDE

Run the routine

  1. Give students a word from the current lesson.
  2. Students sketch a representation and add one sentence explaining it.
  3. Partners exchange work and infer the term from the sketch.
  4. Discuss a strong example and one common misconception.
SAY TO STUDENTS

Draw the idea so a classmate could identify it. Explain one important feature.

EXAMPLE TO USE

Sketch a proportional graph through the origin and label its constant ratio.

LOOK FOR

The representation shows the defining feature of the term.

WHAT STUDENT WORK COULD LOOK LIKE

Example student output: A proportional graph is a straight line through (0,0); “each increase of 1 in x increases y by the same amount.”

IF THIS HAPPENS

If sketches are vague, ask students to label the one defining feature a classmate should notice.

DISCUSSION · ACTIVITY 14

30-Second Partner Teach

TEACHER GUIDE

Run the routine

  1. Pose one focused question and allow a minute to prepare.
  2. Partner A teaches for 30 seconds while Partner B listens.
  3. Partner B restates the idea and asks one clarifying question.
  4. Switch roles with a related prompt; sample a few explanations.
SAY TO STUDENTS

Explain the idea as if your partner missed the lesson.

EXAMPLE TO USE

Explain how to tell whether a table represents a proportional relationship.

LOOK FOR

Both partners speak and the restatement preserves the key idea.

WHAT STUDENT WORK COULD LOOK LIKE

Example student output: “The table is proportional because y ÷ x is 3 in every row, so y = 3x.” Listener: “So the same multiplier works for all rows?”

IF THIS HAPPENS

If partners fall silent, post a frame: “I know ___ because ___.” Give 30 seconds to plan first.

DISCUSSION · ACTIVITY 15

Four Corners with Evidence

TEACHER GUIDE

Run the routine

  1. Post four plausible answers to a debatable or diagnostic prompt.
  2. Students choose a corner and write one reason before moving.
  3. Groups prepare their strongest evidence and share briefly.
  4. Allow students to move after hearing others and explain any change.
SAY TO STUDENTS

Which choice is best supported? What evidence could change your mind?

EXAMPLE TO USE

Which variable would most affect the outcome of a proposed investigation?

LOOK FOR

Students support a choice and can revise it based on evidence.

WHAT STUDENT WORK COULD LOOK LIKE

Ready-to-display choices: To test whether light affects plant growth, vary A. water, B. light exposure, C. soil amount, or D. pot size. Best choice: B, while keeping the others consistent. Ask students which evidence would change their thinking.

IF THIS HAPPENS

If students follow friends to a corner, require an individual written reason before anyone moves.

DISCUSSION · ACTIVITY 16

Question Carousel

TEACHER GUIDE

Run the routine

  1. Place one prompt at each station.
  2. Groups respond in writing for three minutes.
  3. Rotate, read the previous response, and add a new idea or question.
  4. Return to the first station to synthesize the strongest points.
SAY TO STUDENTS

Add something new, challenge an idea respectfully, or ask a useful question.

EXAMPLE TO USE

Stations ask for a model, a counterexample, an everyday application, and a remaining question.

LOOK FOR

Each rotation adds thinking rather than restating what is already written.

WHAT STUDENT WORK COULD LOOK LIKE

Ready-to-use station prompts for a science investigation: 1. Draw a model. 2. Give one piece of evidence. 3. Name an alternative explanation. 4. Write a testable next question.

IF THIS HAPPENS

If groups repeat earlier answers, require each rotation to add evidence, a counterexample, or a genuinely new question.

CHECK UNDERSTANDING · ACTIVITY 17

One-Minute Exit Check

TEACHER GUIDE

Run the routine

  1. Choose one question tied to the day’s most important idea.
  2. Ask students to answer independently in one minute.
  3. Sort responses into ready, almost, and needs support.
  4. Use one common pattern to plan tomorrow’s opening.
SAY TO STUDENTS

What can you now explain or do? Show one piece of evidence.

EXAMPLE TO USE

Write one equation that represents a proportional relationship and explain the constant.

LOOK FOR

The response reveals reasoning, not just confidence.

WHAT STUDENT WORK COULD LOOK LIKE

Ready-to-display prompt: “A table contains (1,3), (2,6), and (4,12). Is the relationship proportional? Explain using a constant.” Sample answer: Yes; y/x = 3 for every pair, so y = 3x.

IF THIS HAPPENS

If sorting takes too long, read a sample of responses and note one pattern to address tomorrow.

CHECK UNDERSTANDING · ACTIVITY 18

Confidence Sort & Next Step

TEACHER GUIDE

Run the routine

  1. Give three short items of increasing complexity.
  2. Students solve one and choose: ready, practicing, or need help.
  3. Ask them to name the evidence behind their choice.
  4. Partners discuss one next step; collect the self-assessment.
SAY TO STUDENTS

Which skill feels secure? What specific result tells you that?

EXAMPLE TO USE

After three integer problems, a student notes correct signs but difficulty explaining why.

LOOK FOR

Confidence matches the student’s work and includes an actionable next step.

WHAT STUDENT WORK COULD LOOK LIKE

Example student output: “I solved two integer additions correctly, but I cannot yet explain why −4 + 7 = 3. My next step is to draw a number line.”

IF THIS HAPPENS

If confidence and work disagree, ask students to point to a specific line in their work before choosing a category.

CHECK UNDERSTANDING · ACTIVITY 19

Two Strengths, One Next Step

TEACHER GUIDE

Run the routine

  1. Share two or three criteria for the work.
  2. Partners identify two visible strengths with evidence.
  3. Each gives one small, actionable next step.
  4. Writers revise one part before turning work in.
SAY TO STUDENTS

Name what works, point to where you see it, and suggest one change.

EXAMPLE TO USE

“Your graph has labeled axes and matching points. Next, explain what the slope means here.”

LOOK FOR

Feedback points to the criteria and leads to a real revision.

WHAT STUDENT WORK COULD LOOK LIKE

Example student feedback: “Your axes are labeled and your plotted points match the table. Next, explain what the slope represents in this situation.”

IF THIS HAPPENS

If feedback says only “good job,” point students back to a specific success criterion and ask where they see it.

CREATE & SHARE · ACTIVITY 20

Student Video Storyboard

TEACHER GUIDE

Run the routine

  1. Give groups one focused question and a target video length.
  2. Assign roles for research, script, visuals, and production; roles may rotate.
  3. Storyboard the opening, two key ideas, evidence, and closing.
  4. Have another group check accuracy and clarity before filming.
SAY TO STUDENTS

What should viewers understand by the end, and what will they see or hear?

EXAMPLE TO USE

Plan a 60-second science tip that explains how to identify a fair test.

LOOK FOR

The storyboard includes accurate information and purposeful visuals.

WHAT STUDENT WORK COULD LOOK LIKE

Example student output: Four storyboard frames show a question, a demonstration, an evidence-backed explanation, and a closing takeaway. Each frame lists visuals and narration.

IF THIS HAPPENS

If groups want to film immediately, require a peer to check the claim and evidence on the storyboard first.

CREATE & SHARE · ACTIVITY 21

Source Check in Pairs

TEACHER GUIDE

Run the routine

  1. Give pairs two sources that address the same question.
  2. Students identify author, date, purpose, and evidence for each.
  3. Pairs mark one claim they can verify and one claim that needs more checking.
  4. Discuss what additional source would increase confidence.
SAY TO STUDENTS

Who made this, what evidence do they give, and what should we check?

EXAMPLE TO USE

Compare two short articles about a new scientific discovery, noting the original study and publication dates.

LOOK FOR

Students cite source details and avoid judging credibility from appearance alone.

WHAT STUDENT WORK COULD LOOK LIKE

Example student output: “Source A names the study and its date; Source B repeats the claim without a link. We should check the original study before sharing the number.”

IF THIS HAPPENS

If students judge a source by appearance alone, redirect them to author, date, original evidence, and what each source actually supports.