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Number Sense Sprint

A foundational numeracy lesson exploring number patterns, skip counting sequences, and progressive multi-digit addition strategies.

CZClaire Zietsman

Number Sense Sprint

A foundational numeracy lesson exploring number patterns, skip counting sequences, and progressive multi-digit addition strategies.

CZClaire Zietsman

Stepwise Sums Addition Worksheet

Math Mission Progressive Skill Builder

Stepwise Sums Addition

Master double-digit addition with guided step-by-step fading cues.

Name:

Date:

Score:

/ 15

Addition Rulebook: Look at the Ones First!

Rule 1

Ones sum is 9 or less? Keep it simple!

No carrying required. Add the ones, then add the tens.

34 + 23: 4 + 3 = 7 ones, 3 + 2 = 5 tens → 57

Rule 2

Ones sum is 10 or more? Regroup!

Leave ones in the ones place. Carry 1 ten to the attic box.

47 + 28: 7 + 8 = 15 → carry 1 ten, write 5 ones → 75

1

Stage 1: Guided Walkthrough

Follow each prompt step by step

Problem 1 (Regrouping) Requires Regrouping

T O

3 8

2 5

Step 1: Add Ones

8 + 5 = 13

Write 3 in ones. Put 1 in the attic.

Step 2: Add Tens

1 (attic) + 3 + 2 =

Write total tens in the tens spot.

Problem 2 (No Regrouping) No Regrouping

T O

×

5 2

3 4

Step 1: Add Ones

2 + 4 =

Is this ≥ 10? [ ] Yes [ ] No

Step 2: Add Tens

5 + 3 =

No attic number! Just add tens.

2

Stage 2: Check & Solve (Moderate Support)

Check the box, use the attic box only when needed!

#3 Tens | Ones

46

+17

Regroup? Y N

#4 Tens | Ones

63

+24

Regroup? Y N

#5 Tens | Ones

29

+35

Regroup? Y N

#6 Tens | Ones

51

+18

Regroup? Y N

Self-check tip: If the ones digit equals 10, write 0 in ones and carry 1 to the tens! Page 1 of 2

Stepwise Sums Addition • Fading Support

Apply your steps independently with minimal scaffolding.

Student Name:

3

Stage 3: Light Cues (Mixed Practice)

Attic circles are there if you need them!

#7 c

57

+26

#8 c

43

+32

#9 c

38

+49

#10 c

71

+16

#11 c

25

+68

#12 c

64

+23

4

Stage 4: Independent Practice

No extra guide lines – you've got this!

#13

48

+37

Standard layout

#14

54

+42

Standard layout

#15 Story Problem

Maya collected 47 blue seashells and 29 striped seashells at the beach. How many seashells did she collect altogether?

Answer:

seashells

Stage 5: Math Detective (Spot the Mistake!)

Critical Thinking

Leo's Incorrect Work:

36

+ 47

713

What mistake did Leo make?

Correct Sum:

Self-Assessment: [ ] I got this! • [ ] Almost there • [ ] Need more practice Page 2 of 2

Skip Counting Sprint Worksheet

Math Mission Pattern Power & Fluency

Skip Counting Sprint

Jump along number paths and build speed with 2s, 5s, and 10s.

Name:

Date:

Score:

/ 20

Jump Cheat-Sheet: Spot the Clues

Jump by 2s

Even numbers end in:

0, 2, 4, 6, 8

Jump by 5s

All numbers end in:

5 or 0

Jump by 10s

All numbers end in:

0 (tens change)

1

Stage 1: Number Line Hops

Fill in the missing landing spots

A. Count by 2s (+2 each hop) 0 to 12

+2

0

+2

2

+2

6

+2

10

+2

B. Count by 5s (+5 each hop) 0 to 30

+5

0

+5

5

+5

10

+5

20

+5

30

C. Count by 10s (+10 each hop) 10 to 60

+10

10

+10

20

+10

40

+10

60

2

Stage 2: Stepping Stone Trails

Fill in the blank stepping stones

Trail #1: Count by 2s +2

14 → 16 →

→ 20 →

→ 24

Trail #2: Count by 5s +5

35 →

→ 45 → 50 →

→ 60

Trail #3: Count by 10s +10

70 → 80 →

→ 100 →

→ 120

Trail #4: Odd Numbers (+2) +2

21 → 23 →

→ 27 →

→ 31

3

Stage 3: Group & Quick Count

Count by groups rather than one by one!

A. Count pairs by 2s:

[2] [2] [2] [2] [2] [2]

6 pairs =

items

B. Count nickels by 5s:

5¢ 5¢ 5¢ 5¢ 5¢

5 nickels =

¢

C. Count rods by 10s:

|10| |10| |10| |10|

4 rods =

units

Tip: Check the last digit to verify if you followed the right jump rule! Page 1 of 2

Skip Count Multiplication Worksheet

Math Mission Repeated Addition to Multiplication

Skip Count Multiplication

Use equal hops on the number line to find multiplication products quickly.

Name:

Date:

Score:

/ 20

The Secret Link: Multiplication is Shortcut Skip Counting!

1. Equal Groups

4 hops of 5

[5] [5] [5] [5]

2. Skip Count Track

Count by 5s

5 • 10 • 15 • 20

3. Multiplication Fact

4 groups × 5 each

4 × 5 = 20

1

Stage 1: Guided Equal Groups

Whisper count each hop, then write the product

A. 5 groups of 2

Skip count by 2s five times:

2 • 4 • 6 • 8 •

5 × 2 =

B. 4 groups of 5

Skip count by 5s four times:

5 • 10 • 15 •

4 × 5 =

C. 3 groups of 10

Skip count by 10s three times:

10 • 20 •

3 × 10 =

2

Stage 2: Number Line Jump Equations

Count the hops and jump size to complete the equation

A. Number Line Track (Jump size: +2)

hops × 2 =

0 → 2 → 4 → 6 → 8 → 10 → 12

B. Number Line Track (Jump size: +5)

hops × 5 =

0 → 5 → 10 → 15 → 20 → 25

C. Number Line Track (Jump size: +10)

hops × 10 =

0 → 10 → 20 → 30 → 40

Stage 3: 3-Way Math Bridge

Fill in the missing blocks in each row

Repeated Addition	Skip Count Track	Multiplication Fact
2 + 2 + 2 + 2	2, 4, 6, 8

5 + 5 + 5

| 3 × 5 = 15 | |

| 10, 20, 30, 40, 50 | 5 × 10 = 50 | | 3 + 3 + 3 + 3 | 3, 6, 9, 12 |

|

Key insight: The first factor tells how many hops; the second factor tells the hop size! Page 1 of 2

Skip Count Multiplication • Fluency & Applications

Build automatic fact recall through mental skip counting.

Name:

4

Stage 4: Fact Fluency Sprint

Whisper the jump line, then solve

Jump by 2s

7 × 2 =

Two Digit Multiplication Worksheet

Math Mission Part 1: 2-Digit × 1-Digit

Two-Digit Multiplication

Master standard vertical multiplication with step-by-step regrouping.

Name:

Date:

Score:

/ 15

How-To: Multiply 2-Digit by 1-Digit Numbers

Model Problem: 36 × 4

2

36

×4

144

1

Step 1: Multiply bottom number by ONES digit

4 × 6 = 24. Write the 4 in the ones place. Carry the 2 to the attic above tens.

2

Step 2: Multiply by TENS digit & add carried attic number

4 × 3 = 12. Add the carried 2: 12 + 2 = 14. Write 14. Total = 144.

1

Stage 1: Guided Practice (Follow the Steps)

Fill in the attic and follow the prompts

Problem #1 28 × 3

28

×3

• 3 × 8 = 24

Write 4 in ones, put 2 in attic.

• 3 × 2 = 6, plus 2 =

Write total in tens spot.

Problem #2 45 × 4

45

×4

• 4 × 5 = 20

Write 0 in ones, put 2 in attic.

• 4 × 4 = 16, plus 2 =

Write total in tens spot.

2

Stage 2: Scaffolded Practice (Use the Attic Box)

Remember to add the carried number!

#3

34

×5

#4

52

×4

#5

67

×3

#6

48

×6

3

Stage 3: Independent Practice

Standard layout – write your own carrying numbers

#7

73

×4

#8

85

×2

#9

91

×5

#10

66

×7

Golden Rule: Always multiply first, then add the carried attic number! Page 1 of 2

Part 2: 2-Digit × 2-Digit Multiplication

Master partial products and the crucial placeholder zero.

Name:

How-To: Multiply 2-Digit by 2-Digit (The 4-Step Method)

Model Problem: 24 × 13

Place Value Power Worksheet

Math Mission Multiple Choice Edition

Place Value Power

Select the best answer for each place value question. Fill in the bubble completely.

Name:

Date:

Score:

/ 14

Place Value Houses:

Hundreds: 1 flat = 100 Tens: 1 rod = 10 Ones: 1 unit = 1

1

Base-Ten Block Models

Count the blocks to identify the number

1. What number is shown by the blocks below?

100

A 246

B 264

C 642

D 240

2. What number is shown by the blocks below?

100

(0 rods)

A 430

B 43

C 403

D 304

2

Expanded Form & Unit Form

Select the matching equivalent form

3. What is the expanded form of 583?

A 50 + 80 + 3

B 500 + 80 + 3

C 500 + 8 + 30

D 5 + 8 + 3

4. Which number equals 7 H + 2 T + 9 O?

A 729

B 792

C 927

D 720

5. What is the standard form of 800 + 4?

A 840

B 84

C 804

D 8004

3

Value of Underlined Digit

Pay close attention to position

6. What is the value of the 7 in 672?

A 7

B 70

C 700

D 72

7. What is the value of the 9 in 918?

A 9

B 90

C 900

D 18

Self-Check: Did you shade each bubble clearly? Page 1 of 2

Place Value Power • Part 2: Applications & Logic

Mental math jumps, number comparisons, and place value riddles.

Name:

4

Mental Math Place Shifts (±10, ±100)

Select the correct jump result

8. What is 10 more than 385?

A 485

B 395

C 386

D 375

9. What is 100 less than 724?

A 714

B 624

C 824

D 723

10. What is 10 less than 500?

Stepwise Math Method Notes

Reference Guide Keep in Math Binder

Stepwise Math Method Notes

Clear, step-by-step breakdowns for addition, place value, and multiplication.

Student:

Class:

Part 1: Addition & Place Value

1

Double-Digit Addition: Step-by-Step Algorithm

Always Start with Ones!

Case A: Regrouping (Sum ≥ 10) 47 + 28

1 ← Attic Box

47

+28

75

Case B: No Regrouping (Sum ≤ 9) 52 + 34

52

+34

86

Step 1: Add the Ones Column First

Look at 7 + 8 = 15. Ask: Is this sum 10 or greater?

• If YES → Regroup! Leave the 5 ones, send 1 ten up to the attic.

• If NO → Write the sum directly below in the ones place.

Step 2: Carry the Ten (The Attic Box)

Write the carried 1 in the small attic box directly above the tens digit. Never forget it!

Step 3: Add the Tens Column

Add all tens digits together: 1 (attic) + 4 + 2 = 7 tens. Write 7 in the tens spot.

2

Place Value & Number Forms Breakdown

Standard Form: 648

Hundreds Place (H)

Digit: 6

Means: 6 Hundreds (flats)

Value = 600

Tens Place (T)

Digit: 4

Means: 4 Tens (rods)

Value = 40

Ones Place (O)

Digit: 8

Means: 8 Ones (units)

Value = 8

• Expanded Form: 600 + 40 + 8 = 648

• Word Form: Six hundred forty-eight

Mental Shift Rule: Adding/subtracting 10 changes only the Tens digit (e.g. 648 → 658). Adding/subtracting 100 changes only the Hundreds digit (e.g. 648 → 748).

Key Reminder: In addition, work right-to-left (Ones first). In comparison, work left-to-right (Hundreds first). Page 1 of 2

Stepwise Math Method Notes • Part 2: Multiplication

Step-by-step algorithms for skip counting bridges, 2-digit × 1-digit, and 2-digit × 2-digit.

Part 2: Multiplication Algorithms

3

The Skip Counting Bridge to Multiplication

Story Problem Solver Worksheet

Math Mission Step-by-Step Story Problems

Story Problem Solver

Break down word problems using clues, bar models, and vertical calculation frames.

Name:

Date:

Score:

/ 10

The 4-Step Word Problem Protocol

Follow Every Step

1

Underline & Circle

Circle numbers, underline the question.

2

Spot Clue Words

Sum, in all = + • Left, less = -

3

Draw Bar Model

Part + Part = Whole diagram.

4

Solve & Label

Write equation and unit sentence.

1 Mission #1: The Bakery Order

Guided Addition Walkthrough

The school bakery baked 48 chocolate cupcakes in the morning. In the afternoon, they baked 37 vanilla cupcakes. How many cupcakes did the bakery bake altogether?

Step 1: Clue Numbers

Numbers: 48 and 37

Step 2: Clue Word & Operation

"altogether" means combine!

Operation: +

Step 3: Part-Part-Whole Model

Total Cupcakes: ?

48

37

Part + Part = Whole

Step 4: Vertical Calculation

48

+37

Complete Sentence Answer:

The bakery made cupcakes altogether.

2 Mission #2: Weekend Reading

Scaffolded Addition

Marcus read 56 pages of his book on Saturday and 29 pages on Sunday. How many pages did Marcus read in total over the weekend?

Clue Word: "in total"

Operation: [ + ]

Equation: 56 + 29 = ?

Fill in the Bar Model:

Total Pages: [ ? ]

56

29

Vertical Solve

56

+29

Complete Sentence Answer:

Marcus read pages in total.

Self-Check: Did you carry 1 ten when the ones column added up to 10 or more? Page 1 of 2

Story Problem Solver • Part 2: Subtraction & Comparisons

Step-by-step subtraction with regrouping (borrowing) and comparison models.

Name:

Subtraction Clues:

Keywords: left, remain, difference, fewer More on the floor? Go next door and get 10 more!

Multi Step Word Problem Notes

5th Grade Math Unit 1, Lesson 14 • Guided Notes

Multi-Step Word Problem Notes

Master multi-step problems using the CUBS strategy and Known & Unknown charts.

Name:

Team:

Adapted from Illustrative Math

The C-U-B-S Problem-Solving Strategy

Close Reading Protocol

C

Circle Numbers

Circle every number AND its unit (e.g., 48 trays).

U

Underline Clues

Underline key action words (same number, each, in all).

B

Bracket Question

[Bracket] what you are solving for: [How many cupcakes...?]

S

State Sentence

State answer in a full sentence with units. Check if reasonable.

The Known & Unknown Chart (K-U Organizer)

Unpack Before Solving

KNOWN (Given Facts from the Text)

List every circled quantity and key condition. Exactly what amounts are provided?

UNKNOWN (Hidden Question & Final Goal)

• Hidden Question: What must I calculate first?
• Final Goal: What does the bracketed question demand?

Task 1 Model: Applying CUBS and the Known & Unknown Chart

Classroom Anchor Problem

• CUBS Annotated Text: A bakery has 48 trays. The trays will be placed in 4 display cabinets so that each cabinet has the same number of trays. Each tray can hold 16 cupcakes. [How many cupcakes can be displayed in each cabinet?]

Known (Given Facts)	Unknown (Target & Hidden Step)
• Total trays = 48 trays
• Display cabinets = 4 cabinets (equal sharing)
• Capacity per tray = 16 cupcakes/tray	• Hidden Question: How many trays per cabinet?
• Final Goal: Cupcakes per cabinet = ?

Pathway 1: Divide First

1. 48 trays ÷ 4 cabinets = 12 trays/cabinet

2. 12 trays × 16 cupcakes = 192 cupcakes

Pathway 2: Multiply First

1. 48 trays × 16 cupcakes = 768 total cupcakes

Skip Counting Sprint • Advanced Patterns

Reverse counts, mystery rules, and real-world counting missions.

Name:

4

Stage 4: Chart Snippets (Missing Values)

Fill in every empty box

Pattern A (+2s) from 42

42

44

48

52

54

Pattern B (+5s) from 65

65

75

80

90

100

Pattern C (+10s) from 110

110

130

140

160

180

5

Stage 5: Backward Leap Challenge

Jump in reverse – numbers get smaller!

A. Count back by 2s:

(-2 each step)

30 ← 28 ←

←

← 22 ←

B. Count back by 5s:

(-5 each step)

60 ← 55 ←

←

← 40 ←

C. Count back by 10s:

(-10 each step)

100 ← 90 ←

←

← 60 ←

Stage 6: Pattern Detective (Find the Rule!)

Investigation

18, 20, 22, 24, 26 ...

What is the rule?

Next 2 numbers:

45, 50, 55, 60, 65 ...

What is the rule?

Next 2 numbers:

30, 40, 50, 60, 70 ...

What is the rule?

Next 2 numbers:

3, 6, 9, 12, 15 ...

What is the rule?

Next 2 numbers:

Stage 7: Real-World Mission

Farmer Dan packed eggs into cartons of 10. He packed 7 full cartons. How many total eggs did Farmer Dan pack?

Count by 10s (7 times):

10, 20, 30, 40, 50, 60, ...

Total: eggs

Self-Assessment: [ ] Speedy Skipper • [ ] Getting the Rhythm • [ ] Need a Guide Page 2 of 2

2, 4, 6, 8, 10, 12, 14

Jump by 5s

6 × 5 =

5, 10, 15, 20, 25, 30

Jump by 10s

8 × 10 =

10, 20, 30 ... 80

Jump by 3s

4 × 3 =

3, 6, 9, 12

Jump by 2s

9 × 2 =

2, 4, 6 ... 18

Jump by 5s

7 × 5 =

5, 10 ... 35

Jump by 10s

6 × 10 =

10, 20 ... 60

Jump by 3s

5 × 3 =

3, 6, 9, 12, 15

Stage 5: Array Jump Explorer (Turn-Around Facts)

Commutative Property

A. 3 rows of 4

• • • • (row 1: 4)

• • • • (row 2: 8)

• • • • (row 3: 12)

Skip count by 4s: 4, 8, 12

Fact:

3 × 4 =

B. 4 rows of 3

• • • (row 1: 3)

• • • (row 2: 6)

• • • (row 3: 9)

• • • (row 4: 12)

Skip count by 3s: 3, 6, 9, 12

Turn-Around Fact:

4 × 3 =

Notice: Both give the exact same total sum!

6

Stage 6: Real-World Word Missions

Show your skip counting whisper line and equation

Mission 1: Sticker Packs

Leo bought 6 packs of stickers. Each pack has 5 stickers. How many stickers does Leo have altogether?

Skip count line (6 jumps of 5):

6 × 5 = stickers total

Mission 2: Spider Legs

Every spider has 8 legs. Sofia spotted 4 spiders in the garden. How many legs are there in all?

Skip count line (4 jumps of 8):

4 × 8 = legs total

Self-Assessment: [ ] Multiplication Master • [ ] Practicing Jumps • [ ] Need more practice Page 2 of 2

24

×13

(24 × 3) → 72

(24 × 10) → 240

Sum → 312

1

Multiply bottom ONES digit (3): 3 × 24 = 72. (First partial product).

2

CRITICAL STEP: Place the "Placeholder Zero (0)" in the ones column of the second row because we are now multiplying by 1 ten (10)!

3

Multiply bottom TENS digit (1): 1 × 24 = 24. With the zero, this is 240.

4

Add the two partial products: 72 + 240 = 312.

4

Stage 4: Guided Partial Products

Notice the placeholder 0 is already placed for you!

#11: 32 × 14 Placeholder Zero Pre-placed

32

×14

0

• Row 1: Multiply 4 × 32

• Row 2: Multiply 1 × 32 (with 0)

• Row 3: Add Row 1 + Row 2

#12: 23 × 21 Placeholder Zero Pre-placed

23

×21

0

• Row 1: Multiply 1 × 23

• Row 2: Multiply 2 × 23 (with 0)

• Row 3: Add Row 1 + Row 2

5

Stage 5: Independent Practice

Don't forget to write your own placeholder zero!

#13

42

×15

#14

35

×23

#15

51

×32

Stage 6: Real-World Delivery Mission

A book publisher ships 24 boxes of math textbooks to a school. Each box contains 18 textbooks. How many textbooks were shipped in total?

24 × 18 =

books

Self-Assessment: [ ] Multiplication Pro • [ ] Remember the Zero! • [ ] Need more practice Page 2 of 2

(Regrouping across zero!)

A 490

B 400

C 510

D 499

5

Comparing Numbers (<, >, =)

Check the greatest place value first

11. Which symbol correctly compares 462 [ ] 426?

A <

B >

C =

D +

12. Which comparison statement is TRUE?

A 581 > 589

B 300+40 = 340

C 607 > 670

D 819 < 812

6

Place Value Mystery Riddles

Use the H-T-O scratchpad to test each clue

13. "My hundreds digit is 4. My tens digit is double my hundreds digit. My ones digit is 1. What number am I?"

HTO

A 481

B 421

C 841

D 441

14. "I have 16 tens and 5 ones. (Hint: Regroup 10 tens into 1 hundred!). What number am I?"

HTO

A 165

B 1065

C 765

D 215

Self-Assessment: [ ] All correct! • [ ] Missed 1-2 • [ ] Need more review Page 2 of 2

Groups × Size

1. Meaning

4 × 5

"4 equal groups of 5"

2. Whisper Track

5, 10, 15, 20

(Take 4 jumps of 5)

3. Product

Product = 20

4 × 5 = 20

Turn-Around Rule (Commutative Property): Factors can flip order and product stays identical! 4 × 5 = 5 × 4 = 20

4

Standard Multiplication Algorithms

2-Digit × 1-Digit & 2-Digit × 2-Digit

Method A: 2-Digit × 1-Digit 36 × 4

2 ← carried 2

36

×4

144

Step 1: Multiply bottom number by ONES: 4 × 6 = 24. Write 4 in ones, carry 2 to attic.

Step 2: Multiply bottom number by TENS: 4 × 3 = 12.

Step 3: Add the attic number: 12 + 2 = 14. Write 14 in tens/hundreds.

Method B: 2-Digit × 2-Digit 24 × 13

24

×13

Row 1 (24 × 3) → 72

Row 2 (24 × 10) → 240

Total Sum → 312

Step 1: Multiply 3 × 24 = 72 (First partial product).

Step 2 (HERO ZERO): Place a 0 in Row 2 ones place!

Step 3: Multiply 1 × 24 = 24 (gives 240 with the zero).

Step 4: Add partial products: 72 + 240 = 312.

Master Checklist: 4 Common Pitfalls to Avoid

×

Pitfall 1: Forgetting the carried attic number. Always write it down immediately above the tens column, and circle it so you remember to add it!

×

Pitfall 2: Forgetting the placeholder zero. In 2-digit × 2-digit, Row 2 represents tens! Write your placeholder zero before multiplying.

×

Pitfall 3: Adding before multiplying. In 2-digit multiplication with regrouping, multiply digits first, then add the carried amount.

×

Pitfall 4: Misaligning columns. Keep your Hundreds, Tens, and Ones lined up in vertical grid tracks to avoid adding the wrong places.

Method Note: Review these 4 steps before every quiz and test! Page 2 of 2

Regrouping Rule:

3 Mission #3: The Toy Store Shelf

Guided Subtraction with Regrouping

The toy store had 72 wooden puzzles on the shelf. By evening, customers bought 38 puzzles. How many puzzles were left on the shelf?

Starting Whole: 72 puzzles

Part Taken Away: 38 puzzles

Clue: "left" → Subtract (-)

Part-Part-Whole Model:

Total Puzzles: 72

Sold: 38

Left: [ ? ]

Vertical Borrowing Frame

7 12

72

-38

Complete Sentence Answer:

There were puzzles left on the shelf.

4 Mission #4: Stamp Collector Showdown

Comparison Model

Emma collected 64 colorful stamps. Liam collected 47 stamps. How many more stamps did Emma collect than Liam?

Comparison Bars:

Emma:

64 stamps

Liam:

47

Diff [ ? ]

64 - 47

64

-47

Complete Sentence Answer:

Emma collected more stamps than Liam.

5 Mission #5: Fresh Fruit Stand (You Choose the Operation!)

Decision Challenge

A local fruit stand had 85 fresh oranges. They sold 56 oranges before lunch. How many oranges remain?

Check the correct operation:

Addition (+) Subtraction (-)

Equation:

Answer: oranges remain

Self-Assessment: [ ] Word Problem Pro • [ ] Can identify operations • [ ] Need more practice Page 2 of 2

2. 768 cupcakes ÷ 4 cabinets = 192 cupcakes

State Answer Sentence (S): "There can be 192 cupcakes displayed in each cabinet."

Golden Habit: Fill out your Known & Unknown chart BEFORE touching your calculator or pencil to solve! Page 1 of 2

Multi-Step Word Problem Notes • Part 2: Applications & Remainders

Execute CUBS and K-U charts across common archetypes and real-world remainder situations.

Lesson 14 Reference Guide

Mission 1: Package & Distribute (Multiply → Divide)

Independent Practice #1

There are 12 packages of jerseys. Each package has 24 jerseys. The manager will give 16 jerseys to each team. [What is the number of teams in the league?]

Known	Unknown
12 packs • 24 jerseys/pack • 16 jerseys/team	Hidden: Total jerseys
Target: [Number of teams]

1. 12 × 24 = 288 total jerseys

2. 288 ÷ 16 = 18 teams

State Sentence (S): "There are 18 teams in the league."

Mission 2: Interpreting Remainders — Round UP

Independent Practice #12

A school has 12 homerooms with 31 people each. Buses each hold 42 people. [How many buses are needed?] • [How many empty seats will there be?]

Known	Unknown
12 rooms • 31 people/room • 42 people/bus	Hidden: Total people
Targets: [Buses] and [Empty seats]

1. 12 × 31 = 372 total people

2. 372 ÷ 42 = 8 R 36 → 9 buses

3. (9 × 42) - 372 = 378 - 372 = 6 seats

State Sentence (S): "The school needs 9 buses, and there will be 6 empty seats."

Mission 3: Interpreting Remainders — Drop Remainder

Independent Practice #13

A pizza shop has 15 packages of pepperoni with 36 slices each. Each pie needs 28 slices. [How many pies can they make?] • [How many extra slices are left?]

Known	Unknown
15 packs • 36 slices/pack • 28 slices/pie	Hidden: Total slices
Targets: [Pies made] and [Extra slices]

1. 15 × 36 = 540 total slices

2. 540 ÷ 28 = 19 R 8 → 19 full pies

3. Remainder = 8 extra slices

State Sentence (S): "The shop can make 19 pepperoni pies, and 8 slices will be left over."

The only way to learn mathematics is to do mathematics. • Uncommon Schools Math Team Page 2 of 2

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A comprehensive multi-day division unit introducing students to the partial quotients method with one-digit divisors. The sequence moves from conceptual area models and friendly multiplication chunks to the standard Big Seven algorithm, remainder problem solving, and error analysis.

DM

Deborah Marshall

9

Array and Strategy Stations

Days 1 and 2 of the multiplication station rotation circuit focusing on concrete array construction, area models, equal grouping strategies, and distributive property decomposition across differentiated student tiers.

TA

tara aguilar

3

Fact Power Answer Key

A two-page teacher reference and answer key for the Fact Power Worksheet, featuring completed solutions, strategy explanations, and common misconception notes.

LG

Leslie Gerken

Number Chompers

A comprehensive two-day mathematics sequence for early elementary students focusing on comparing two-digit numbers. Day 1 emphasizes concrete, hands-on place value modeling with base-ten manipulatives and cut-out symbols, while Day 2 cements conceptual mastery through visual representations, structured paper-based practice, and reasoning tasks.

EB

Emily Brown

8

Array Studio Student Passport

A 2-page printable student recording passport for Stations 1 and 2 where students sketch arrays, record equations, demonstrate distributive strategies, and self-assess.

TA