Direct Instruction & Guided Practice

Timing: 25 Mins

I Do: Example 1 — 448 ÷ 16

SLIDE 4

1. Estimate

16 is near 20. \(20 \times 20 = 400\). Target is ~28.

2. Multiples

• 16 × 10 = 160
• 16 × 20 = 320
• 16 × 5 = 80

Sum: 20 + 5 + 3 = 28

I Do: Example 2 — 364 ÷ 14

SLIDE 5

1. Estimate

14 is near 15. \(15 \times 20 = 300\). Target is ~26.

2. Multiples

• 14 × 10 = 140
• 14 × 20 = 280

Sum: 20 + 6 = 26

We Do: Guided Practice (15 Mins) — Selected walkthroughs

SLIDES 6-11, 14-17

1. We Do: 308 ÷ 14 = 22

Estimate first: \(14 \approx 15\). \(15 \times 20 = 300\).

\(14 \times 20 = 280 \implies 308 - 280 = 28 \implies 14 \times 2 = 28\)

Checkpoint: Check if students carried the divisor correctly.

2. We Do: 252 ÷ 12 = 21

Estimate first: \(12 \approx 10\). \(10 \times 20 = 200\).

\(12 \times 20 = 240 \implies 252 - 240 = 12 \implies 12 \times 1 = 12\)

Checkpoint: Ask, "Why was 12 x 20 such an efficient first chunk?"

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Unit 1 • Lesson 6

Collaborative Play, CFU & Triage Check

Timing: 20 Mins

Segment 6: Collaborative Partner Practice (10 Mins)

SLIDE 19

Work in pairs. Estimate first, then solve. Compare chunks with partners.

1. 868 ÷ 14

Quotient: 62

2. 972 ÷ 18

Quotient: 54

3. 1,428 ÷ 21

Quotient: 68

4. 1,764 ÷ 21

Quotient: 84

5. 2,352 ÷ 28

Quotient: 84

6. 1,296 ÷ 24

Quotient: 54

Pair Discussion Prompts "How did your estimate prevent you from making giant subtraction mistakes? Did you and your partner choose different chunks but end up with the same final answer?"

Segment 7: CFU & 100% Triage Check (5 Mins) — 912 ÷ 16

SLIDE 18

Students complete independently. You must check 100% of student answers on this CFU to instantly identify and route them into their target practice levels!

CFU 100% Check & Assignment Guide

Level 1: Under 50% Mastery

Look For: Student has no estimate, or selects extremely small chunks (e.g. \(16 \times 2 = 32\)), leading to massive subtraction chains. ← Assign Level 1

Level 2: Conceptual Mastery

Look For: Student uses correct estimation to subtract 800, but has a simple math error in the subtraction steps. ← Assign Level 2

Level 3: Full Mastery

Look For: Quick, efficient chunking using estimation. Found exactly 57 in 2 clean subtraction steps. ← Assign Level 3

Segment 8: Closure, Summary & Reflection (5 Mins)

SLIDE 23

1. ESTIMATE FIRST Catch big errors early.

2. FRIENDLY MULTIPLES Use 10, 20, 5, and 2.

3. ADD CHUNKS Sum up all partial quotients.

Exit Reflection Task Find \(912 \div 16\) using partial quotients. Show your work and your final quotient on your exit slip!

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Unit 1 • Lesson 6

Independent Practice Exhaustive Key

LEVELS 1 - 3 SOLUTIONS

Level 1 (Slide 20)

1. 540 ÷ 15

15 × 30 = 450 (Rem: 90)

15 × 6 = 90

Ans: 36

2. 432 ÷ 16

16 × 20 = 320 (Rem: 112)

16 × 7 = 112

Ans: 27

3. 672 ÷ 21

21 × 30 = 630 (Rem: 42)

21 × 2 = 42

Ans: 32

4. 396 ÷ 12

12 × 30 = 360 (Rem: 36)

12 × 3 = 36

Ans: 33

Level 2 (Slide 21)

5. 1,428 ÷ 17

17 × 80 = 1360 (Rem: 68)

17 × 4 = 68

Ans: 84

6. 1,176 ÷ 14

14 × 80 = 1120 (Rem: 56)

14 × 4 = 56

Ans: 84

7. 1,092 ÷ 21

21 × 50 = 1050 (Rem: 42)

21 × 2 = 42

Ans: 52

8. 1,260 ÷ 18

18 × 70 = 1260

Ans: 70

Level 3 (Slide 22)

9. 2,856 ÷ 24

24 × 100 = 2400 (Rem: 456)

24 × 10 = 240 (Rem: 216)

24 × 9 = 216

Ans: 119

10. 3,024 ÷ 16

16 × 100 = 1600 (Rem: 1424)

16 × 80 = 1280 (Rem: 144)

16 × 9 = 144

Ans: 189

11. 4,290 ÷ 22

22 × 100 = 2200 (Rem: 2090)

22 × 90 = 1980 (Rem: 110)

22 × 5 = 110

Ans: 195

12. 3,388 ÷ 26

26 × 100 = 2600 (Rem: 788)

26 × 30 = 780 (Rem: 8)

Ans: 130 R 8

Substitute Diagnostic Cheat Sheet (Where are they failing?)

Estimation errors? Students are failing to round the divisor effectively, leading to over-estimating or under-estimating the first friendly multiple. Have them write multiples of the estimated tens first.

Handling Remainders? For Level 3, problem 12, check if students are stopping too early or trying to subtract chunks larger than the remainder. Remind them: "The remainder must be smaller than the divisor."

Dropped zero values? Watch for students dropping digit values in multi-digit sums (e.g., adding 100 + 10 + 9 as 119, but writing it as 1019 or 19). Check place value alignment columns.

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Check: \(12 \times 41 = 492\) ✓

I Do: Example 2 — 153 ÷ 11 (With Remainder)

SLIDE 7

Steps

• D: How many 11s in 15? 1.
• M: \(11 \times 1 = 11\).
• S: \(15 - 11 = 4\).
• B: Bring down 3 → 43.
• Repeat: 11 goes into 43 three times.

Check: \((11 \times 13) + 10 = 153\) ✓

We Do: Guided Practice (15 Mins) — Walkthroughs

SLIDES 8-13

1. We Do: 630 ÷ 15 = 42

How many 15s in 63? 4 (\(15 \times 4 = 60\)).

\(63 - 60 = 3 \implies \text{Bring down } 0 \implies 30 \implies 15 \times 2 = 30\)

Checkpoint: Check for correct alignment of 4 and 2 above the bracket.

2. We Do: 364 ÷ 14 = 26

How many 14s in 36? 2 (\(14 \times 2 = 28\)).

\(36 - 28 = 8 \implies \text{Bring down } 4 \implies 84 \implies 14 \times 6 = 84\)

Checkpoint: Ask, "Why would standard algorithm be faster here than partial quotients?"

Lenny Educational Resources

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Unit 1 • Lesson 7

Collaborative Play, CFU & Triage Check

Timing: 20 Mins

Segment 6: Collaborative Partner Practice (10 Mins)

SLIDE 16

Work in groups of 3-4. Solve using standard algorithm and write one sentence explaining reasonableness.

1. 12,648 ÷ 36

Ans: 351 R 12

2. 10,584 ÷ 22

Ans: 481 R 2

3. 14,850 ÷ 25

Ans: 594

4. 16,428 ÷ 18

Ans: 912 R 12

5. 18,720 ÷ 30

Ans: 624

Post Work Gallery Walk Compare strategies with groups. Ensure students are writing clear sentences checking divisor times quotient + remainder equals dividend.

Segment 7: CFU & 100% Triage Check (5 Mins) — 7,992 ÷ 24

SLIDE 14

Students complete independently on half-sheets. You must check 100% of student answers on this CFU to instantly identify and route them into their target practice levels!

CFU 100% Check & Assignment Guide

Level 1: Under 50% Mastery

Look For: Students who do not know standard setup; misaligned place value digits; unable to run steps. ← Assign Level 1

Level 2: Conceptual Mastery

Look For: Correct setup and steps, but made a minor calculation or subtraction step mistake. ← Assign Level 2

Level 3: Full Mastery

Look For: Clean, fast computation showing exactly 333 with multiplication verification checked. ← Assign Level 3

Segment 8: Closure, Summary & Reflection (5 Mins)

SLIDE 20

1. DMSB Divide, Multiply, Subtract, Bring Down.

2. PLACE VALUE ALIGN Quotient digits line up above values.

3. VERIFY & CHECK Check with division families.

Whole-Class Reflection "What is the most important step in the division algorithm and why? How can multiplication help us catch mistakes?"

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Unit 1 • Lesson 7

Independent Practice Exhaustive Key

LEVELS 1 - 3 SOLUTIONS

Level 1 (Slide 17)

1. 4,356 ÷ 12

12×3=36 (Rem: 7)

12×6=72 (Rem: 3)

12×3=36 (Rem: 0)

Ans: 363

2. 5,940 ÷ 15

15×3=45 (Rem: 14)

15×9=135 (Rem: 9)

15×6=90 (Rem: 0)

Ans: 396

3. 6,468 ÷ 18

18×3=54 (Rem: 10)

18×5=90 (Rem: 16)

18×9=162 (Rem: 6)

Ans: 359 R 6

4. 8,232 ÷ 24

24×3=72 (Rem: 10)

24×4=96 (Rem: 7)

24×3=72 (Rem: 0)

Ans: 343

Level 2 (Slide 18)

6. 12,984 ÷ 36

36×3=108 (Rem: 21)

36×6=216 (Rem: 2)

36×0=0 (Rem: 24)

Ans: 360 R 24

7. 14,256 ÷ 42

42×3=126 (Rem: 16)

42×3=126 (Rem: 39)

42×9=378 (Rem: 18)

Ans: 339 R 18

8. 17,910 ÷ 45

45×3=135 (Rem: 44)

45×9=405 (Rem: 36)

45×8=360 (Rem: 0)

Ans: 398

9. 21,684 ÷ 27

27×8=216 (Rem: 0)

27×0=0 (Rem: 8)

27×3=81 (Rem: 3)

Ans: 803 R 3

Level 3 (Slide 19)

11. 32,864 ÷ 56

56×5=280 (Rem: 48)

56×8=448 (Rem: 38)

56×6=336 (Rem: 48)

Ans: 586 R 48

12. 45,792 ÷ 64

64×7=448 (Rem: 9)

64×1=64 (Rem: 35)

64×5=320 (Rem: 32)

Ans: 715 R 32

13. 50,960 ÷ 80

80×6=480 (Rem: 29)

80×3=240 (Rem: 56)

80×7=560 (Rem: 0)

Ans: 637

14. 62,496 ÷ 72

72×8=576 (Rem: 48)

72×6=432 (Rem: 57)

72×8=576 (Rem: 0)

Ans: 868

Substitute Diagnostic Cheat Sheet (Where are they failing?)

Place value alignment errors? Students are failing to write 0 in the quotient when the divisor is too large for the sub-step remainder (e.g. Problem 6). Prompt: "Use placeholder zero."

Handling zero subtraction? If subtraction results in 0, make sure they still drop the next digit down properly rather than starting a new bracket step completely.

Computation checks? Students must multiply quotient × divisor and add remainder to ensure it equals the exact dividend. Make this mandatory for Level 1 small groups.

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Timing: 25 Mins

I Do: Example 1 — 972 ÷ 18 (No Remainder)

SLIDE 6

Steps

• D: How many 18s in 97? 5.
• M: \(18 \times 5 = 90\).
• S: \(97 - 90 = 7\).
• B: Bring down 2 → 72.
• Repeat: 18 goes into 72 exactly 4 times.

Check: \(18 \times 54 = 972\) ✓

I Do: Example 2 — 747 ÷ 24 (With Remainder)

SLIDE 7

Steps

• D: How many 24s in 74? 3.
• M: \(24 \times 3 = 72\).
• S: \(74 - 72 = 2\).
• B: Bring down 7 → 27.
• Repeat: 24 goes into 27 once.

Check: \((24 \times 31) + 3 = 747\) ✓

We Do: Guided Practice — Walkthroughs

SLIDES 9-12

1. We Do: 768 ÷ 16 = 48

How many 16s in 76? 4 (\(16 \times 4 = 64\)).

\(76 - 64 = 12 \implies \text{Bring down } 8 \implies 128 \implies 16 \times 8 = 128\)

2. We Do: 1,307 ÷ 29 = 45 R 2

How many 29s in 130? 4 (\(29 \times 4 = 116\)).

\(130 - 116 = 14 \implies \text{Bring down } 7 \implies 147 \implies 29 \times 5 = 145 \implies \text{Rem: } 2\)

Lenny Educational Resources

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Unit 1 • Lesson 8

Collaborative Play, CFU & Triage Check

Timing: 20 Mins

Segment 6: Collaborative Partner Practice — Remainder Rumble (10 Mins)

SLIDE 16

Remainder Rumble! Roll dice, standard algorithm divide. The remainder equals student points. Play 5 rounds.

We Do 3. 8,715 ÷ 21

Ans: 415

We Do 4. 6,575 ÷ 53

Ans: 124 R 3

Partner Checking Mnemonic

\((\text{Divisor} \times \text{Quotient}) + \text{Remainder} = \text{Dividend}\)

Remainder Rumble Peer Check Script "Encourage students to act as math auditors for their partners, verifying each round's calculations before awarding points!"

Segment 7: CFU & 100% Triage Check (5 Mins) — 1,656 ÷ 46

SLIDE 8, 14

Students complete independently on half-sheets. You must check 100% of student answers on this CFU to instantly identify and route them into their target practice levels!

CFU 100% Check & Assignment Guide

Level 1: Under 50% Mastery

Look For: Students who try dividing 46 into 16; misaligned place value digits; cannot run subtract-bring down steps. ← Assign Level 1

Level 2: Conceptual Mastery

Look For: Setup is 100% correct, but student made a basic computation/subtraction error. ← Assign Level 2

Level 3: Full Mastery

Look For: Extremely fast, neat computation showing exactly 36 with standard verification check. ← Assign Level 3

Segment 8: Closure, Summary & Reflection (5 Mins)

SLIDE 20

1. FIVE STEPS REPEAT DMSB, repeat until empty.

2. INTERPRET REMAINDER Remainder is always < divisor.

3. ALWAYS CHECK Verify with reverse calculation.

Whole-Class Reflection "What is the trickiest step in standard algorithm and why? How does checking our answer with multiplication help us find precise errors?"

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Unit 1 • Lesson 8

Independent Practice Exhaustive Key

LEVELS 1 - 3 SOLUTIONS

Level 1 (Slide 17)

1. 4,356 ÷ 12

12×3=36 (Rem: 7)

12×6=72 (Rem: 3)

12×3=36 (Rem: 0)

Ans: 363

2. 5,940 ÷ 15

15×3=45 (Rem: 14)

15×9=135 (Rem: 9)

15×6=90 (Rem: 0)

Ans: 396

3. 6,468 ÷ 18

18×3=54 (Rem: 10)

18×5=90 (Rem: 16)

18×9=162 (Rem: 6)

Ans: 359 R 6

4. 8,232 ÷ 24

24×3=72 (Rem: 10)

24×4=96 (Rem: 7)

24×3=72 (Rem: 0)

Ans: 343

Level 2 (Slide 18)

6. 12,984 ÷ 36

36×3=108 (Rem: 21)

36×6=216 (Rem: 2)

36×0=0 (Rem: 24)

Ans: 360 R 24

7. 14,256 ÷ 42

42×3=126 (Rem: 16)

42×3=126 (Rem: 39)

42×9=378 (Rem: 18)

Ans: 339 R 18

8. 17,910 ÷ 45

45×3=135 (Rem: 44)

45×9=405 (Rem: 36)

45×8=360 (Rem: 0)

Ans: 398

9. 21,684 ÷ 27

27×8=216 (Rem: 0)

27×0=0 (Rem: 8)

27×3=81 (Rem: 3)

Ans: 803 R 3

Level 3 (Slide 19)

11. 32,864 ÷ 56

56×5=280 (Rem: 48)

56×8=448 (Rem: 38)

56×6=336 (Rem: 48)

Ans: 586 R 48

12. 45,792 ÷ 64

64×7=448 (Rem: 9)

64×1=64 (Rem: 35)

64×5=320 (Rem: 32)

Ans: 715 R 32

13. 50,960 ÷ 80

80×6=480 (Rem: 29)

80×3=240 (Rem: 56)

80×7=560 (Rem: 0)

Ans: 637

14. 62,496 ÷ 72

72×8=576 (Rem: 48)

72×6=432 (Rem: 57)

72×8=576 (Rem: 0)

Ans: 868

Substitute Diagnostic Cheat Sheet (Where are they failing?)

dropped zeros? Make sure students are writing 0 in the quotient when subtracting (e.g. Problem 6). A skipped place value shifts the entire product row!

Remainder checks? Students frequently fail to bring down the remaining digits after finding a remainder, stopping prematurely. Prompt: "Are there digits left to drop?"

Verification check? Multiplication checks must be explicitly run to prove mastery before students can claim completion on Level 3 exercises.

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6. Check for Understanding Gate (5 Mins) — 1,656 ÷ 46 Slide 8, 14

Triage Execution: Administer the problem 1,656 ÷ 46 on half-sheets. You must check 100% of student papers before they can move to independent work.

Level 1 (<50% Correct) Setup or place value steps broken. Fails to run algorithm correctly. Action: Small Group pull

Level 2 (Concept Ready) Setup and steps are correct, but has simple math error. Action: Self-correct error

Level 3 (100% Mastery) Solved 36 cleanly. Showed reverse multiplication proof. Action: Peer Coach / Level 3

7. Independent Practice: Leveled Practice (15 Mins) Slides 17-19

Teacher Action: Release students to their diagnosed Level 1, 2, or 3 practice sheets. Pull Level 1 students to the back table for direct modeling and guided multiplication support.

8. Closure, Summary & Reflection (5 Mins) Slide 20

Teacher Action: Synthesize learning objectives. Read reflection aloud and take 3 hands.

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D. 14,256 ÷ 42 = 339 R 18

\(42 \times 300 = 12600 \implies \text{Rem: } 1656\); \(42 \times 30 = 1260 \implies \text{Rem: } 396\); \(42 \times 9 = 378\)

E. 62,496 ÷ 72 = 868

\(72 \times 800 = 57600 \implies \text{Rem: } 4896\); \(72 \times 60 = 4320 \implies \text{Rem: } 576\); \(72 \times 8 = 576\)

F. 864 ÷ 24 = 36 books per shelf

\(24 \times 30 = 720 \implies \text{Rem: } 144\); \(24 \times 6 = 144\)

4. Closure, Summary & Reflection (5 Mins) SLIDE 5

Summarize division rules: DMSB, remainders smaller than divisors, and inverse multiplication checks.

Quick Reflection Script "How did running our reverse multiplication checks prevent us from making small addition/subtraction slips on our assessments today?"

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Unit 1 • Lesson 9

Direct Instruction & Guided Practice

Timing: 25 Mins

I Do: Order of Operations: PEMDAS Rules

SLIDE 6

Introduce PEMDAS. Highlight that Multiplication/Division and Addition/Subtraction have equal priority and are evaluated left-to-right.

Mnemonic

"Please Excuse My Dear Aunt Sally"

• P: Parentheses / Brackets [ ]
• E: Exponents
• M/D: Multiply / Divide
• A/S: Add / Subtract

Common Mistake Alert

Wrong: \(6 + 2 \times 3 \implies 8 \times 3 = 24\)

Correct: \(6 + 2 \times 3 \implies 6 + 6 = 12\)

* Multiply & Divide are EQUAL priority (do left to right)

Guided Practice: Evaluating Expressions

SLIDES 8-11, 14-17

1. I Do & We Do Examples

I Do 1: 8 + 3 × 4

→ 8 + 12 = 20

We Do 1: 15 - 3 × 4

→ 15 - 12 = 3

I Do 2: 20 - (6 + 2) × 2

→ 20 - 8 × 2 = 20 - 16 = 4

2. Left-to-Right Priority Examples

We Do 2: 20 ÷ 4 + 6

→ 5 + 6 = 11

We Do 5: 24 ÷ 6 × 2

*(Divide first because it's on left!)*

→ 4 × 2 = 8

We Do 6: 3 × (12 - 4) + 6

→ 3 × 8 + 6 = 24 + 6 = 30

Processing Check Script "In We Do 5, why did we divide before we multiplied? Multiply does not beat divide! They have equal status, so we simply go from left to right."

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Unit 1 • Lesson 9

Grouping Symbols & Triage Check

Timing: 20 Mins

Part 2: Inserting Parentheses or Brackets

SLIDES 18-22, 24-27

Teach students how to run trial operations to figure out where to place grouping symbols to reach target values.

I Do 1: Target 33

\(4 + 2 \times 6 - 3\)

→ (4 + 2) × 6 - 3 = 33

We Do 1: Target 24

\(3 \times 8 - 2 + 6\)

→ 3 × (8 - 2) + 6 = 24

We Do 2: Target 42

\(5 \times 12 - 4 + 2\)

→ 5 × [12 - 4] + 2 = 42

We Do 4: Target 7

\(10 + 6 \div 2 - 1\)

→ (10 + 6) ÷ 2 - 1 = 7

Segment 7: CFU & 100% Triage Check (5 Mins) — Slide 29

SLIDE 29

Students complete on paper. You must check 100% of student answers on this CFU to instantly identify and route them into their target practice levels!

CFU Answer Key:

1. 32 - 4 × 6 + 8

\(32 - 24 + 8 = 8 + 8 = 16\)

2. (32 - 4) × 6 + 8

\(28 \times 6 + 8 = 168 + 8 = 176\)

3. Write target equals 20

e.g., \((15 - 5) \times 2 = 20\)

CFU 100% Check & Assignment Guide

Level 1: Under 50% Mastery

Fails priority operations (e.g. subtracted \(32-4=28\) first in problem 1). ← Assign Level 1

Level 2: Conceptual Mastery

Used correct PEMDAS steps but made a simple arithmetic multiplication or subtraction error. ← Assign Level 2

Level 3: Full Mastery

100% correct answers with clean work. Correct custom expression. ← Assign Level 3

Lenny Educational Resources

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Unit 1 • Lesson 9

Independent Practice Exhaustive Key

LEVELS 1 - 3 SOLUTIONS

Level 1 (Slide 30)

1. 12 + 4 × 2

\(12 + 8 = 20\)

Ans: 20

2. 15 - 8 ÷ 2

\(15 - 4 = 11\)

Ans: 11

3. (6 + 4) × 3

\(10 \times 3 = 30\)

Ans: 30

4. 24 ÷ (2 × 3)

\(24 \div 6 = 4\)

Ans: 4

Level 2 (Slide 30)

5. (18 - 6) ÷ 3 × 2

\(12 \div 3 \times 2 = 4 \times 2 = 8\)

Ans: 8

6. 5 × (4 + 6) - 12

\(5 \times 10 - 12 = 50 - 12 = 38\)

Ans: 38

7. Parentheses for 36

\(6 + 3 \times 4 = 36\)

\((6 + 3) \times 4 = 36\)

Ans: (6+3) × 4

8. \(45 \div 5 \times 3 - 2\)

\(9 \times 3 - 2 = 27 - 2 = 25\)

Ans: 25

Level 3 (Slide 30)

9. 4 × [15 - (3 + 2)] ÷ 8

\(4 \times [15 - 5] \div 8\)

\(4 \times 10 \div 8 = 40 \div 8 = 5\)

Ans: 5

10. 36 ÷ [2 × (12 - 9)] + 5

\(36 \div [2 \times 3] + 5\)

\(36 \div 6 + 5 = 6 + 5 = 11\)

Ans: 11

11. Write Expression

Double the sum of 8 and 4, then subtract 5.

Ans: 2 × (8 + 4) - 5

12. Brackets for 32

\(2 \times 3 + 5 \times 2 = 32\)

\(2 \times (3 + 5) \times 2 = 32\)

Ans: 2 × (3+5) × 2

Substitute Diagnostic Cheat Sheet (Where are they failing?)

PEMDAS Myths? Students frequently evaluate multiplication before division purely because M precedes D in PEMDAS. Reiterate they have equal priority, solved left to right!

Dropped groupings? Make sure brackets [ ] and parentheses ( ) are solved completely from inside out before running outer operations.

Target value checks? When inserting parentheses to hit target values, make sure students evaluate their complete trial expressions rather than guessing.

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I Do: Interpret an Expression — \(4 \times (12 + 7)\)

SLIDE 8

Interpretation Steps

1. See the outer operation: 4 times something.
2. Analyze inside parentheses: sum of 12 and 7.
3. Combine into verbal sentence: "4 times the sum of 12 and 7."

Additional Examples

\(5 \times (30 + 9) \implies\) "5 times the sum of 30 and 9"

No need to solve to interpret!

We Do: Guided Write & Interpret Walkthroughs

SLIDES 14-17, 19-21

1. Translating Verbal to Codes

"Subtract 4 from 20, then multiply by 6."

→ (20 - 4) × 6

"Multiply 7 by 5, then add 13."

→ (7 × 5) + 13

2. Translating Codes to Verbal

\((80 - 32) \times 5\)

→ "5 times the difference of 80 and 32"

\((3 \times 14) + 50\)

→ "The product of 3 and 14, plus 50"

Lenny Educational Resources

Page 2 of 4

Unit 1 • Lesson 10

Grouping Symbols & Triage Check

Day 2 Execution

Compare Without Evaluating — Size Relationships

SLIDES 10-11, 22-23

Teach students to compare expression sizes by identifying scaling factors, completely avoiding calculation.

I Do: \(3 \times (18,932 + 921)\) vs. \((18,932 + 921)\)

"Multiplying the sum by 3 makes it exactly 3 times as large as the original sum. No addition is required."

→ 3 times the size

We Do: Is \((12 + 8) \times 6\) twice as large as \((12 + 8) \times 3\)?

"Since \(6 = 2 \times 3\), multiplying by 6 means there are twice as many groups of the sum."

→ Yes, twice as large

Segment 7: CFU & 100% Triage Check (5 Mins) — Slide 24

SLIDE 24

Students complete on paper. You must check 100% of student answers on this CFU to instantly identify and route them into their target practice levels!

CFU Answer Key:

A. "Subtract 15 from 60, then multiply by 4."

→ (60 - 15) × 4

B. Interpret: \(8 \times (25 + 14)\)

→ "8 times the sum of 25 and 14"

C. Compare: Is \(7 \times (100 + 50)\) seven times as large?

→ Yes, multiplying by 7 creates 7 groups.

CFU 100% Check & Assignment Guide

Level 1: Under 50% Mastery

Writes expressions without parentheses (e.g. \(60 - 15 \times 4\)); misses basic translation terms. ← Assign Level 1

Level 2: Conceptual Mastery

Swaps values (writes \(15-60\) instead of \(60-15\)) but has parenthetical structure. ← Assign Level 2

Level 3: Full Mastery

100% perfect translation and justification for Task C. ← Assign Level 3

Lenny Educational Resources

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Unit 1 • Lesson 10

Independent Practice Exhaustive Key

LEVELS 1 - 3 SOLUTIONS

Level 1 (Slide 27)

1. Write: Add 6 and 9, then multiply by 5.

Ans: (6 + 9) × 5

2. Write: Subtract 8 from 30, then multiply by 2.

Ans: (30 - 8) × 2

3. Write: Multiply 4 by 7, then add 10.

Ans: (4 × 7) + 10

4. Interpret: (5 + 3) × 9

Ans: 9 times the sum of 5 and 3

5. Interpret: 7 × (20 - 4)

Ans: 7 times the difference of 20 and 4

Level 2 (Slide 28)

6. Write: Add 25 and 15, then divide by 4.

Ans: (25 + 15) ÷ 4

7. Write: Multiply sum of 18 and 7 by 6.

Ans: (18 + 7) × 6

8. Interpret: 8 × (14 + 36)

Ans: 8 times the sum of 14 and 36

9. Interpret: (90 - 25) × 4

Ans: 4 times the difference of 90 and 25

10. Compare size

Ans: Yes, multiplying by 4 makes it 4 times as large.

Level 3 (Slide 29)

11. Write: Multiply 7 by sum of 124 and 39.

Ans: 7 × (124 + 39)

12. Write: Difference of 500 and 85, divided by 5.

Ans: (500 - 85) ÷ 5

13. Explain 2 × sum size

Ans: Multiplying by 2 means there are 2 equal groups of that sum, making it twice as large.

14. Reza's claim

Ans: Yes, correct due to commutative property of multiplication.

15. 2 Verbal statements for \( 5 \times (40 - 16) \)

Ans: 1) "5 times the difference of 40 and 16" and 2) "Subtract 16 from 40, then multiply by 5."

Substitute Diagnostic Cheat Sheet (Where are they failing?)

Missing parenthesis? Students drop parenthesis because they think the left-to-right reading order naturally handles addition first. Counter-example: \(5 \times 12 - 4\).

Evaluating instead of interpreting? Make sure students are writing clear verbal sentences explaining size relationships, rather than calculating long math sums to verify.

Over-complicating sum groups? For scaling questions, emphasize that \(A \times B\) means "A groups of B". Thus, \(5 \times \text{sum}\) is exactly 5 times as large as 1 group of that sum.

Lenny Educational Resources

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