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Chapter 3: Composing and Decomposing Numbers

Learn Grade 2 mathematics with very-beginner explanations, original worked examples, practice, reasoning, and review.

Grade 2Very Beginner Friendly10 Examples Per Topic30 Q&APractice + Review
Estimated reading time0% read
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Chapter Overview

This chapter teaches Composing and Decomposing Numbers with simple explanations, visual thinking, worked examples, practice, and review.

3.1 Composing two-digit numbers

Place value tells how much a digit is worth because of its position in a number. Use objects, drawings, number lines, tables, or number sentences when useful.

10 Worked Examples with Answers

Worked Example 1

Problem: How many hundreds, tens, and ones are in 137?

  1. Read the hundreds digit.
  2. Read the tens digit.
  3. Read the ones digit.

Very beginner explanation: Position tells place value.

Answer: 1 hundred, 3 tens, 7 ones

Worked Example 2

Problem: How many hundreds, tens, and ones are in 185?

  1. Read the hundreds digit.
  2. Read the tens digit.
  3. Read the ones digit.

Very beginner explanation: Position tells place value.

Answer: 1 hundred, 8 tens, 5 ones

Worked Example 3

Problem: How many hundreds, tens, and ones are in 180?

  1. Read the hundreds digit.
  2. Read the tens digit.
  3. Read the ones digit.

Very beginner explanation: Position tells place value.

Answer: 1 hundred, 8 tens, 0 ones

Worked Example 4

Problem: How many hundreds, tens, and ones are in 184?

  1. Read the hundreds digit.
  2. Read the tens digit.
  3. Read the ones digit.

Very beginner explanation: Position tells place value.

Answer: 1 hundred, 8 tens, 4 ones

Worked Example 5

Problem: How many hundreds, tens, and ones are in 145?

  1. Read the hundreds digit.
  2. Read the tens digit.
  3. Read the ones digit.

Very beginner explanation: Position tells place value.

Answer: 1 hundred, 4 tens, 5 ones

Worked Example 6

Problem: How many hundreds, tens, and ones are in 152?

  1. Read the hundreds digit.
  2. Read the tens digit.
  3. Read the ones digit.

Very beginner explanation: Position tells place value.

Answer: 1 hundred, 5 tens, 2 ones

Worked Example 7

Problem: How many hundreds, tens, and ones are in 130?

  1. Read the hundreds digit.
  2. Read the tens digit.
  3. Read the ones digit.

Very beginner explanation: Position tells place value.

Answer: 1 hundred, 3 tens, 0 ones

Worked Example 8

Problem: How many hundreds, tens, and ones are in 169?

  1. Read the hundreds digit.
  2. Read the tens digit.
  3. Read the ones digit.

Very beginner explanation: Position tells place value.

Answer: 1 hundred, 6 tens, 9 ones

Worked Example 9

Problem: How many hundreds, tens, and ones are in 199?

  1. Read the hundreds digit.
  2. Read the tens digit.
  3. Read the ones digit.

Very beginner explanation: Position tells place value.

Answer: 1 hundred, 9 tens, 9 ones

Worked Example 10

Problem: How many hundreds, tens, and ones are in 104?

  1. Read the hundreds digit.
  2. Read the tens digit.
  3. Read the ones digit.

Very beginner explanation: Position tells place value.

Answer: 1 hundred, 0 tens, 4 ones

3.2 Composing three-digit numbers to 200

Place value tells how much a digit is worth because of its position in a number. Use objects, drawings, number lines, tables, or number sentences when useful.

10 Worked Examples with Answers

Worked Example 1

Problem: How many hundreds, tens, and ones are in 149?

  1. Read the hundreds digit.
  2. Read the tens digit.
  3. Read the ones digit.

Very beginner explanation: Position tells place value.

Answer: 1 hundred, 4 tens, 9 ones

Worked Example 2

Problem: How many hundreds, tens, and ones are in 199?

  1. Read the hundreds digit.
  2. Read the tens digit.
  3. Read the ones digit.

Very beginner explanation: Position tells place value.

Answer: 1 hundred, 9 tens, 9 ones

Worked Example 3

Problem: How many hundreds, tens, and ones are in 145?

  1. Read the hundreds digit.
  2. Read the tens digit.
  3. Read the ones digit.

Very beginner explanation: Position tells place value.

Answer: 1 hundred, 4 tens, 5 ones

Worked Example 4

Problem: How many hundreds, tens, and ones are in 136?

  1. Read the hundreds digit.
  2. Read the tens digit.
  3. Read the ones digit.

Very beginner explanation: Position tells place value.

Answer: 1 hundred, 3 tens, 6 ones

Worked Example 5

Problem: How many hundreds, tens, and ones are in 182?

  1. Read the hundreds digit.
  2. Read the tens digit.
  3. Read the ones digit.

Very beginner explanation: Position tells place value.

Answer: 1 hundred, 8 tens, 2 ones

Worked Example 6

Problem: How many hundreds, tens, and ones are in 105?

  1. Read the hundreds digit.
  2. Read the tens digit.
  3. Read the ones digit.

Very beginner explanation: Position tells place value.

Answer: 1 hundred, 0 tens, 5 ones

Worked Example 7

Problem: How many hundreds, tens, and ones are in 136?

  1. Read the hundreds digit.
  2. Read the tens digit.
  3. Read the ones digit.

Very beginner explanation: Position tells place value.

Answer: 1 hundred, 3 tens, 6 ones

Worked Example 8

Problem: How many hundreds, tens, and ones are in 105?

  1. Read the hundreds digit.
  2. Read the tens digit.
  3. Read the ones digit.

Very beginner explanation: Position tells place value.

Answer: 1 hundred, 0 tens, 5 ones

Worked Example 9

Problem: How many hundreds, tens, and ones are in 141?

  1. Read the hundreds digit.
  2. Read the tens digit.
  3. Read the ones digit.

Very beginner explanation: Position tells place value.

Answer: 1 hundred, 4 tens, 1 ones

Worked Example 10

Problem: How many hundreds, tens, and ones are in 182?

  1. Read the hundreds digit.
  2. Read the tens digit.
  3. Read the ones digit.

Very beginner explanation: Position tells place value.

Answer: 1 hundred, 8 tens, 2 ones

3.3 Decomposing into hundreds tens and ones

Place value tells how much a digit is worth because of its position in a number. Use objects, drawings, number lines, tables, or number sentences when useful.

10 Worked Examples with Answers

Worked Example 1

Problem: How many hundreds, tens, and ones are in 196?

  1. Read the hundreds digit.
  2. Read the tens digit.
  3. Read the ones digit.

Very beginner explanation: Position tells place value.

Answer: 1 hundred, 9 tens, 6 ones

Worked Example 2

Problem: How many hundreds, tens, and ones are in 119?

  1. Read the hundreds digit.
  2. Read the tens digit.
  3. Read the ones digit.

Very beginner explanation: Position tells place value.

Answer: 1 hundred, 1 tens, 9 ones

Worked Example 3

Problem: How many hundreds, tens, and ones are in 129?

  1. Read the hundreds digit.
  2. Read the tens digit.
  3. Read the ones digit.

Very beginner explanation: Position tells place value.

Answer: 1 hundred, 2 tens, 9 ones

Worked Example 4

Problem: How many hundreds, tens, and ones are in 152?

  1. Read the hundreds digit.
  2. Read the tens digit.
  3. Read the ones digit.

Very beginner explanation: Position tells place value.

Answer: 1 hundred, 5 tens, 2 ones

Worked Example 5

Problem: How many hundreds, tens, and ones are in 195?

  1. Read the hundreds digit.
  2. Read the tens digit.
  3. Read the ones digit.

Very beginner explanation: Position tells place value.

Answer: 1 hundred, 9 tens, 5 ones

Worked Example 6

Problem: How many hundreds, tens, and ones are in 140?

  1. Read the hundreds digit.
  2. Read the tens digit.
  3. Read the ones digit.

Very beginner explanation: Position tells place value.

Answer: 1 hundred, 4 tens, 0 ones

Worked Example 7

Problem: How many hundreds, tens, and ones are in 179?

  1. Read the hundreds digit.
  2. Read the tens digit.
  3. Read the ones digit.

Very beginner explanation: Position tells place value.

Answer: 1 hundred, 7 tens, 9 ones

Worked Example 8

Problem: How many hundreds, tens, and ones are in 123?

  1. Read the hundreds digit.
  2. Read the tens digit.
  3. Read the ones digit.

Very beginner explanation: Position tells place value.

Answer: 1 hundred, 2 tens, 3 ones

Worked Example 9

Problem: How many hundreds, tens, and ones are in 141?

  1. Read the hundreds digit.
  2. Read the tens digit.
  3. Read the ones digit.

Very beginner explanation: Position tells place value.

Answer: 1 hundred, 4 tens, 1 ones

Worked Example 10

Problem: How many hundreds, tens, and ones are in 167?

  1. Read the hundreds digit.
  2. Read the tens digit.
  3. Read the ones digit.

Very beginner explanation: Position tells place value.

Answer: 1 hundred, 6 tens, 7 ones

3.4 Expanded form with addition

Addition combines quantities. Counting on, making ten, drawings, and place value can help. Use objects, drawings, number lines, tables, or number sentences when useful.

10 Worked Examples with Answers

Worked Example 1

Problem: Find 33 + 43.

  1. Start with the larger number.
  2. Add tens or make a ten if helpful.
  3. Add the remaining ones.

Very beginner explanation: Addition combines quantities.

Answer: 76

Worked Example 2

Problem: Find 38 + 55.

  1. Start with the larger number.
  2. Add tens or make a ten if helpful.
  3. Add the remaining ones.

Very beginner explanation: Addition combines quantities.

Answer: 93

Worked Example 3

Problem: Find 40 + 20.

  1. Start with the larger number.
  2. Add tens or make a ten if helpful.
  3. Add the remaining ones.

Very beginner explanation: Addition combines quantities.

Answer: 60

Worked Example 4

Problem: Find 34 + 18.

  1. Start with the larger number.
  2. Add tens or make a ten if helpful.
  3. Add the remaining ones.

Very beginner explanation: Addition combines quantities.

Answer: 52

Worked Example 5

Problem: Find 70 + 57.

  1. Start with the larger number.
  2. Add tens or make a ten if helpful.
  3. Add the remaining ones.

Very beginner explanation: Addition combines quantities.

Answer: 127

Worked Example 6

Problem: Find 58 + 5.

  1. Start with the larger number.
  2. Add tens or make a ten if helpful.
  3. Add the remaining ones.

Very beginner explanation: Addition combines quantities.

Answer: 63

Worked Example 7

Problem: Find 24 + 39.

  1. Start with the larger number.
  2. Add tens or make a ten if helpful.
  3. Add the remaining ones.

Very beginner explanation: Addition combines quantities.

Answer: 63

Worked Example 8

Problem: Find 35 + 8.

  1. Start with the larger number.
  2. Add tens or make a ten if helpful.
  3. Add the remaining ones.

Very beginner explanation: Addition combines quantities.

Answer: 43

Worked Example 9

Problem: Find 7 + 31.

  1. Start with the larger number.
  2. Add tens or make a ten if helpful.
  3. Add the remaining ones.

Very beginner explanation: Addition combines quantities.

Answer: 38

Worked Example 10

Problem: Find 24 + 29.

  1. Start with the larger number.
  2. Add tens or make a ten if helpful.
  3. Add the remaining ones.

Very beginner explanation: Addition combines quantities.

Answer: 53

3.5 Making the same number in different ways

Making the same number in different ways is a Grade 2 math idea best learned with simple numbers, objects, drawings, and clear words. Use objects, drawings, number lines, tables, or number sentences when useful.

10 Worked Examples with Answers

Worked Example 1

Problem: Use 4 and 14 to make a simple example about Making the same number in different ways.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Making the same number in different ways.

Worked Example 2

Problem: Use 12 and 14 to make a simple example about Making the same number in different ways.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Making the same number in different ways.

Worked Example 3

Problem: Use 4 and 10 to make a simple example about Making the same number in different ways.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Making the same number in different ways.

Worked Example 4

Problem: Use 1 and 11 to make a simple example about Making the same number in different ways.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Making the same number in different ways.

Worked Example 5

Problem: Use 5 and 7 to make a simple example about Making the same number in different ways.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Making the same number in different ways.

Worked Example 6

Problem: Use 12 and 10 to make a simple example about Making the same number in different ways.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Making the same number in different ways.

Worked Example 7

Problem: Use 10 and 17 to make a simple example about Making the same number in different ways.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Making the same number in different ways.

Worked Example 8

Problem: Use 19 and 16 to make a simple example about Making the same number in different ways.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Making the same number in different ways.

Worked Example 9

Problem: Use 15 and 17 to make a simple example about Making the same number in different ways.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Making the same number in different ways.

Worked Example 10

Problem: Use 9 and 10 to make a simple example about Making the same number in different ways.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Making the same number in different ways.

3.6 Using base-ten drawings

Using base-ten drawings is a Grade 2 math idea best learned with simple numbers, objects, drawings, and clear words. Use objects, drawings, number lines, tables, or number sentences when useful.

10 Worked Examples with Answers

Worked Example 1

Problem: Use 8 and 17 to make a simple example about Using base-ten drawings.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Using base-ten drawings.

Worked Example 2

Problem: Use 4 and 9 to make a simple example about Using base-ten drawings.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Using base-ten drawings.

Worked Example 3

Problem: Use 10 and 16 to make a simple example about Using base-ten drawings.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Using base-ten drawings.

Worked Example 4

Problem: Use 10 and 3 to make a simple example about Using base-ten drawings.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Using base-ten drawings.

Worked Example 5

Problem: Use 20 and 4 to make a simple example about Using base-ten drawings.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Using base-ten drawings.

Worked Example 6

Problem: Use 6 and 5 to make a simple example about Using base-ten drawings.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Using base-ten drawings.

Worked Example 7

Problem: Use 11 and 19 to make a simple example about Using base-ten drawings.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Using base-ten drawings.

Worked Example 8

Problem: Use 10 and 7 to make a simple example about Using base-ten drawings.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Using base-ten drawings.

Worked Example 9

Problem: Use 14 and 18 to make a simple example about Using base-ten drawings.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Using base-ten drawings.

Worked Example 10

Problem: Use 8 and 13 to make a simple example about Using base-ten drawings.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Using base-ten drawings.

3.7 Using ten frames

Using ten frames is a Grade 2 math idea best learned with simple numbers, objects, drawings, and clear words. Use objects, drawings, number lines, tables, or number sentences when useful.

10 Worked Examples with Answers

Worked Example 1

Problem: Use 16 and 14 to make a simple example about Using ten frames.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Using ten frames.

Worked Example 2

Problem: Use 17 and 11 to make a simple example about Using ten frames.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Using ten frames.

Worked Example 3

Problem: Use 18 and 17 to make a simple example about Using ten frames.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Using ten frames.

Worked Example 4

Problem: Use 11 and 9 to make a simple example about Using ten frames.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Using ten frames.

Worked Example 5

Problem: Use 8 and 3 to make a simple example about Using ten frames.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Using ten frames.

Worked Example 6

Problem: Use 7 and 3 to make a simple example about Using ten frames.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Using ten frames.

Worked Example 7

Problem: Use 3 and 15 to make a simple example about Using ten frames.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Using ten frames.

Worked Example 8

Problem: Use 18 and 15 to make a simple example about Using ten frames.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Using ten frames.

Worked Example 9

Problem: Use 5 and 14 to make a simple example about Using ten frames.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Using ten frames.

Worked Example 10

Problem: Use 3 and 19 to make a simple example about Using ten frames.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Using ten frames.

3.8 Using counters and groups of ten

Using counters and groups of ten is a Grade 2 math idea best learned with simple numbers, objects, drawings, and clear words. Use objects, drawings, number lines, tables, or number sentences when useful.

10 Worked Examples with Answers

Worked Example 1

Problem: Use 20 and 8 to make a simple example about Using counters and groups of ten.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Using counters and groups of ten.

Worked Example 2

Problem: Use 20 and 20 to make a simple example about Using counters and groups of ten.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Using counters and groups of ten.

Worked Example 3

Problem: Use 11 and 6 to make a simple example about Using counters and groups of ten.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Using counters and groups of ten.

Worked Example 4

Problem: Use 19 and 13 to make a simple example about Using counters and groups of ten.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Using counters and groups of ten.

Worked Example 5

Problem: Use 17 and 7 to make a simple example about Using counters and groups of ten.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Using counters and groups of ten.

Worked Example 6

Problem: Use 10 and 8 to make a simple example about Using counters and groups of ten.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Using counters and groups of ten.

Worked Example 7

Problem: Use 17 and 17 to make a simple example about Using counters and groups of ten.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Using counters and groups of ten.

Worked Example 8

Problem: Use 20 and 15 to make a simple example about Using counters and groups of ten.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Using counters and groups of ten.

Worked Example 9

Problem: Use 3 and 6 to make a simple example about Using counters and groups of ten.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Using counters and groups of ten.

Worked Example 10

Problem: Use 16 and 11 to make a simple example about Using counters and groups of ten.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Using counters and groups of ten.

3.9 Flexible decomposition

Flexible decomposition is a Grade 2 math idea best learned with simple numbers, objects, drawings, and clear words. Use objects, drawings, number lines, tables, or number sentences when useful.

10 Worked Examples with Answers

Worked Example 1

Problem: Use 6 and 11 to make a simple example about Flexible decomposition.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Flexible decomposition.

Worked Example 2

Problem: Use 17 and 10 to make a simple example about Flexible decomposition.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Flexible decomposition.

Worked Example 3

Problem: Use 9 and 5 to make a simple example about Flexible decomposition.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Flexible decomposition.

Worked Example 4

Problem: Use 6 and 4 to make a simple example about Flexible decomposition.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Flexible decomposition.

Worked Example 5

Problem: Use 3 and 17 to make a simple example about Flexible decomposition.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Flexible decomposition.

Worked Example 6

Problem: Use 10 and 19 to make a simple example about Flexible decomposition.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Flexible decomposition.

Worked Example 7

Problem: Use 13 and 8 to make a simple example about Flexible decomposition.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Flexible decomposition.

Worked Example 8

Problem: Use 13 and 2 to make a simple example about Flexible decomposition.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Flexible decomposition.

Worked Example 9

Problem: Use 18 and 19 to make a simple example about Flexible decomposition.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Flexible decomposition.

Worked Example 10

Problem: Use 15 and 13 to make a simple example about Flexible decomposition.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Flexible decomposition.

3.10 Decomposing money amounts

Money amounts can be represented in different ways. Different combinations of coins and bills can have the same value. Use objects, drawings, number lines, tables, or number sentences when useful.

10 Worked Examples with Answers

Worked Example 1

Problem: Make 100 cents using common coin values.

  1. Choose coin values.
  2. Add them to check the total.

Very beginner explanation: The same amount can be made in different ways.

Answer: Any correct combination totaling 100 cents

Worked Example 2

Problem: Make 75 cents using common coin values.

  1. Choose coin values.
  2. Add them to check the total.

Very beginner explanation: The same amount can be made in different ways.

Answer: Any correct combination totaling 75 cents

Worked Example 3

Problem: Make 75 cents using common coin values.

  1. Choose coin values.
  2. Add them to check the total.

Very beginner explanation: The same amount can be made in different ways.

Answer: Any correct combination totaling 75 cents

Worked Example 4

Problem: Make 50 cents using common coin values.

  1. Choose coin values.
  2. Add them to check the total.

Very beginner explanation: The same amount can be made in different ways.

Answer: Any correct combination totaling 50 cents

Worked Example 5

Problem: Make 25 cents using common coin values.

  1. Choose coin values.
  2. Add them to check the total.

Very beginner explanation: The same amount can be made in different ways.

Answer: Any correct combination totaling 25 cents

Worked Example 6

Problem: Make 75 cents using common coin values.

  1. Choose coin values.
  2. Add them to check the total.

Very beginner explanation: The same amount can be made in different ways.

Answer: Any correct combination totaling 75 cents

Worked Example 7

Problem: Make 50 cents using common coin values.

  1. Choose coin values.
  2. Add them to check the total.

Very beginner explanation: The same amount can be made in different ways.

Answer: Any correct combination totaling 50 cents

Worked Example 8

Problem: Make 75 cents using common coin values.

  1. Choose coin values.
  2. Add them to check the total.

Very beginner explanation: The same amount can be made in different ways.

Answer: Any correct combination totaling 75 cents

Worked Example 9

Problem: Make 50 cents using common coin values.

  1. Choose coin values.
  2. Add them to check the total.

Very beginner explanation: The same amount can be made in different ways.

Answer: Any correct combination totaling 50 cents

Worked Example 10

Problem: Make 100 cents using common coin values.

  1. Choose coin values.
  2. Add them to check the total.

Very beginner explanation: The same amount can be made in different ways.

Answer: Any correct combination totaling 100 cents

3.11 Explaining a decomposition

Explaining a decomposition is a Grade 2 math idea best learned with simple numbers, objects, drawings, and clear words. Use objects, drawings, number lines, tables, or number sentences when useful.

10 Worked Examples with Answers

Worked Example 1

Problem: Use 18 and 20 to make a simple example about Explaining a decomposition.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Explaining a decomposition.

Worked Example 2

Problem: Use 6 and 6 to make a simple example about Explaining a decomposition.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Explaining a decomposition.

Worked Example 3

Problem: Use 13 and 5 to make a simple example about Explaining a decomposition.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Explaining a decomposition.

Worked Example 4

Problem: Use 17 and 2 to make a simple example about Explaining a decomposition.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Explaining a decomposition.

Worked Example 5

Problem: Use 13 and 17 to make a simple example about Explaining a decomposition.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Explaining a decomposition.

Worked Example 6

Problem: Use 3 and 15 to make a simple example about Explaining a decomposition.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Explaining a decomposition.

Worked Example 7

Problem: Use 13 and 12 to make a simple example about Explaining a decomposition.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Explaining a decomposition.

Worked Example 8

Problem: Use 3 and 20 to make a simple example about Explaining a decomposition.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Explaining a decomposition.

Worked Example 9

Problem: Use 13 and 16 to make a simple example about Explaining a decomposition.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Explaining a decomposition.

Worked Example 10

Problem: Use 15 and 17 to make a simple example about Explaining a decomposition.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Explaining a decomposition.

3.12 Real-life composition problems

Real-life composition problems is a Grade 2 math idea best learned with simple numbers, objects, drawings, and clear words. Use objects, drawings, number lines, tables, or number sentences when useful.

10 Worked Examples with Answers

Worked Example 1

Problem: Use 16 and 17 to make a simple example about Real-life composition problems.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Real-life composition problems.

Worked Example 2

Problem: Use 15 and 12 to make a simple example about Real-life composition problems.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Real-life composition problems.

Worked Example 3

Problem: Use 14 and 6 to make a simple example about Real-life composition problems.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Real-life composition problems.

Worked Example 4

Problem: Use 19 and 7 to make a simple example about Real-life composition problems.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Real-life composition problems.

Worked Example 5

Problem: Use 1 and 6 to make a simple example about Real-life composition problems.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Real-life composition problems.

Worked Example 6

Problem: Use 20 and 16 to make a simple example about Real-life composition problems.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Real-life composition problems.

Worked Example 7

Problem: Use 6 and 14 to make a simple example about Real-life composition problems.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Real-life composition problems.

Worked Example 8

Problem: Use 17 and 1 to make a simple example about Real-life composition problems.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Real-life composition problems.

Worked Example 9

Problem: Use 4 and 3 to make a simple example about Real-life composition problems.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Real-life composition problems.

Worked Example 10

Problem: Use 12 and 7 to make a simple example about Real-life composition problems.

  1. Recall the topic meaning.
  2. Use objects, a drawing, or a number sentence.
  3. Check that the example matches the idea.

Very beginner explanation: Simple models make Grade 2 ideas easier to understand.

Answer: A correct Grade 2 example of Real-life composition problems.

30 Review Questions and Answers

Q1. What should a Grade 2 learner understand about Composing two-digit numbers?

Answer: Place value tells how much a digit is worth because of its position in a number.

Q2. What should a Grade 2 learner understand about Composing three-digit numbers to 200?

Answer: Place value tells how much a digit is worth because of its position in a number.

Q3. What should a Grade 2 learner understand about Decomposing into hundreds tens and ones?

Answer: Place value tells how much a digit is worth because of its position in a number.

Q4. What should a Grade 2 learner understand about Expanded form with addition?

Answer: Addition combines quantities. Counting on, making ten, drawings, and place value can help.

Q5. What should a Grade 2 learner understand about Making the same number in different ways?

Answer: Making the same number in different ways is a Grade 2 math idea best learned with simple numbers, objects, drawings, and clear words.

Q6. What should a Grade 2 learner understand about Using base-ten drawings?

Answer: Using base-ten drawings is a Grade 2 math idea best learned with simple numbers, objects, drawings, and clear words.

Q7. What should a Grade 2 learner understand about Using ten frames?

Answer: Using ten frames is a Grade 2 math idea best learned with simple numbers, objects, drawings, and clear words.

Q8. What should a Grade 2 learner understand about Using counters and groups of ten?

Answer: Using counters and groups of ten is a Grade 2 math idea best learned with simple numbers, objects, drawings, and clear words.

Q9. What should a Grade 2 learner understand about Flexible decomposition?

Answer: Flexible decomposition is a Grade 2 math idea best learned with simple numbers, objects, drawings, and clear words.

Q10. What should a Grade 2 learner understand about Decomposing money amounts?

Answer: Money amounts can be represented in different ways. Different combinations of coins and bills can have the same value.

Q11. What should a Grade 2 learner understand about Explaining a decomposition?

Answer: Explaining a decomposition is a Grade 2 math idea best learned with simple numbers, objects, drawings, and clear words.

Q12. What should a Grade 2 learner understand about Real-life composition problems?

Answer: Real-life composition problems is a Grade 2 math idea best learned with simple numbers, objects, drawings, and clear words.

Q13. What should a Grade 2 learner understand about Composing two-digit numbers?

Answer: Place value tells how much a digit is worth because of its position in a number.

Q14. What should a Grade 2 learner understand about Composing three-digit numbers to 200?

Answer: Place value tells how much a digit is worth because of its position in a number.

Q15. What should a Grade 2 learner understand about Decomposing into hundreds tens and ones?

Answer: Place value tells how much a digit is worth because of its position in a number.

Q16. What should a Grade 2 learner understand about Expanded form with addition?

Answer: Addition combines quantities. Counting on, making ten, drawings, and place value can help.

Q17. What should a Grade 2 learner understand about Making the same number in different ways?

Answer: Making the same number in different ways is a Grade 2 math idea best learned with simple numbers, objects, drawings, and clear words.

Q18. What should a Grade 2 learner understand about Using base-ten drawings?

Answer: Using base-ten drawings is a Grade 2 math idea best learned with simple numbers, objects, drawings, and clear words.

Q19. What should a Grade 2 learner understand about Using ten frames?

Answer: Using ten frames is a Grade 2 math idea best learned with simple numbers, objects, drawings, and clear words.

Q20. What should a Grade 2 learner understand about Using counters and groups of ten?

Answer: Using counters and groups of ten is a Grade 2 math idea best learned with simple numbers, objects, drawings, and clear words.

Q21. What should a Grade 2 learner understand about Flexible decomposition?

Answer: Flexible decomposition is a Grade 2 math idea best learned with simple numbers, objects, drawings, and clear words.

Q22. What should a Grade 2 learner understand about Decomposing money amounts?

Answer: Money amounts can be represented in different ways. Different combinations of coins and bills can have the same value.

Q23. What should a Grade 2 learner understand about Explaining a decomposition?

Answer: Explaining a decomposition is a Grade 2 math idea best learned with simple numbers, objects, drawings, and clear words.

Q24. What should a Grade 2 learner understand about Real-life composition problems?

Answer: Real-life composition problems is a Grade 2 math idea best learned with simple numbers, objects, drawings, and clear words.

Q25. What should a Grade 2 learner understand about Composing two-digit numbers?

Answer: Place value tells how much a digit is worth because of its position in a number.

Q26. What should a Grade 2 learner understand about Composing three-digit numbers to 200?

Answer: Place value tells how much a digit is worth because of its position in a number.

Q27. What should a Grade 2 learner understand about Decomposing into hundreds tens and ones?

Answer: Place value tells how much a digit is worth because of its position in a number.

Q28. What should a Grade 2 learner understand about Expanded form with addition?

Answer: Addition combines quantities. Counting on, making ten, drawings, and place value can help.

Q29. What should a Grade 2 learner understand about Making the same number in different ways?

Answer: Making the same number in different ways is a Grade 2 math idea best learned with simple numbers, objects, drawings, and clear words.

Q30. What should a Grade 2 learner understand about Using base-ten drawings?

Answer: Using base-ten drawings is a Grade 2 math idea best learned with simple numbers, objects, drawings, and clear words.