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Chapter 35: Variables and Unknown 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 Variables and Unknown Numbers with simple explanations, visual thinking, worked examples, practice, and review.

35.1 Unknown numbers in boxes

Equality means both sides have the same value. An unknown is the number needed to make a statement true. Use objects, drawings, number lines, tables, or number sentences when useful.

10 Worked Examples with Answers

Worked Example 1

Problem: Find □: □ + 4 = 9.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 5

Worked Example 2

Problem: Find □: □ + 2 = 4.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 2

Worked Example 3

Problem: Find □: □ + 9 = 24.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 15

Worked Example 4

Problem: Find □: □ + 3 = 18.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 15

Worked Example 5

Problem: Find □: □ + 2 = 11.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 9

Worked Example 6

Problem: Find □: □ + 4 = 16.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 12

Worked Example 7

Problem: Find □: □ + 10 = 21.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 11

Worked Example 8

Problem: Find □: □ + 7 = 13.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 6

Worked Example 9

Problem: Find □: □ + 4 = 5.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 1

Worked Example 10

Problem: Find □: □ + 5 = 12.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 7

35.2 Unknown addends

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 37 + 13.

  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: 50

Worked Example 2

Problem: Find 9 + 23.

  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: 32

Worked Example 3

Problem: Find 64 + 28.

  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: 92

Worked Example 4

Problem: Find 11 + 12.

  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: 23

Worked Example 5

Problem: Find 29 + 30.

  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: 59

Worked Example 6

Problem: Find 12 + 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: 55

Worked Example 7

Problem: Find 30 + 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: 73

Worked Example 8

Problem: Find 25 + 56.

  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: 81

Worked Example 9

Problem: Find 28 + 58.

  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: 86

Worked Example 10

Problem: Find 44 + 3.

  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: 47

35.3 Unknown differences

Subtraction can mean taking away, finding a difference, or finding a missing part. Addition can check the answer. Use objects, drawings, number lines, tables, or number sentences when useful.

10 Worked Examples with Answers

Worked Example 1

Problem: Find 89 − 13.

  1. Start with the larger number.
  2. Take away or count up.
  3. Check with addition.

Very beginner explanation: Subtraction finds what remains or the difference.

Answer: 76

Worked Example 2

Problem: Find 144 − 93.

  1. Start with the larger number.
  2. Take away or count up.
  3. Check with addition.

Very beginner explanation: Subtraction finds what remains or the difference.

Answer: 51

Worked Example 3

Problem: Find 71 − 23.

  1. Start with the larger number.
  2. Take away or count up.
  3. Check with addition.

Very beginner explanation: Subtraction finds what remains or the difference.

Answer: 48

Worked Example 4

Problem: Find 142 − 76.

  1. Start with the larger number.
  2. Take away or count up.
  3. Check with addition.

Very beginner explanation: Subtraction finds what remains or the difference.

Answer: 66

Worked Example 5

Problem: Find 33 − 1.

  1. Start with the larger number.
  2. Take away or count up.
  3. Check with addition.

Very beginner explanation: Subtraction finds what remains or the difference.

Answer: 32

Worked Example 6

Problem: Find 110 − 104.

  1. Start with the larger number.
  2. Take away or count up.
  3. Check with addition.

Very beginner explanation: Subtraction finds what remains or the difference.

Answer: 6

Worked Example 7

Problem: Find 123 − 75.

  1. Start with the larger number.
  2. Take away or count up.
  3. Check with addition.

Very beginner explanation: Subtraction finds what remains or the difference.

Answer: 48

Worked Example 8

Problem: Find 98 − 89.

  1. Start with the larger number.
  2. Take away or count up.
  3. Check with addition.

Very beginner explanation: Subtraction finds what remains or the difference.

Answer: 9

Worked Example 9

Problem: Find 140 − 106.

  1. Start with the larger number.
  2. Take away or count up.
  3. Check with addition.

Very beginner explanation: Subtraction finds what remains or the difference.

Answer: 34

Worked Example 10

Problem: Find 68 − 6.

  1. Start with the larger number.
  2. Take away or count up.
  3. Check with addition.

Very beginner explanation: Subtraction finds what remains or the difference.

Answer: 62

35.4 Letters as simple unknowns

Equality means both sides have the same value. An unknown is the number needed to make a statement true. Use objects, drawings, number lines, tables, or number sentences when useful.

10 Worked Examples with Answers

Worked Example 1

Problem: Find □: □ + 3 = 11.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 8

Worked Example 2

Problem: Find □: □ + 3 = 13.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 10

Worked Example 3

Problem: Find □: □ + 10 = 13.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 3

Worked Example 4

Problem: Find □: □ + 2 = 14.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 12

Worked Example 5

Problem: Find □: □ + 4 = 6.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 2

Worked Example 6

Problem: Find □: □ + 8 = 14.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 6

Worked Example 7

Problem: Find □: □ + 8 = 10.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 2

Worked Example 8

Problem: Find □: □ + 9 = 23.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 14

Worked Example 9

Problem: Find □: □ + 8 = 10.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 2

Worked Example 10

Problem: Find □: □ + 5 = 6.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 1

35.5 Using a symbol for a missing number

Using a symbol for a missing number 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 15 and 11 to make a simple example about Using a symbol for a missing number.

  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 a symbol for a missing number.

Worked Example 2

Problem: Use 5 and 7 to make a simple example about Using a symbol for a missing number.

  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 a symbol for a missing number.

Worked Example 3

Problem: Use 20 and 9 to make a simple example about Using a symbol for a missing number.

  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 a symbol for a missing number.

Worked Example 4

Problem: Use 5 and 12 to make a simple example about Using a symbol for a missing number.

  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 a symbol for a missing number.

Worked Example 5

Problem: Use 15 and 20 to make a simple example about Using a symbol for a missing number.

  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 a symbol for a missing number.

Worked Example 6

Problem: Use 10 and 5 to make a simple example about Using a symbol for a missing number.

  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 a symbol for a missing number.

Worked Example 7

Problem: Use 11 and 17 to make a simple example about Using a symbol for a missing number.

  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 a symbol for a missing number.

Worked Example 8

Problem: Use 9 and 11 to make a simple example about Using a symbol for a missing number.

  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 a symbol for a missing number.

Worked Example 9

Problem: Use 9 and 5 to make a simple example about Using a symbol for a missing number.

  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 a symbol for a missing number.

Worked Example 10

Problem: Use 9 and 8 to make a simple example about Using a symbol for a missing number.

  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 a symbol for a missing number.

35.6 Finding an unknown 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 42 + 63.

  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: 105

Worked Example 2

Problem: Find 34 + 66.

  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: 100

Worked Example 3

Problem: Find 62 + 36.

  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: 98

Worked Example 4

Problem: Find 36 + 27.

  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 5

Problem: Find 33 + 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: 64

Worked Example 6

Problem: Find 63 + 69.

  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: 132

Worked Example 7

Problem: Find 19 + 27.

  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: 46

Worked Example 8

Problem: Find 63 + 15.

  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: 78

Worked Example 9

Problem: Find 55 + 24.

  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: 79

Worked Example 10

Problem: Find 22 + 10.

  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: 32

35.7 Finding an unknown with subtraction

Subtraction can mean taking away, finding a difference, or finding a missing part. Addition can check the answer. Use objects, drawings, number lines, tables, or number sentences when useful.

10 Worked Examples with Answers

Worked Example 1

Problem: Find 131 − 63.

  1. Start with the larger number.
  2. Take away or count up.
  3. Check with addition.

Very beginner explanation: Subtraction finds what remains or the difference.

Answer: 68

Worked Example 2

Problem: Find 97 − 46.

  1. Start with the larger number.
  2. Take away or count up.
  3. Check with addition.

Very beginner explanation: Subtraction finds what remains or the difference.

Answer: 51

Worked Example 3

Problem: Find 59 − 19.

  1. Start with the larger number.
  2. Take away or count up.
  3. Check with addition.

Very beginner explanation: Subtraction finds what remains or the difference.

Answer: 40

Worked Example 4

Problem: Find 58 − 26.

  1. Start with the larger number.
  2. Take away or count up.
  3. Check with addition.

Very beginner explanation: Subtraction finds what remains or the difference.

Answer: 32

Worked Example 5

Problem: Find 124 − 56.

  1. Start with the larger number.
  2. Take away or count up.
  3. Check with addition.

Very beginner explanation: Subtraction finds what remains or the difference.

Answer: 68

Worked Example 6

Problem: Find 34 − 9.

  1. Start with the larger number.
  2. Take away or count up.
  3. Check with addition.

Very beginner explanation: Subtraction finds what remains or the difference.

Answer: 25

Worked Example 7

Problem: Find 94 − 86.

  1. Start with the larger number.
  2. Take away or count up.
  3. Check with addition.

Very beginner explanation: Subtraction finds what remains or the difference.

Answer: 8

Worked Example 8

Problem: Find 136 − 35.

  1. Start with the larger number.
  2. Take away or count up.
  3. Check with addition.

Very beginner explanation: Subtraction finds what remains or the difference.

Answer: 101

Worked Example 9

Problem: Find 147 − 16.

  1. Start with the larger number.
  2. Take away or count up.
  3. Check with addition.

Very beginner explanation: Subtraction finds what remains or the difference.

Answer: 131

Worked Example 10

Problem: Find 105 − 93.

  1. Start with the larger number.
  2. Take away or count up.
  3. Check with addition.

Very beginner explanation: Subtraction finds what remains or the difference.

Answer: 12

35.8 Checking an unknown value

Equality means both sides have the same value. An unknown is the number needed to make a statement true. Use objects, drawings, number lines, tables, or number sentences when useful.

10 Worked Examples with Answers

Worked Example 1

Problem: Find □: □ + 8 = 12.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 4

Worked Example 2

Problem: Find □: □ + 5 = 11.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 6

Worked Example 3

Problem: Find □: □ + 1 = 16.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 15

Worked Example 4

Problem: Find □: □ + 10 = 19.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 9

Worked Example 5

Problem: Find □: □ + 7 = 18.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 11

Worked Example 6

Problem: Find □: □ + 1 = 2.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 1

Worked Example 7

Problem: Find □: □ + 10 = 12.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 2

Worked Example 8

Problem: Find □: □ + 6 = 14.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 8

Worked Example 9

Problem: Find □: □ + 3 = 9.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 6

Worked Example 10

Problem: Find □: □ + 3 = 10.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 7

35.9 Unknowns in story problems

Equality means both sides have the same value. An unknown is the number needed to make a statement true. Use objects, drawings, number lines, tables, or number sentences when useful.

10 Worked Examples with Answers

Worked Example 1

Problem: Find □: □ + 7 = 13.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 6

Worked Example 2

Problem: Find □: □ + 9 = 19.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 10

Worked Example 3

Problem: Find □: □ + 6 = 13.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 7

Worked Example 4

Problem: Find □: □ + 10 = 20.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 10

Worked Example 5

Problem: Find □: □ + 1 = 8.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 7

Worked Example 6

Problem: Find □: □ + 9 = 11.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 2

Worked Example 7

Problem: Find □: □ + 2 = 9.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 7

Worked Example 8

Problem: Find □: □ + 10 = 17.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 7

Worked Example 9

Problem: Find □: □ + 1 = 12.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 11

Worked Example 10

Problem: Find □: □ + 9 = 13.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 4

35.10 Writing a number sentence with an unknown

Equality means both sides have the same value. An unknown is the number needed to make a statement true. Use objects, drawings, number lines, tables, or number sentences when useful.

10 Worked Examples with Answers

Worked Example 1

Problem: Find □: □ + 6 = 18.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 12

Worked Example 2

Problem: Find □: □ + 9 = 21.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 12

Worked Example 3

Problem: Find □: □ + 9 = 15.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 6

Worked Example 4

Problem: Find □: □ + 4 = 16.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 12

Worked Example 5

Problem: Find □: □ + 8 = 19.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 11

Worked Example 6

Problem: Find □: □ + 7 = 18.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 11

Worked Example 7

Problem: Find □: □ + 6 = 20.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 14

Worked Example 8

Problem: Find □: □ + 9 = 21.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 12

Worked Example 9

Problem: Find □: □ + 4 = 8.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 4

Worked Example 10

Problem: Find □: □ + 5 = 11.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 6

35.11 Different symbols can represent unknowns

Equality means both sides have the same value. An unknown is the number needed to make a statement true. Use objects, drawings, number lines, tables, or number sentences when useful.

10 Worked Examples with Answers

Worked Example 1

Problem: Find □: □ + 1 = 10.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 9

Worked Example 2

Problem: Find □: □ + 4 = 11.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 7

Worked Example 3

Problem: Find □: □ + 3 = 17.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 14

Worked Example 4

Problem: Find □: □ + 5 = 13.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 8

Worked Example 5

Problem: Find □: □ + 5 = 14.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 9

Worked Example 6

Problem: Find □: □ + 2 = 16.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 14

Worked Example 7

Problem: Find □: □ + 9 = 11.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 2

Worked Example 8

Problem: Find □: □ + 9 = 21.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 12

Worked Example 9

Problem: Find □: □ + 5 = 7.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 2

Worked Example 10

Problem: Find □: □ + 3 = 18.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 15

35.12 Explaining how an unknown was found

Equality means both sides have the same value. An unknown is the number needed to make a statement true. Use objects, drawings, number lines, tables, or number sentences when useful.

10 Worked Examples with Answers

Worked Example 1

Problem: Find □: □ + 5 = 8.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 3

Worked Example 2

Problem: Find □: □ + 8 = 12.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 4

Worked Example 3

Problem: Find □: □ + 1 = 12.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 11

Worked Example 4

Problem: Find □: □ + 1 = 13.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 12

Worked Example 5

Problem: Find □: □ + 5 = 17.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 12

Worked Example 6

Problem: Find □: □ + 5 = 7.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 2

Worked Example 7

Problem: Find □: □ + 1 = 14.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 13

Worked Example 8

Problem: Find □: □ + 10 = 18.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 8

Worked Example 9

Problem: Find □: □ + 9 = 13.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 4

Worked Example 10

Problem: Find □: □ + 10 = 24.

  1. Find the missing part.
  2. Use subtraction if helpful.

Very beginner explanation: The unknown must make both sides equal.

Answer: 14

30 Review Questions and Answers

Q1. What should a Grade 2 learner understand about Unknown numbers in boxes?

Answer: Equality means both sides have the same value. An unknown is the number needed to make a statement true.

Q2. What should a Grade 2 learner understand about Unknown addends?

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

Q3. What should a Grade 2 learner understand about Unknown differences?

Answer: Subtraction can mean taking away, finding a difference, or finding a missing part. Addition can check the answer.

Q4. What should a Grade 2 learner understand about Letters as simple unknowns?

Answer: Equality means both sides have the same value. An unknown is the number needed to make a statement true.

Q5. What should a Grade 2 learner understand about Using a symbol for a missing number?

Answer: Using a symbol for a missing number 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 Finding an unknown with addition?

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

Q7. What should a Grade 2 learner understand about Finding an unknown with subtraction?

Answer: Subtraction can mean taking away, finding a difference, or finding a missing part. Addition can check the answer.

Q8. What should a Grade 2 learner understand about Checking an unknown value?

Answer: Equality means both sides have the same value. An unknown is the number needed to make a statement true.

Q9. What should a Grade 2 learner understand about Unknowns in story problems?

Answer: Equality means both sides have the same value. An unknown is the number needed to make a statement true.

Q10. What should a Grade 2 learner understand about Writing a number sentence with an unknown?

Answer: Equality means both sides have the same value. An unknown is the number needed to make a statement true.

Q11. What should a Grade 2 learner understand about Different symbols can represent unknowns?

Answer: Equality means both sides have the same value. An unknown is the number needed to make a statement true.

Q12. What should a Grade 2 learner understand about Explaining how an unknown was found?

Answer: Equality means both sides have the same value. An unknown is the number needed to make a statement true.

Q13. What should a Grade 2 learner understand about Unknown numbers in boxes?

Answer: Equality means both sides have the same value. An unknown is the number needed to make a statement true.

Q14. What should a Grade 2 learner understand about Unknown addends?

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

Q15. What should a Grade 2 learner understand about Unknown differences?

Answer: Subtraction can mean taking away, finding a difference, or finding a missing part. Addition can check the answer.

Q16. What should a Grade 2 learner understand about Letters as simple unknowns?

Answer: Equality means both sides have the same value. An unknown is the number needed to make a statement true.

Q17. What should a Grade 2 learner understand about Using a symbol for a missing number?

Answer: Using a symbol for a missing number 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 Finding an unknown with addition?

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

Q19. What should a Grade 2 learner understand about Finding an unknown with subtraction?

Answer: Subtraction can mean taking away, finding a difference, or finding a missing part. Addition can check the answer.

Q20. What should a Grade 2 learner understand about Checking an unknown value?

Answer: Equality means both sides have the same value. An unknown is the number needed to make a statement true.

Q21. What should a Grade 2 learner understand about Unknowns in story problems?

Answer: Equality means both sides have the same value. An unknown is the number needed to make a statement true.

Q22. What should a Grade 2 learner understand about Writing a number sentence with an unknown?

Answer: Equality means both sides have the same value. An unknown is the number needed to make a statement true.

Q23. What should a Grade 2 learner understand about Different symbols can represent unknowns?

Answer: Equality means both sides have the same value. An unknown is the number needed to make a statement true.

Q24. What should a Grade 2 learner understand about Explaining how an unknown was found?

Answer: Equality means both sides have the same value. An unknown is the number needed to make a statement true.

Q25. What should a Grade 2 learner understand about Unknown numbers in boxes?

Answer: Equality means both sides have the same value. An unknown is the number needed to make a statement true.

Q26. What should a Grade 2 learner understand about Unknown addends?

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

Q27. What should a Grade 2 learner understand about Unknown differences?

Answer: Subtraction can mean taking away, finding a difference, or finding a missing part. Addition can check the answer.

Q28. What should a Grade 2 learner understand about Letters as simple unknowns?

Answer: Equality means both sides have the same value. An unknown is the number needed to make a statement true.

Q29. What should a Grade 2 learner understand about Using a symbol for a missing number?

Answer: Using a symbol for a missing number 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 Finding an unknown with addition?

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