Learn on PengiIllustrative Mathematics, Grade 5Chapter 5: Place Value Patterns and Decimal Operations

Lesson 7: Analyze Addition Mistakes

In this Grade 5 lesson from Illustrative Mathematics Chapter 5, students learn to add decimals to the hundredths place using the standard algorithm with correct place value alignment. The lesson focuses on a common error in which decimal numbers are right-aligned like whole numbers, causing digits of different place values — such as tenths and hundredths — to be added together incorrectly. Students identify and correct these alignment mistakes, reinforcing that decimal numbers must be lined up by place value, not by their rightmost digit.

Section 1

Application: Approximate vs. Exact Quantities

Property

Most conversions between customary and metric systems are approximate (\approx), meaning they are rounded. An exact conversion (==) is a defined relationship. The primary exact conversion between systems is for inches and centimeters.

1 kg2.2 lb(Approximate)1 \text{ kg} \approx 2.2 \text{ lb} \quad (\text{Approximate})
1 in=2.54 cm(Exact)1 \text{ in} = 2.54 \text{ cm} \quad (\text{Exact})

Examples

Section 2

Context and Measurement Precision

Property

The precision of a measurement is limited by the measuring tool. The context of a situation determines the necessary level of precision, which is how detailed a measurement needs to be to be useful.

Examples

Book overview

Jump across lessons in the current chapter without opening the full course modal.

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Chapter 5: Place Value Patterns and Decimal Operations

  1. Lesson 1

    Lesson 1: Thousandths: Introduction and Representation

  2. Lesson 2

    Lesson 2: Thousandths and Place Value Relationships

  3. Lesson 3

    Lesson 3: Compare Decimals

  4. Lesson 4

    Lesson 4: Round Decimals

  5. Lesson 5

    Lesson 5: Order and Solve Problems with Decimals

  6. Lesson 6

    Lesson 6: Decimal Addition: Sense Making and Estimation

  7. Lesson 7Current

    Lesson 7: Analyze Addition Mistakes

  8. Lesson 8

    Lesson 8: Decimal Subtraction: Sense Making and Estimation

  9. Lesson 9

    Lesson 9: Addition and Subtraction

  10. Lesson 10

    Lesson 10: Multiply Decimals by Whole Numbers

  11. Lesson 11

    Lesson 11: Multiply Decimals: Properties and Hundredths

  12. Lesson 12

    Lesson 12: Multiply More Decimals

  13. Lesson 13

    Lesson 13: Divide by Decimals

  14. Lesson 14

    Lesson 14: Divide Decimals

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Application: Approximate vs. Exact Quantities

Property

Most conversions between customary and metric systems are approximate (\approx), meaning they are rounded. An exact conversion (==) is a defined relationship. The primary exact conversion between systems is for inches and centimeters.

1 kg2.2 lb(Approximate)1 \text{ kg} \approx 2.2 \text{ lb} \quad (\text{Approximate})
1 in=2.54 cm(Exact)1 \text{ in} = 2.54 \text{ cm} \quad (\text{Exact})

Examples

Section 2

Context and Measurement Precision

Property

The precision of a measurement is limited by the measuring tool. The context of a situation determines the necessary level of precision, which is how detailed a measurement needs to be to be useful.

Examples

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 5: Place Value Patterns and Decimal Operations

  1. Lesson 1

    Lesson 1: Thousandths: Introduction and Representation

  2. Lesson 2

    Lesson 2: Thousandths and Place Value Relationships

  3. Lesson 3

    Lesson 3: Compare Decimals

  4. Lesson 4

    Lesson 4: Round Decimals

  5. Lesson 5

    Lesson 5: Order and Solve Problems with Decimals

  6. Lesson 6

    Lesson 6: Decimal Addition: Sense Making and Estimation

  7. Lesson 7Current

    Lesson 7: Analyze Addition Mistakes

  8. Lesson 8

    Lesson 8: Decimal Subtraction: Sense Making and Estimation

  9. Lesson 9

    Lesson 9: Addition and Subtraction

  10. Lesson 10

    Lesson 10: Multiply Decimals by Whole Numbers

  11. Lesson 11

    Lesson 11: Multiply Decimals: Properties and Hundredths

  12. Lesson 12

    Lesson 12: Multiply More Decimals

  13. Lesson 13

    Lesson 13: Divide by Decimals

  14. Lesson 14

    Lesson 14: Divide Decimals