Learn on PengiSaxon Math, Intermediate 4Chapter 4: Lessons 31–40, Investigation 4

Lesson 39: Reading an Inch Scale to the Nearest Fourth, Activity Make a Ruler and Measure

In this Grade 4 Saxon Math lesson, students learn to read an inch scale to the nearest quarter inch, including recognizing equivalent fractions such as two-fourths equaling one-half. Students practice measuring objects like toothpicks and notebook paper, drawing precise line segments with fractional inch lengths, and solving problems involving combined measurements. The lesson is part of Chapter 4 in Saxon Math Intermediate 4.

Section 1

πŸ“˜ Reading an Inch Scale to the Nearest Fourth

New Concept

To measure lengths in inches, we use an inch scale. These scales let us read to the nearest half inch, quarter inch, or eighth inch.

What’s next

Next, you’ll practice reading an inch scale to the nearest quarter inch and see how equivalent fractions like 24\frac{2}{4} and 12\frac{1}{2} are used.

Section 2

Reading to the nearest quarter inch

Property

Inch scales have tick marks between the inch marks that let us read the scale to the nearest quarter inch. Remember that one quarter inch is the same as one fourth inch, which can be written as 14\frac{1}{4} in.

Example

A paperclip measures past the 1-inch mark to the first small tick.
Its length is 14\tfrac{1}{4} inches.

A crayon stops at the third tick mark after the 3-inch line.
Its length is 3343\tfrac{3}{4} inches.

Section 3

Two fourths equals one half

Property

When reading inch scales, keep in mind that 24\frac{2}{4} equals 12\frac{1}{2}.

Example

A toothpick measures 2242\tfrac{2}{4} inches.
We simplify this to its proper form: 2122\tfrac{1}{2} inches.

An arrow points to 24\tfrac{2}{4} on a ruler.
The correct way to name this point is 12\tfrac{1}{2} inch.

Section 4

Combining mixed number lengths

Property

To find the combined thickness of stacked objects, add their individual thicknesses. First, add the whole numbers, then add the fractions. If the fractions add up to a whole number or more, simplify and add it to the whole number total.

Example

A 1121\tfrac{1}{2} inch board on a 2 inch board:
1+2=31 + 2 = 3, so the total is 3123\tfrac{1}{2} inches.

A 1121\tfrac{1}{2} inch block on a 2122\tfrac{1}{2} inch block:
(1+2)+(12+12)=3+1=4(1+2) + (\tfrac{1}{2} + \tfrac{1}{2}) = 3 + 1 = 4 inches.

Book overview

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Chapter 4: Lessons 31–40, Investigation 4

  1. Lesson 1

    Lesson 31: Word Problems About Comparing

  2. Lesson 2

    Lesson 32: Multiplication Facts: 9s, 10s, 11s, 12s

  3. Lesson 3

    Lesson 33: Writing Numbers Through Hundred Thousands

  4. Lesson 4

    Lesson 34: Writing Numbers Through Hundred Millions

  5. Lesson 5

    Lesson 35: Naming Mixed Numbers and Money

  6. Lesson 6

    Lesson 36: Fractions of a Dollar

  7. Lesson 7

    Lesson 37: Reading Fractions and Mixed Numbers from a Number Line

  8. Lesson 8

    Lesson 38: Multiplication Facts (Memory Group)

  9. Lesson 9Current

    Lesson 39: Reading an Inch Scale to the Nearest Fourth, Activity Make a Ruler and Measure

  10. Lesson 10

    Lesson 40: Capacity

  11. Lesson 11

    Investigation 4A: Tenths and Hundredths

  12. Lesson 12

    Investigation 4B: Relating Fractions and Decimals

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

πŸ“˜ Reading an Inch Scale to the Nearest Fourth

New Concept

To measure lengths in inches, we use an inch scale. These scales let us read to the nearest half inch, quarter inch, or eighth inch.

What’s next

Next, you’ll practice reading an inch scale to the nearest quarter inch and see how equivalent fractions like 24\frac{2}{4} and 12\frac{1}{2} are used.

Section 2

Reading to the nearest quarter inch

Property

Inch scales have tick marks between the inch marks that let us read the scale to the nearest quarter inch. Remember that one quarter inch is the same as one fourth inch, which can be written as 14\frac{1}{4} in.

Example

A paperclip measures past the 1-inch mark to the first small tick.
Its length is 14\tfrac{1}{4} inches.

A crayon stops at the third tick mark after the 3-inch line.
Its length is 3343\tfrac{3}{4} inches.

Section 3

Two fourths equals one half

Property

When reading inch scales, keep in mind that 24\frac{2}{4} equals 12\frac{1}{2}.

Example

A toothpick measures 2242\tfrac{2}{4} inches.
We simplify this to its proper form: 2122\tfrac{1}{2} inches.

An arrow points to 24\tfrac{2}{4} on a ruler.
The correct way to name this point is 12\tfrac{1}{2} inch.

Section 4

Combining mixed number lengths

Property

To find the combined thickness of stacked objects, add their individual thicknesses. First, add the whole numbers, then add the fractions. If the fractions add up to a whole number or more, simplify and add it to the whole number total.

Example

A 1121\tfrac{1}{2} inch board on a 2 inch board:
1+2=31 + 2 = 3, so the total is 3123\tfrac{1}{2} inches.

A 1121\tfrac{1}{2} inch block on a 2122\tfrac{1}{2} inch block:
(1+2)+(12+12)=3+1=4(1+2) + (\tfrac{1}{2} + \tfrac{1}{2}) = 3 + 1 = 4 inches.

Book overview

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

Continue this chapter

Chapter 4: Lessons 31–40, Investigation 4

  1. Lesson 1

    Lesson 31: Word Problems About Comparing

  2. Lesson 2

    Lesson 32: Multiplication Facts: 9s, 10s, 11s, 12s

  3. Lesson 3

    Lesson 33: Writing Numbers Through Hundred Thousands

  4. Lesson 4

    Lesson 34: Writing Numbers Through Hundred Millions

  5. Lesson 5

    Lesson 35: Naming Mixed Numbers and Money

  6. Lesson 6

    Lesson 36: Fractions of a Dollar

  7. Lesson 7

    Lesson 37: Reading Fractions and Mixed Numbers from a Number Line

  8. Lesson 8

    Lesson 38: Multiplication Facts (Memory Group)

  9. Lesson 9Current

    Lesson 39: Reading an Inch Scale to the Nearest Fourth, Activity Make a Ruler and Measure

  10. Lesson 10

    Lesson 40: Capacity

  11. Lesson 11

    Investigation 4A: Tenths and Hundredths

  12. Lesson 12

    Investigation 4B: Relating Fractions and Decimals