## Inch by Inch

- Lesson

In this lesson, students use a ruler to represent various fractions as lengths. This lesson builds on the work done in the previous lessons with as students use a standard instrument to measure a variety of items, including items which can be measured to the nearest half and quarter of an inch.

To assess students' prior knowledge, invite them to reflect on the previous lesson. Ask them to describe what they learned that make fractions easier to understand and use.

To begin the lesson, give students an inch ruler and the Inch by Inch Activity Sheet. Tell them that today they will use a standard inch ruler to measure lengths.

Inch by Inch Activity Sheet |

Ask students how long their ruler is in inches. Remind them that a ruler is usually 12 inches long. Tell students that a long time ago, people used to measure things with their fingers, hands, and feet. The only problem was that every finger, hand, and foot was not the same length. This caused problems when trying to measure accurately.

Today, we know that the standard unit, "one foot," is equivalent to 12 inches. Using standard units like the foot or the inch helps people measure accurately.

Tell students that when they measure using an inch ruler, each inch ends at the long line above the number and that each inch is further divided into smaller parts. They can represent these parts using fractions.

The half-inch (1/2 inch) mark is exactly halfway between each number. Half-inch (1/2 inch) marks are the next longest lines. The quarter-inch (1/4 inch) marks show 1/4 of an inch and 3/4 of an inch. These markings are slightly shorter than the 1/2 inch markings. The ruler also includes smaller divisions.

Have students determine the fractional part for each of the small markings. Students should discover that each inch is further divided into 16 smaller sections. Remind students that when they measure, they always begin measuring from the left end of the ruler.

Have students use the Inch by Inch Activity Sheet to practice measuring various lengths. Assign each student a partner. Go over a few examples as a class to ensure that students are reading the ruler accurately, and then allow them to complete the remainder of the Student Learning Guide independently.

As students complete the exercise, ask them to compare their responses to their partner’s responses. If their answers differ, students should continue to work on the items until they have reached agreement. Once everyone has reached agreement, go over the answers as a class.

Next, have pairs work together to measure the items on Part II of the Inch by Inch Activity Sheet. Students should estimate the length in inches before actually measuring.

As pairs complete the actual measurements, ask them to compare their responses to another pair’s responses. If their answers differ, students should remeasure and continue to work on the items until they have reached agreement. Once everyone has reached agreement, discuss measurements as a class.

- Standard inch ruler for each student
- Inch by Inch Activity Sheet

**Assessments**

- At this stage of the unit, students should be able to do the following:
- demonstrate understanding that a fraction can be represented as part of a linear region
- describe part of a linear region using fractions
- measure lengths in fractions using a standard ruler

- Examining student recordings on the Inch by Inch Activity Sheet can be helpful in making instructional decisions about students’ understanding of measuring with fractions.

**Extensions**

A great book to illustrate the need for standard measurement is *How Big Is a Foot* by Rolf Myller.

**Questions for Students**

1. How many inches does a standard inch ruler represent?

[12.]

2. What divisions are included on the ruler to help you measure in fractional parts?

[Students should mention that each inch is divided into halves, then into fourths, and finally, into sixteenths.]

3. Which fractional part is longer, 1/4 inch or 1/2 inch?

[1/2 inch.]

4. Which fractional part is longer, 1/4 or 3/4 inch?

[3/4 inch.]

5. Which fractional part is longer, 1/2 or 7/16 inch?

[1/2 inch.]

6. Which fractional part is longer, 8/16 or 3/4 inch?

[3/4 inch.]

7. How do you go about measuring a length that is longer than one whole inch?

[First, you measure the whole inches, and then the fractional part.]

**Teacher Reflection**

- Which students understand that a fraction can be represented as part of a linear region? What activities are appropriate for students who have not yet developed this understanding?
- Which students can describe part of a linear region using fractions? What activities are appropriate for students who have not yet developed this understanding?
- Which students can measure lengths in fractions using a standard ruler? What activities are appropriate for students who have not yet developed this understanding?
- What parts of the lesson went smoothly? What parts should be modified for the future?

### Fun With Fractions: Making and Investigating Fraction Strips

### More Fun with Fraction Strips

### Investigating Fraction Relationships with Relationship Rods

Students use relationship rods to explore fraction relationships. This work with relationships lays the foundation for work with more challenging fraction concepts.

Relationship rods are wooden or plastic rods in ten different colors. They range in length from one to ten centimeters. Each length is a different color.

### Investigating Equivalent Fractions with Relationship Rods

### Learning Objectives

Students will:

- Demonstrate understanding that a fraction can be represented as part of a linear region
- Describe part of a linear region using fractions
- Measure fractional lengths using a standard ruler

### Common Core State Standards – Mathematics

Grade 3, Num & Ops Fractions

- CCSS.Math.Content.3.NF.A.1

Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

Grade 3, Measurement & Data

- CCSS.Math.Content.3.MD.B.4

Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units-- whole numbers, halves, or quarters.

Grade 5, Num & Ops Fractions

- CCSS.Math.Content.5.NF.B.3

Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?

### Common Core State Standards – Practice

- CCSS.Math.Practice.MP5

Use appropriate tools strategically.