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$: wrzochulmathematics.files.wordpress.com · Web viewThis lesson also reviews Day 3’s lesson with pattern-block fractions. Connections with the New York State. Core Curriculum S$
Wrzochul Mathematics

Fractions, Decimals, and Percents Unit –Lesson 4

Reviewing Fractions on a Ruler

Day: 4

Grade Level: 5

Rationale: This lesson introduces fractions on a ruler. Students will review fractions using a ruler. This lesson also reviews Day 3’s lesson with pattern-block fractions.

Connections with the New York State Core Curriculum Standards: Problem Solving Strand:

5.PS.6 Translate from a picture/diagram to a numeric expression5.PS.8 Select an appropriate representation of a problem5.PS.13 Model problems with pictures/diagrams or physical objects5.PS.23 Verify results of a problem

Communication Strand:5.CM.4 Share organized mathematical ideas through the manipulations of objects, numerical tables, drawings, pictures, charts, graphs, tables, diagrams, models, and symbols in written and verbal form.

Representation Strand5.R.1 Use physical objects, drawings, charts, tables, graphs, symbols, equations, or objects created using technology as representations

Number Sense and Operations Strand5.N.4 Create equivalent fractions, given a fraction

Connections with NCTM standards:Numbers and Operations

• develop understanding of fractions as parts of unit wholes, as parts of a collection, as locations on number lines, and as divisions of whole numbers;

• use models, benchmarks, and equivalent forms to judge the size of fractions;• recognize and generate equivalent forms of commonly used fractions, decimals, and percents;• develop and use strategies to estimate the results of whole-number computations and to judge

the reasonableness of such results;• develop and use strategies to estimate computations involving fractions and decimals in

situations relevant to students’ experience;• use visual models, benchmarks, and equivalent forms to add and subtract commonly used

fractions and decimals;Geometry Standard

• identify, compare, and analyze attributes of two- and three-dimensional shapes and develop vocabulary to describe the attributes;

• explore congruence and similarity;• make and test conjectures about geometric properties and relationships and develop logical

arguments to justify conclusions.

Adapted from:Bell, M., Bretzlauf, J., Dillard, A., Hartfield, R., Isaacs, A., McBride, J., Pitvorec, K., Saecker, P., Balfanz, and R., Carroll, W. (2002).

Everyday mathematics: Teacher’s lesson guide fifth grade. Chicago: Everyday Learning Corporation.


• use geometric models to solve problems in other areas of mathematics, such as number and measurement;

Measurement Standard• understand such attributes as length, area, weight, volume, and size of angle and select the

appropriate type of unit for measuring each attribute;• understand that measurements are approximations and how differences in units affect

precision;Process Standards

Problem Solving• Build new mathematical knowledge through problem solving• Solve problems that arise in mathematics and in other contextsCommunication• Organize and consolidate their mathematical thinking through communication• Communicate their mathematical thinking coherently and clearly to peers, teachers, and others• Analyze and evaluate the mathematical thinking and strategies of others;• Use the language of mathematics to express mathematical ideas precisely.Connections• Create and use representations to organize, record, and communicate mathematical ideas

Objectives: The students will:

Locate fractions and mixed numbers on a rulerThe students will:

Analyze mistakes in placing fraction labels on a number lineThe students will:

Find fractions of a whole with pattern blocks

Materials: Student Worksheets #5: Fractions on a Ruler Student Worksheets #6: Pattern Blocks and Fractions Rulers Pattern blocks

Specific step-by-step sequence for the lesson.

1.) Introduction or Anticipatory set Distribute pattern blocks to individual students Display problems from Student Worksheet #6: Pattern-Block Patterns on the board Students solve independently Call on students to provide answers and explain their reasoning

2.) Reviewing Fractions on a Ruler Complete Student Worksheet #5: Fractions on a Ruler together as a class

o Students first complete each question independently then review answer as whole class




Assessment: Student Worksheets #5 and #6

Differentiated Curriculum/Instruction: For students having difficulty reading the ruler, suggest that they use colored pencils to

highlight different markings.o For example, students can trace the ½” marks with blue, the ¼” marks with

orange, and the 1/8” marks with greeno Note that the marks are different lengthso Having students determine patterns between the different lengths




Student Worksheet #5

Name: ____________________________________________

Fractions on a Ruler

1. Find the mark for each of the lengths on the ruler below. Write the letter above the mark. Letters A and B are done for you.

A. 5” B. ½” C. 3 ½” D. 2 ½”

E. 4 ¾” F. ¼” G. 4 1/8” H. 1 7/8”

I. 1 3/8” J. 15/16” K. 3 1/16” L. 5 9/16”

2. On the ruler above, how many fractions are shown between 0 and 1? Explain.

______________________________________________________________________________

3. Grace was supposed to mark ½ on a number line. This is what she did.

Explain Grace’s mistake. _________________________________________________________

______________________________________________________________________________Adapted from:

Bell, M., Bretzlauf, J., Dillard, A., Hartfield, R., Isaacs, A., McBride, J., Pitvorec, K., Saecker, P., Balfanz, and R., Carroll, W. (2002). Everyday mathematics: Teacher’s lesson guide fifth grade. Chicago: Everyday Learning Corporation.


4. Rocco said his stick was 4 3/16 inches long.

Explain his mistake. _____________________________________________________________

______________________________________________________________________________




Student Worksheet #5 - KEYFractions on a Ruler

1. Find the mark for each of the lengths on the ruler below. Write the letter above the mark. Letters A and B are done for you.

A. 5” B. ½” C. 3 ½” D. 2 ½”

E. 4 ¾” F. ¼” G. 4 1/8” H. 1 7/8”

I. 1 3/8” J. 15/16” K. 3 1/16” L. 5 9/16”

2. On the ruler above, how many fractions are shown between 0 and 1? Explain.

Sample answer: 15; the fraction 1/16 through 15/16 name marks between 0 and 1.

3. Grace was supposed to mark ½ on a number line. This is what she did.

Explain Grace’s mistake. Sample answer: Grace marked 1 ½. She should have placed ½ between 0 and

4. Rocco said his stick was 4 3/16 inches long.

Explain his mistake. Sample answer: Rocco lined up his stick at 1 and not at 0. Rocco’s stick is really 3 3/16 inches long.




Student Worksheet #6

Name: __________________________________________________

Pattern-Block Fractions

For Problems 1-3, Shape A is the Whole.

1. What fraction of the shape is covered by 1 trapezoid? __________________________

2. What fraction of the shape is covered by 1 rhombus? __________________________

3. What fraction of the shape is covered by 1 triangle? __________________________

For problems 4-7, Shape B is the Whole.




4. What fraction of the shape is covered by 1 hexagon? _________________________

5. What fraction of the shape is covered by 1 trapezoid? ________________________

6. What fractions of the shape is covered by 1 rhombus? ________________________

What fraction of the shape is covered by 1 triangle? __________________________




Student Worksheet #6 - KEY

Pattern-Block Fractions

For Problems 1-3, Shape A is the Whole.

1. What fraction of the shape is covered by 1 trapezoid? ½

2. What fraction of the shape is covered by 1 rhombus? 1/3

3. What fraction of the shape is covered by 1 triangle? 1/6

For problems 4-7, Shape B is the Whole.

4. What fraction of the shape is covered by 1 hexagon? ½

5. What fraction of the shape is covered by 1 trapezoid? ¼

6. What fractions of the shape is covered by 1 rhombus? 1/6

7. What fraction of the shape is covered by 1 triangle? 1/12



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