Wrzochul Mathematics Fractions, Decimals, and Percents Unit –Lesson 1 Fraction Review Day: 1 Grade Level: 5 Rationale: This is the initial lesson of the fractions, decimals and percents unit. The students will first complete the unit pre-test. The students will then review key fraction concepts from previous grade levels. The students will use mathematics manipulatives to solve a variety of parts-and-whole problems. Connections with the New York State Core Curriculum Standards: 5.PS.6 Translate from a picture/diagram to a numeric expression 5.PS.8 Select an appropriate representation of a problem Students will apply and adapt a variety of appropriate strategies to solve problems. 5.PS.13 Model problems with pictures/diagrams or physical objects 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. 5.R.1 Use physical objects, drawings, charts, tables, graphs, symbols, equations, or objects created using technology as representations 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; Process Standards 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.
Transcript
Wrzochul Mathematics
Fractions, Decimals, and Percents Unit –Lesson 1
Fraction Review
Day: 1
Grade Level: 5
Rationale: This is the initial lesson of the fractions, decimals and percents unit. The students will first complete the unit pre-test. The students will then review key fraction concepts from previous grade levels. The students will use mathematics manipulatives to solve a variety of parts-and-whole problems.
Connections with the New York State Core Curriculum Standards: 5.PS.6 Translate from a picture/diagram to a numeric expression5.PS.8 Select an appropriate representation of a problemStudents will apply and adapt a variety of appropriate strategies to solve problems.5.PS.13 Model problems with pictures/diagrams or physical objects5.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.5.R.1 Use physical objects, drawings, charts, tables, graphs, symbols, equations, or objects created using technology as representations
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;
Process StandardsProblem Solving• Build new mathematical knowledge through problem solvingCommunication 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;
Objectives: The students will:
Complete the unit pre-testThe students will:
Review fractions using manipulativesThe students will:
Find fractional parts of whole numbers
Adapted from:Bell, M., Bretzlauf, J., Dillard, A., Hartfield, R., Isaacs, A., McBride, J., Pitvorec, K., Saecker, P., Balfanz, and R., Carroll, W. (2002).
Materials: Student Worksheets #1: Parts and Wholes dry-erase boards and markers 20 “counters” per partnership
Specific step-by-step sequence for the lesson.
1.) Introduction or Anticipatory set Students will write any five fractions on their white board and circle the least fraction and
the greatest fraction Post questions with fractions on the board or verbally explain. Specify whether the
answer is a fraction or a whole number. Example questions include, “An hour is what fraction of a day?” 1/24 and “1/2 hour is how many minutes?” 30
2.) Whole-class Discussion Have students share their fractions with the class. Use student examples to review
fraction concepts. Ask students how they knew which was the least and greatest. Examples of key concepts include:
o Fractions were invented to express numbers that are between whole numbers.o Fractions can show measures between whole numbers on rulers and scales.o Fractions can name part of a whole object.o Fractions can name part of a collection of objects.o Fractions can compare two quantities as ratios or rates.o Fractions can express chance or probability.o Fractions can represent division.
3.) Other key concepts to review: Draw a unit or whole box on the board and have students do the same on their boards Review that fractions are written vertically (a/b) Review denominator and numerator
4.) Solving Parts-and Whole Problems with Fractions Distribute 20 counters to each partnership of students Circulate as students work in partners to complete Student Worksheet #1: Parts and
Wholes Review answers to Student Worksheet #1 together as whole group
Assessment: Unit pre-test and Student Worksheet #1
Differentiated Curriculum/Instruction:
Adapted from:Bell, M., Bretzlauf, J., Dillard, A., Hartfield, R., Isaacs, A., McBride, J., Pitvorec, K., Saecker, P., Balfanz, and R., Carroll, W. (2002).
Adapted from:Bell, M., Bretzlauf, J., Dillard, A., Hartfield, R., Isaacs, A., McBride, J., Pitvorec, K., Saecker, P., Balfanz, and R., Carroll, W. (2002).
9. First, estimate the size of each piece of the circle graph at the right. Then use your Percent Circle to find the actual percent.
Flavor Estimate Percent
Chocolate ________ ________
Strawberry ________ ________
Vanilla ________ ________
Cookie Dough ________ ________
Other ________ ________
Adapted from:Bell, M., Bretzlauf, J., Dillard, A., Hartfield, R., Isaacs, A., McBride, J., Pitvorec, K., Saecker, P., Balfanz, and R., Carroll, W. (2002).
Write at least one equivalent fraction for the fractions below.SAMPLE ANSWERS:1. 2 2. 6 4 ½; 3/6; or 6/12 9 2/3; 12/18; or 18/27
Rename the fraction as a mixed number.SAMPLE ANSWERS:3. 12 4. 18 5 1 7/5; or 2 2/5 8 2 ¼; or 2 2/8
Add the fractions below.
5. 1 + 3 6. 1 + 1 8 8 = 4/8; or ½ 2 4 = 3/4
Write <, =, or > to make the sentence true.
7. 3 3 8. 6 9 8 < 5 8 = 12
9. First, estimate the size of each piece of the circle graph at the right. Then use your Percent Circle to find the actual percent.
Adapted from:Bell, M., Bretzlauf, J., Dillard, A., Hartfield, R., Isaacs, A., McBride, J., Pitvorec, K., Saecker, P., Balfanz, and R., Carroll, W. (2002).
Adapted from:Bell, M., Bretzlauf, J., Dillard, A., Hartfield, R., Isaacs, A., McBride, J., Pitvorec, K., Saecker, P., Balfanz, and R., Carroll, W. (2002).
Work with a partner. Use counters to help you solve the problems.
1. This set has 15 counters. What fraction of the set is green?
_______________________
2. If 12 counters are the whole set, what fractions of the set is 8 counters?
_______________________
3. If 12 counters are the whole set, how many counters is ¼ of a set?
______________________ counters
4. If 20 counters are a whole set, how many counters make 4/5?
Adapted from:Bell, M., Bretzlauf, J., Dillard, A., Hartfield, R., Isaacs, A., McBride, J., Pitvorec, K., Saecker, P., Balfanz, and R., Carroll, W. (2002).
5. If 6 counters are ½ of a set, how big is the set?
_______________________ counters
6. If 12 counters are ¾ of a set, how many counters are in the whole set?
_______________________ counters
7. If 8 counters are a whole set, how many counters are in one and one-half sets?
_______________________ counters
8. If 6 counters are two-thirds of a set, how many counters are in one and two-thirds sets?
Adapted from:Bell, M., Bretzlauf, J., Dillard, A., Hartfield, R., Isaacs, A., McBride, J., Pitvorec, K., Saecker, P., Balfanz, and R., Carroll, W. (2002).
Work with a partner. Use counters to help you solve the problems.
1. This set has 15 counters. What fraction of the set is green?
6/15 or 2/5
2. If 12 counters are the whole set, what fractions of the set is 8 counters?
8/12 or 2/3
3. If 12 counters are the whole set, how many counters is ¼ of a set?
Adapted from:Bell, M., Bretzlauf, J., Dillard, A., Hartfield, R., Isaacs, A., McBride, J., Pitvorec, K., Saecker, P., Balfanz, and R., Carroll, W. (2002).
4. If 20 counters are a whole set, how many counters make 4/5?
16 counters
5. If 6 counters are ½ of a set, how big is the set?
12 counters
6. If 12 counters are ¾ of a set, how many counters are in the whole set?
16 counters
7. If 8 counters are a whole set, how many counters are in one and one-half sets?
Adapted from:Bell, M., Bretzlauf, J., Dillard, A., Hartfield, R., Isaacs, A., McBride, J., Pitvorec, K., Saecker, P., Balfanz, and R., Carroll, W. (2002).
8. If 6 counters are two-thirds of a set, how many counters are in one and two-thirds sets?
15 counters
Adapted from:Bell, M., Bretzlauf, J., Dillard, A., Hartfield, R., Isaacs, A., McBride, J., Pitvorec, K., Saecker, P., Balfanz, and R., Carroll, W. (2002).
