Unit Overview



Supplemental

Fraction Unit

for

Grade Three

based on the

Common Core Standards

[pic]

SCLME ((((((

South Carolina Leaders of Mathematics Education

2011

SCLME recommends that district mathematics curriculum leaders support teachers with the implementation of this unit by providing the necessary content knowledge so that students gain a strong conceptual foundation of fractions.

Revised 3/30/12

Time: 10-12 days (60 minute class periods)

Unit Overview

Fractions are very difficult for students to learn and teachers to teach. This supplemental unit seeks to bridge a gap for students as we transition to Common Core standards. The learning activities provided herein should engage students in both hands-on and minds-on experiences. Students should have multiple opportunities to communicate about their thinking and reasoning in order to build understanding. Teachers should listen carefully to students’ ideas and encourage flexibility in their thinking.

In order for students to have a deep conceptual understanding of fractions, the focus on teaching should be with concrete materials and pictorial representations. In using best practices, virtual manipulatives should not take the place of concrete materials.

Anchor charts should be created and used throughout the unit. An anchor chart is a visual recording of students’ ideas and thinking about a certain concept. It serves to connect past teaching and learning to future teaching and learning. For example, on a piece of chart paper, the teacher will record students’ ideas about what[pic] means to them. This should include illustrations and labels of different representations of[pic]. (See Appendix A)

Models for Fractions

Area or Region Models – Fractions are based on parts of an area or region. Examples include: circular pie pieces, pattern blocks, regular/square tiles, folded paper strips (any shape), drawings on grids and partitioning shapes on geoboards.

Linear or Length Models – With length models the whole is partitioned and lengths are compared instead of area. Materials are compared on the basis of length. Examples include: fraction strips, Cuisenaire rods, number lines, rulers, and folded paper strips.

Set Models – In set models, the whole is understood to be a set of objects or group of objects, and subsets of the whole make up fractional parts. Examples; in a set of 6 marbles, [pic] is 3 marbles. This concept should be taught with concrete materials so that there would be 2 groups of 3 marbles so that each group is[pic] of 6.

Big Ideas

• Understanding Unit Fractions

• Building on Unit Fractions

• Understanding Equivalent Fractions

Common Core Standards (Grade 3)

Number and Operations-Fractions (3.NF)

Develop understanding of fractions as numbers.

1. Understand a fraction [pic]as the quantity formed by 1 part when a whole is portioned into b equal parts; understand a fraction [pic] as the quantity formed by a parts of size[pic].

2. Understand a fraction as a number on the number line; represent fractions on a number line diagram.

a. Represent a fraction [pic]on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size [pic]and that the endpoint of the part based at 0 locates the number[pic] on the number line.

b. Represent a fraction [pic]on a number line diagram by marking off a lengths [pic] from 0. Recognize that the resulting interval has size [pic] and that its endpoint locates the number [pic]on the number line.

3. Explain equivalencies of fractions in special cases, and compare fractions by reasoning about their size.

a. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.

b. Recognize and generate simple equivalent fractions, (e.g.,[pic]=[pic], [pic]= [pic]). Explain why the fractions are equivalent, e.g., by using a visual fraction model.

c. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 =[pic]; recognize that [pic] = 6; locate [pic]and 1 at the same point on a number line diagram.

d. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or , > > > > > >

Fraction Action 22 (Taken from AIMS: Actions with Fractions) – Use after the lesson Exploring with Pattern Blocks.

Show the named fraction in the hexagon on the left. In the right hexagon, build an equivalent fraction. Name the second fraction.

a. b.

[pic] = [pic] =

c. d.

[pic] = [pic] =

Formative assessment, such as student responses to teacher discussions, student interviews, oral and written activities, should be an ongoing process in the unit of study. Listed below is a bank of items from which a summative assessment may be developed.

1. Which fraction matches this chain of unit fractions?

[pic]

2. Shannon collects paper for recycling. If she collects [pic]of a pound of paper each week, how much paper will she collect in 4 weeks?

3. Use the fraction strips to answer the question.

[pic]

Which is more one twelfth or one fourth?

4. The triangle is one third of a polygon. Which polygon shows this?

[pic][pic][pic]

5. Sue rode her bike [pic] mile. Draw a picture to show this. Use the number line below.

6. Jim ate one sixth bag of cookies. Show the correct amount using the circles below.

7. One half of the pizza is pepperoni. Draw a picture to show this. Use the circle below.

8. Sarah cut her candy into pieces each the same size. She ate one eighth of her candy. Into how many pieces could she have cut her candy? Draw a picture.

9. Bob lives three miles from the library. He walked 1 mile alone then met a friend who walked with him. What fraction of the distance did he walk alone?

10. Shameka and Kia both have the same size pizza. Shemaka cut her pizza into 8 pieces each the same size. Kia cut her pizza into four pieces each the same size. Each girl ate one piece of their pizza. Who ate a larger slice?

11. Carol said that she sharpened 1/4 of the box of pencils. How many pencils could have been in the box? A. 1, B. 2, C. 3, D. 4

12. Are these figures equivalent? Why or why not?

ο

13. The picture below shows the amount of chocolate milk Lance drank. About what fraction of the container did he drink?

| |

| |

14. The picture below represents the whole. Use the picture below to answer the questions.

| | | | | | | | | | | | | | | | | | | | | | | | | |[pic] is _______________ piece(s) of the whole

[pic] is _______________ piece(s) of the whole

[pic]is ________________ piece(s) of the whole

[pic] is ________________ piece(s) of the whole

[pic] is ________________ piece(s) of the whole

15. Mark[pic]on the number line.

16. You and your friend have a Hershey bar. You both eat [pic]of your own Hershey Bar. Your friend eats more of her Hershey bar than you do. Draw a picture and explain how it is possible for your friend to have eaten more of the bar even though you both have eaten [pic] of your own Hershey bar.

17. What fraction of the shape below is shaded?

A. [pic], B. [pic], C. [pic], D. [pic]

18. Mark is offered the choice of a third of a pizza or a half of a pizza. He is very hungry and chooses the third of a pizza because it is larger. Draw a picture to show the two pizzas. Explain why he knows the third is larger.

19. Four friends are running a race. The fractions tell how much of the distance each has run.

Sandy [pic] Dale [pic] Christie [pic] Rita [pic] Carla [pic]

Place the friend on a line to show where they are between the start and finish.

20. Three children share four brownies. Each child will get[pic]. Draw a picture to show how the children should equally share the brownies.

21. Which figures(s) is correctly portioned in fourths?

Unit Resources: The resources listed below can be referenced for activities to supplement this unit of study.

Fabulous Fractions/AIMS Activities Grades 3-6 pg. 1-19

Fair Shares/Grade 3/Sharing Brownies pg. 2-37

Math Expressions/Grade 3/Unit 11/ lessons 1, 2, 3,

Beyond Pizzas and Pies/Top or Bottom With one Matters/Pg. 15-22

Lessons for introducing Fractions by Marilyn Burns

• Fractions as Parts of Sets/ pg 1

• Exploring Fractions with Pattern Blocks/pg 39

• Only One/pg 122

• Put in Order/ pg 105

Everything Coming Up Fractions with Cuisenaire Rods Pg. 1-10 John Bradford

A Collection of Math Lessons From Grades 3 through 6 by Marilyn Burns

• Fractions with Cookies/Grade 3/pg. 37-43

Teaching Student-Centered Mathematics Grade K-3 by John Van de Walle

• Unit Fractions/pg 252-258

• Models for Fractions/ pg 254-256

• Correct Shares/ pg 257

Teaching Student-Centered Mathematics Grade 3-5 by John Van de Walle

• Different Fillers/pg 152

• Dot Paper Equivalencies/pg 152

• Group the Counters, Find the Names/pg 153

• Divide and Divide Again/ pg 154

• Missing Number Equivalencies/ pg 155

• Correct Shares/ pg 136

Children’s Literature:

• Fraction Fun by David A. Adler

• Full House: An Invitation to Fractions by Dayle Ann Dodds and

Abby Carter

• Apple Fractions by Jerry Pallotta and Rob Bolster

• Piece = Part = Portion by Scott Gifford and Shmuel Thaler

• Working With Fractions by David A. Adler and Edward Miller

• The Hershey's Milk Chocolate Bar Fractions Book by Jerry Pallotta and Robert C. Bolster

• If You Were a Fraction (Math Fun) by Speed Shaskan, Trisha, Carabelli, and Francesca

• Whole-y Cow: Fractions Are Fun by Taryn Souders and Tatjiana Mai-Wyss

• Fraction Action by Loreen Leedy

• Equal Shmequal (Math Adventures) by Virginia L. Kroll and Philomena O'Neill

• Gator Pie by Louise Matthews

Appendix A

Sample Anchor Chart

[0δδδδδδδδ1δ]

1∃ 1” 3∃ Φ

3⊥

; π

4∗

1” Ξ

ω one-half

<

Appendix B

Sample Concept Chart

As you work through the lessons in the unit, create and post a list or chart to highlight key concepts that students should learn.

Fractions

• A fraction is the quantity formed when a whole is portioned into equal parts.

• A fraction with 1 as the numerator, such as [pic] is called a unit fraction.

• Fractions can be represented on a number line.

• Fractions are equivalent (equal) if they are the same size, or the same point on a number line.

• Whole numbers can be expressed as fractions (3 = [pic] or [pic]= 1).

• Fractions with the same numerator or same denominator can be compared by reasoning about their size. The two fractions must refer to the same whole.

• Unit fractions can be copied to create other fractions. Such as[pic] +[pic] =[pic]

• The numerator tells how many of the equal parts you are talking about (the counting number).

• The denominator is how many equal parts the whole is divided into (what’s being counted).

• Fractional parts are equal shares or equal-sized portions of a whole or unit. A unit can be an object or a collection of things. More abstractly, the unit is counted as 1. On the number line, the distance from 0 to 1 is the unit.

• The more fractional parts used to make a whole, the smaller the parts (the larger the denominator, the smaller the part). For example, eighths are smaller than fifths.

-----------------------

16 is 2 groups of 8

3

2

1

[pic]

[pic]

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download