Fun With Fractions - Kathy Reck's Teaching...

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Fun With

Fractions

2nd Grade Unit Plan CCSS 2.G.3.

Kathy Reck

EDI 685

November 5, 2013

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Table of Contents Page

Unit Overview 2

Lesson 1 – Roomy Rectangles 4

Lesson 2 – A Party with Pattern Blocks 10

Lesson 3 – Estimation Station 14

Lesson 4 – Friendly Fractions 19

Lesson 5 – Dare to Compare 23

Lesson 6 – Groovy Groups 39

Lesson 7 – Fraction Flags 46

Assessment of Student Learning 50

Bibliography 51

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Unit overview By CCSS’s, in first grade students learned how to partition circles and squares into two and four parts. Students have also had exposure to hexagons, pentagons, trapezoids, squares, rectangles, triangles, and circles. In this second grade unit lesson about fractions, students will explore fractions of geometric shapes, leading them to proficiency of the following Common Core State Standard:

CCSS.Math.Content.2.G.3. Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.

In lesson one, students will do a hands-on folding activity in order to help them describe and compare fractional parts. This lesson helps students understand how to partition circles and rectangles into two, three, or four equal shares, and describe the whole as two halves, three thirds, four fourths. Literature, art, and technology are incorporated into this lesson. Lesson two contains hands-on activities with pattern blocks to help solidify the lesson from yesterday. Students learning objectives will be to understand how to partition circles and rectangles into two, three, or four equal shares, and describe the whole as two halves, three thirds, four fourths. Technology is incorporated into this lesson. In lesson three, students will learn to estimate fractional parts in a variety of hands-on activities in order to describe the shares using the words halves, thirds, half of, a third of, and to describe the whole as two halves, three thirds, four fourths. Literature and student movement around the room is incorporated into this lesson. Lesson four has students comparing fractional parts. In this lesson students will partition circles and rectangles into fractional parts and describe the parts using fractional terms. This lesson is rich in technology. In lesson five, students compare fractional parts of shapes. Students will partition circles and rectangles into fractional parts and describe the parts using fractional terms. This lesson has a literature component along with activities requiring technology. Lesson six teaches students how to describe shares or parts of groups as halves, thirds, and fourths. This lesson is rich in movement and hands on activities. This lesson incorporates some movement around the room is part of this lesson. Lesson seven is the culminating lesson which integrates social studies with math. Students will explore flags from around the world and analyze their fractional patterns.

http://www.corestandards.org/Math/Content/2/G/A/1

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Students will replicate a flag to hang on our Fraction Flags bulletin board. This lesson is rich in literature, the arts, and also incorporates some use of technology. All lessons in this unit begin and end with reviewing learning objectives with the students. In addition, each lesson is rich with cooperative learning in pairs, small groups, and whole class discussions.

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Grade Level

2nd

Time Needed

60 minutes

Materials Needed

90 rectangles – approx. 4x6 inches each

Book: Full House An Invitation to Fractions by Dayle Ann Dodds 3 hershey bars to demonstrate sharing (and optional bag of mini’s to share with class) Access to Youtube denominator video: http://www.youtube.com/watch?v=x8VXW1GakB8

Lesson 1: Roomy Rectangles

Introduction: In today’s lesson we build on students’ prior

knowledge in a hands-on activity which has students folding rectangles into 2, 4, and 8 equal parts. Students describe fractions and compare the various rectangles to one another.

Background: By CCSS, in 1st grade, students learned basic

concepts of half and fourths (quarters) as equal parts of a whole. Today we introduce eighths and the concept of numerator and denominator. Although these are not part of the CCSS, the concepts are included in the lesson since they are tested as part of the Everyday Math curriculum used by the school district.

GLCE(s):


Engagement:

Read aloud: Full House: An Invitation to Fractions by Dayle Ann Dodds

Ask students: Does anyone remember a time when you used a fraction? Turn and talk with a partner. Have a group discussion about personal connections to fractions, asking students to describe their partner’s connection. Possible answers: Students may recall their work with fractions from kindergarten and first grade where they were introduced to

Unit Lesson – Fantastically Fun Fractions

http://www.youtube.com/watch?v=x8VXW1GakB8




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identifying fractions of regions. They may or may not be able to identify ½ as used in sharing “half” of something.

Exploration: Tell students that their learning objectives for today are: “I can partition circles and rectangles into two, three, or four equal shares” “I can describe the whole as two halves, three thirds, four fourths.”

Hand out three rectangles to each student. Invite students to fold their rectangle into two equal parts, without giving further instructions. Students might make the error of folding two times. This is okay. It is part of the learning. The purpose is to see how many ways students can find to fold their rectangle in half. There will be two ways: diagonal and horizontal/vertical. Have students compare their squares. Draw answers on board. Ask students: What is the word we use for one of these two equal parts of a whole? (Half, halves) What are the different ways we can write/represent one of these two equal parts? (possible answers: 1/2, half, halves, half-of, one out of two, two out of two) Label these parts on the drawings. How many ways did we find to make two halves? (two (or more, if students determine that the horizontal fold is different than the vertical fold, etc.)). Next, invite students to take their 2nd rectangle and fold it into four equal parts. Students might make the error of folding four times. This is okay. It is part of the learning. Time permitting, this would be a good extension conversation to have with the group. Ask students to compare this newly folded rectangle with the students in their group. Ask for student volunteers to model their different rectangles. Draw answers on board to show comparisons. There will be three (or more possible ways to fold the square into four equal parts, depending on the orientation of the paper). Ask students: What is the word we use for one of these four equal parts of a whole? (fourths, quarters)

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What are the different ways we can write/represent one of these four equal parts? (possible answers: 1/4, fourth, quarter, one-fourth-of, one-quarter-of, one-out-of-four) Label these parts on the drawings. How many ways did we find to make four equal parts? (three (or more, depending if students determine that the horizontal fold is different than the vertical fold). Watch for the error of folding the rectangle diagonally. Folding diagonally can create two equal parts, but not four equal parts. Invite students to fold their 3rd rectangle into eight equal parts. This will require three folds, but again, students might make the error of folding eight times. This is okay. It is part of the learning. Time permitting, this would be a good extension conversation to have with the group. Ask for student volunteers to model their different folded rectangles. There will be 3 (or more ways to show the folds, depending on student perspective of orientation of the paper). If students have not arrived at all the ways to fold the paper, have them brainstorm together in groups of four. Ask students: What is the word we use for one of these eight equal parts of a whole? (eighths) What are the different ways we can write/represent one of these eight equal parts? (possible answers: 1/8, eighth, one-eighth-of, one-out-of-eight) How many ways did we find to make eight equal parts? (three (or more, depending if students determine that the horizontal fold is different than the vertical fold)).

Explanation:

As students are doing this part of the activity, teacher should be showing the work on the Smartboard. For rectangle number one, we determined that the parts of the whole were called halves. Have students write ½ on each half of the rectangle. Ask: “How many halves make up this whole rectangle?” (two). Count out loud as a class “one-half, two halves.” “When we add the two halves together, we have the

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whole.” Write ½ + ½ = 2/2 and 2/2 = 1, on the board. Explain that ½ is called a fraction. Ask students: Must the parts be equal to be half? (Yes) Hopefully a few students will say no. Write the tally of yes and no answers on the board to be addressed later in a sharing demonstration. Don’t give away answer yet. Ask students to color ½ of their rectangle yellow. Repeat this with rectangle two (the one folded into quarters). Recall the information written on the board about this rectangle. Have students write ¼ in each section of the rectangle. Ask students: Must the parts be equal to be fourths? (Yes) Hopefully a few students will say no. Write the tally of yes and no answers on the board to be addressed later in a sharing demonstration. Don’t give away answer yet. Ask: “How many fourths make up the whole rectangle?” (four) Count out loud as a class “one-fourth, two-fourths, three-fourths, four-fourths.” When we add all of these together, we have one whole.” Write ¼ + ¼ + ¼ + ¼ = 4/4 and 4/4 = 1, on the board. Remind students that we are writing fractions. Ask students to color in ¼ of the rectangle with red. Then color another ¼ of the rectangle with blue. Finally color the remaining part of the rectangle with green. (It is important that all students use the same colors.) Ask students: “How much of the rectangle is colored red?” ( ¼ ) “Blue?” ( ¼ ) “Green?” (2/4 or ½ ) Write 2/4 and/or ½ on the board. “How do you know that the green section is two-fourths?” (Count one-fourth, two-fourths) “Can anyone tell me what the bottom number represents?” (The total number of parts of the whole) “Can anyone tell me what the top number represents?” (the number of parts of the whole that we colored) “Compare the red and blue sections together to the green section. What do you notice?” (they are the same size) “How much of the rectangle is purple?” (0/4) “How do we write this?” (zero over four) “How much of the rectangle is colored in any color?” (4/4) “How do we write this?” (four over four)

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“How much of the rectangle is not red?” (3/4) “How do we write this? (three over four) “Compare this rectangle to the “halves” rectangle. What do you notice?” (the green section is the same size as the yellow section). “How much of the “halves” rectangle is black? (0/2) Repeat this process with the eighths rectangle and make similar comparisons. Revisit the question asked earlier: Do the parts need to be equal? Ask students if anyone wants to change his/her answer. If anyone is still in doubt, do the following sharing demonstration: Ask a student to help demonstrate sharing. Offer that student part of your candy bar. Break the candy bar into 2 unequal parts. Ask the student which part he/she would prefer (whisper that he should pick the larger part). Ask: “Why would you want the larger part of the candy bar?” Possible answer: “Because it is bigger than the other part.” Ask: “Do is it half of the candy bar?” Draw the candy bar on the board with a dashed line where the break occurred so the whole class can see.

Extension:

Write one of the fractions on the board. Recall that students said the top number represents the number of colored parts and that the bottom number represents the total number of parts. Introduce the terms Numerator and Denominator. The numerator is the number on the top. The Denominator is the number on the bottom. We will watch a short video clip about this: http://www.youtube.com/watch?v=x8VXW1GakB8 Take quiz that goes along with this video. Teacher will need to pause the video after each question is presented. Have students “think-pair-share” for answers. Have students go to the A, B,C, D corners of their choice. Repeat for each question. Pause after each answer to clarify any questions.

For struggling students, have them log onto Sheppard Software website for fraction work. www.sheppardsoftware.com


http://www.sheppardsoftware.com/

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Evaluation:

Have students chorus read the learning objectives with teacher. Ask students to rate their own knowledge of our learning objectives on a scale of 1-4. Students should keep their eyes closed as they hold up 1, 2, 3, or 4 fingers. Tell students that they are making a drawing of a rectangular summer vegetable garden. On a clean sheet of paper, with name and student number on the top, students should include the following:

rectangular garden Color 1/4 red for tomatoes Color ¼ green for green peppers Color 2/4 yellow for corn

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Grade Level

2nd

Time Needed

60 minutes

Materials Needed

Pattern Blocks for the

whole class: hexagons, trapezoids, rhombuses,

triangles

Internet access to

http://www.youtube.com/watch?v=DnFrOetuUKg 27 copies of Fraction message sheet (attached)

Unit Lesson 2: A Party with Pattern Blocks

Introduction: In this lesson students will identify parts of

whole shapes as fractional parts of those geometric shapes.

Background: In the previous lesson, students learned to

partition a rectangle into two, four, and eight parts. They were also introduced to the concept of numerator and denominator. Today we will work on thirds and sixths, in addition to halves, and fourths.

GLCE(s):


Engagement: Play Mr. R’s Fractions, Fractions song

http://www.youtube.com/watch?v=DnFrOetuUKg

Invite students to turn and talk to a partner about connections they made with the video. Give students 1 minute to discuss. Talk as a group about a few of their connections. Possible answers: four quarters makes one whole, denominator down, numerator on top, one-fourth, equal pieces (an important concept to tease out), parts of a whole (an important concept to tease out).







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Exploration: Tell students that their learning objectives for today are: “I can partition circles and rectangles into two, three, or four equal shares” “I can describe the whole as two halves, three thirds, four fourths.” Distribute pattern blocks to each student. In pairs, students should determine the answer to the following teacher lead questions, recording answers and illustrate pictures of their work.

1. How many green triangles fit onto the blue rhombus? (2) 2. If the blue rhombus is one whole, what fraction of does one green triangle

represent? (1/2) 3. How many green triangles fit onto the red trapezoid? (3) 4. If the red trapezoid is one whole, what fraction of one is the green triangle?

(1/3) 5. How many red trapezoids fit onto the yellow hexagon? (2) 6. If the yellow hexagon is one whole, what fraction of one is the red trapezoid?

(1/2 ) 7. How many green triangles fit onto the yellow hexagon? (6) 8. If the yellow hexagon is one whole, what fraction of one is the green

triangle?(1/6) 9. How many blue rhombuses fit onto the yellow hexagon? (3) 10. If the yellow hexagon is one whole, what fraction of one is the blue rhombus?

(1/3) 11. How many blue rhombuses fit onto the red trapezoid? (1 and a half, or one

plus a green triangle) 12. If the red trapezoid is one whole, what fraction of one is the green triangle?

(1/3)

More challenging questions:

If the red trapezoid is one whole, how much is the yellow hexagon? (2) If the blue rhombus is one whole, how much is the yellow hexagon? (3)

If the green triangle is one whole, how much is the blue rhombus? (2) If the green triangle is one whole, how much is the red trapezoid? (3)

Teacher should attend to questions and make sure students have the right idea.

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Explanation:

Let’s look at the yellow hexagon. How many red trapezoids covered it? How many blue rhombuses covered it? How many green triangles covered it? What do you notice?

Extension:

Tell students they will be creating their own geometric pattern. Model the putting four squares together to make a large square. Illustrate this shape by outlining the square and partitioning it into the four smaller squares. Label each square ¼. Students: Make a geometric pattern using 3 to 8 of the same pattern blocks. Illustrate your geometric shape. What fraction of the shape is each of your pattern blocks? If you take one pattern block away from your creation, what fraction of blocks is left? Have students repeat this activity using a different pattern block.

Evaluation:

Have students chorus read the learning objectives with teacher. Ask students to rate their own knowledge of our learning objectives on a scale of 1-4. Students should keep their eyes closed as they hold up 1, 2, 3, or 4 fingers. Hand out the Fraction Message sheet for students to complete. Clarify any questions about terminology with students: first, last, middle, second, third, fourth, fifth, sixth (meanings of the capitalized words are not needed). Model numbers one, two, and 15 with the students. This is an independent activity.

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Grade Level

2nd

Time Needed

60 minutes

Materials Needed

Book: Give Me Half by Stuart J. Murphy 28 copies of each activity (attached):

Halfness What’s Left? Activity materials:

Four thick books, different thicknesses

4 clear cups

4 cups of dried beans in a big container

12 coins Four pieces of

string approx. 36 inches. Tied each piece closed so that it makes a loop.

16 Measuring tapes

16 yardsticks 16 rulers 1 piece of paper with a line at ¼. Color in the ¼ with red.

Unit Lesson 3: Estimation Station

Introduction: In this lesson, students will sharpen their

estimation skills through a variety of hands-on activities.

Background: Teacher will need to set up 7 stations for the

Exploration part of this lesson. Key words to identify with students: estimation, irregular shape, and verify.

GLCE(s):


Engagement:

Read aloud: Give Me Half by Stuart J. Murphy Who can tell me what “half” means? (two EQUAL parts) – if students do not remember the word equal, tease this out by asking questions such as, “So if I want so share half of my granola bar with you, I can do this?” - illustrate an uneven amount for “half” on the board.”



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Exploration:

Tell students that their learning objectives for today are: “I can describe the shares using the words halves, thirds, half of, a third of” “I can describe the whole as two halves, three thirds, four fourths.” “I can recognize that equal shares of identical wholes need not have the same shape.” Prior to this activity, set up 7 stations, with a ruler, yardstick, and measuring tape at each: 1. Four thick books 2. 4 clear cups, one large container of beans 3. 12 coins 4. Several extra measuring tapes, yardsticks, and rulers 5. Several extra measuring tapes, yardsticks, and rulers 6. 4 loops of string 7. Several extra measuring tapes, yardsticks, and rulers Teacher: “Today we will be using our senses to “estimate” half of something. Turn and talk with a partner about the word estimate.’“(means to guess or judge) Invite partners to share their opinions with the class: Possible answers: guess, judge Halfness Activity. Hand out the activity page. Teacher explains to students that they will work in small groups of four. Show students each of the seven stations and model what they will do at each, while reading the directions from the activity page. “There are seven estimation stations for the students to rotate through. For some of the stations, students may want to do the activity individually, while other activities require partner work. Each group will begin at a different station. Do each activity 3 times, recording answers on your paper. You will need to come up with a way to check your estimation in order to check your guess.” Teacher should circulate around room to answer questions and make sure students are on track. When all groups have had a chance to visit the seven stations, reconvene as a class.

Explanation:

Ask students if their estimations got better each of the 3 guesses? Visual assessment: ask the students for a thumbs-up, sideways, or down.

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At which stations did your estimates get better with each try? (they each likely got better, but for the distance activities, the students may use the information from their first guess to make their second guess perfect.) Explain why your estimates got better. Ask students how they checked their visual estimates. Possible answers: measured with a ruler, measured by comparing both parts Which visual estimations were the hardest? Which visual estimations were the easiest?

Extension:

Distribute the What’s Left? Activity to each student. This will be a whole class activity. Tell students that, together, we will be estimating how much food is showing in each problem. These 4 problems get progressively harder, so don’t rush the last two questions. Give students time to explain their reasoning. Homework for tonight: Find something at home to estimate. Ideas: estimate how much water is in a cup, estimate the half-way point across your room?, estimate 1/3 of a pile of pennies, estimate ¾ of your pile of stuffed animals. Find a way to verify your guess. Illustrate your estimate on paper and write a sentence about how close your estimate was to your guess.

Evaluation:

Formative Assessments: Have students chorus read the learning objectives with teacher. Ask students to rate their own knowledge of our learning objectives on a scale of 1-4. Students should keep their eyes closed as they hold up 1, 2, 3, or 4 fingers. Hold up a piece of paper with a line at ¼. (Color ¼ of paper red) Ask students to estimate how much of the paper is colored red and write a sentence about their estimation.

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Grade Level

2nd

Time Needed

60 minutes

Materials Needed

28 copies of Fraction Strips activity sheet (attached)

C.O.W

Internet access to: YouTube video: http://www.youtube.com/watch?v=wL4hICyMLKU Promethean Planet: http://www.prometheanplanet.com/en/Resources/Item/76426/comparing-fractions-and-equivalent-fractions#.UnVD2vkqhng Sheppard Software: http://www.sheppardsoftware.com/mathgames/fractions/equivalent_fractions_shoot.htm Fraction Pizza: http://math.rice.edu/~lanius/fractions/frac4.html

Unit Lesson 4: Friendly Fractions

Introduction: In this lesson, students will learn how to identify

equivalent fractions (friendly fractions).

Background: Prior to this lesson, students have learned halves,

thirds, fourths, fifths, sixths, and eighths. In this lesson students will learn to identify equivalent fractions. Equivalent will be a new term, which the video introduces very well.

GLCE(s):


Engagement:

Watch Equivalent Fractions video: http://www.youtube.com/watch?v=wL4hICyMLKU Pause video at each visual in order to talk through meanings with students. The middle of this video has a cute animated cartoon that illustrates equivalent bars of gold. After the video, ask students to turn and talk with a partner about the meaning of equivalent. Ask students to share their answers. Possible answers: the same as, two fractions that are different but mean the same, equal to.


http://www.youtube.com/watch?v=wL4hICyMLKU



http://www.prometheanplanet.com/en/Resources/Item/76426/comparing-fractions-and-equivalent-fractions#.UnVD2vkqhng







http://www.sheppardsoftware.com/mathgames/fractions/equivalent_fractions_shoot.htm





http://math.rice.edu/~lanius/fractions/frac4.html





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Exploration: Tell students that their learning objectives for today are: “I can describe the shares using the words halves, thirds, half of, a third of” “I can describe the whole as two halves, three thirds, four fourths.”

Load the following Smartboard interactive flipchart about equivalent fractions. Begin this presentation on slide 7. http://www.prometheanplanet.com/en/Resources/Item/76426/comparing-fractions-and-equivalent-fractions#.UnVD2vkqhng Hand out Fraction Strips sheet to all students: Students will work in pairs to complete this sheet. Model the first 3 lines of the sheet: First bar: 1/2 2nd bar: 1/3, 1/3 3rd bar: invite students to help with this: 1/4, 1/4, 1/4 Invite students to complete the sheet, excluding the bottom three rows. Students who find this easy may want to experiment with the bottom three rows. Model coloring each bar a different color (all halves will be one color, all fourths will be one color, etc.). Students cut out each bar and fractions. Explain that it will be important for them to cut on the lines so that the fractions are the right size. Explore what fractions are equivalent to each other. Model: ½ = two ¼’s. Have students write down their findings in their journal, using illustrations. We will have a discussion about findings shortly. Teacher should circulate around room to answer questions and make sure students have the right idea.

Explanation:

Have students display their findings to the class. After each presentation, say to the class, “If you also discovered that ___ = ____, give me a thumbs up/wink/pat yourself on the shoulder.” Possible answers: ½ = ¼, ¼ = 2/4 = 1/8, 1/8, 1/8, 1/8 = 4/8 1/3 = 1/6, 1/6 2/3 = 1/6, 1/6, 1/6, 1/6 ¼ = 1/8, 1/8 2/4 = 1/8, 1/8, 1/8, 1/8 ¾ = 1/8, 1/8, 1/8, 1/8, 1/8, 1/8 = 6/8



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Watch for and clear up misconceptions about equivalent fractions. Say “I’m so glad you brought this up Johnny. We should talk about this because I am sure some of your classmates got this answer, too.” Possible problem areas: students did not cut on the lines. Some fractions look like they might be equivalent, but they are not.

Extension:

Get computers from Computer Cart on Wheels. Have students log-on to one of two programs, both of which allow students to practice equivalent fractions. Sheppard Software activity: Instruct students to begin on Level 1 of Game 1. Students should email me their results at [email protected] http://www.sheppardsoftware.com/mathgames/fractions/equivalent_fractions_shoot.htm or Fraction pizza only the Intro and Part 2 (the other parts can be completed by the more advanced students) http://math.rice.edu/~lanius/fractions/frac4.html

Evaluation:

Exit slip: students should write down three sets of equivalent fractions they can identify. It is okay to use the strips of paper we used in the Exploration activity.




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Grade Level

2nd

Time Needed

60 minutes

Materials Needed

Book Gator Pie by Louise Mathews Pie pictures (attached) 28 copies of Compare Activity Packet (attached) C.O.W. Internet access to: Promethean Planet flipchart for Smartboard: http://www.prometheanplanet.com/en/Resources/Item/76426/comparing-fractions-and-equivalent-fractions#.UnVQ3Pkqhni Fraction Monkeys interactive activity: http://www.fractionmonkeys.co.uk/activity/

Unit Lesson 5: Dare to Compare

Introduction: In this lesson, students learn to compare the

sizes of fractions.

Background: Students have already learned about halves,

thirds, and fourths. Now they will learn how to compare the sizes as greater than, less than, or equal to. Remind students that the greater than sign opens toward the larger number/fraction and points to the small fraction.

GLCE(s):


Engagement:

Have students predict which series of fractions is smallest to largest: ½, 1/3, ¼, 1/6, 1/8 1/8, 1/6, ¼, 1/3, ½ Ask students to hold up one finger if they think it is the first series of fractions; hold up two fingers if they think it is the second series of fractions. Read aloud Gator Pie by Louise Mathews While reading the book, show pie pictures cut into halves, thirds, fourths, eights, hundredths. Ask students: What happened at the end of the story?


http://www.prometheanplanet.com/en/Resources/Item/76426/comparing-fractions-and-equivalent-fractions#.UnVQ3Pkqhni







http://www.fractionmonkeys.co.uk/activity/




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Exploration: Tell students that their learning objectives for today are: “I can describe the shares using the words halves, thirds, half of, a third of” “I can describe the whole as two halves, three thirds, four fourths.” We are going to figure out how fractions compare in size to each other. Ask for volunteers to hold pie pictures (shown during story) so students can put the pies into order from largest to smallest fractions. Students will be standing in order ½, 1/3, ¼, 1/8, 1/100th What do we notice about the denominator? Ask for clarification about which number is the denominator. Students should notice that the denominator gets bigger as the fractions get bigger from left to right. Teacher: “Who can tell me what happens to the slices of pie, going from left to right)?” (the pie slices get smaller) Teacher: “So you are telling me that as the denominator gets bigger, the pieces of pie get smaller?” (Yes!!) Teacher: “Then what happens to the pieces of pie as the denominator gets smaller (going from right to left)?” (They get bigger.) Teacher: “Now let’s say this is your very favorite kind of pie. Which share would you like to have, and why?” Possible answers: ½ because it is biggest, 1/8 because I could share it with some friends, 1/4 because ½ would be too much at one time. Thank students for volunteering with the pies. They can be seated Today we will explore this notion of comparing the sizes of fractions. Show Promethean Planet Flip chart slides 1-6, which explain comparisons of fractions a little bit differently: http://www.prometheanplanet.com/en/Resources/Item/76426/comparing-fractions-and-equivalent-fractions#.UnVQ3Pkqhni



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The activity sheet I am going to give you has a lot of “pies” on it. We are going to color our pies according to the fractions shown. On the second page, we move to color coding number lines. We will decide which fraction is greater than, less than, or equal to the other. Remind students that the greater than sign opens toward the larger number/fraction and points to the small fraction. Work sheets and answer sheets attached and available at: http://www.visualfractions.com/worksheets/compare/compareworksheets.pdf

Explanation:

Ask students why the fractions get smaller as the denominator gets bigger. Possible answers: the whole must be divided into more pieces. What happens if we have the same denominator and different numerators? How can we tell if one fraction is bigger than the other? Give the example of 2/4 and ¾. Which fraction is larger?

Extension:

Have students each get a computer from the C.O.W. Have students log onto Fraction Monkeys interactive program: http://www.fractionmonkeys.co.uk/activity/ Point out that in this activity, students are working on a number line from zero to one. They will determine the arrangement of fractions on that number line. This requires some knowledge of equivalent fractions learned in the prior lesson.

Evaluation:

Formative assessments: Have students chorus read the learning objectives with teacher. Ask students to rate their own knowledge of our learning objectives on a scale of 1-4. Students should keep their eyes closed as they hold up 1, 2, 3, or 4 fingers. Give students a similar question to the one they did at the beginning of the lesson. Have them put the following fractions in order from biggest to smallest. 1/3, 1/100, ½, 1/8, ¼

http://www.visualfractions.com/worksheets/compare/compareworksheets.pdf


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Grade Level

2nd

Time Needed

60 minutes

Materials Needed

52 pretzel rods Pictures: 1 square showing

halves

1 square showing 2 unequal parts

1 circle showing pie wedges in thirds

1 circle showing 3 unequal sections horizontally

1 rectangle showing fourths

1 rectangle showing 4 unequal parts

Manipulatives such as colored counters – 25 per student 9 stacks of activity questions (attached) – cut and group ahead of time Individual questions for formative assessment-attached

Unit Lesson 6: Groovy Groups

Introduction: In today’s lesson, we will explore how fractions

can show equal parts of a group of objects.

Background: By the end of today’s lessons students can

identify fractional parts (halves, thirds, fourths).

GLCE(s):


Engagement:

Show the students a bowl of 52 pretzel rods. Ask the students how these pretzels could be related to our math lesson for today. Possible answers: we are going to measure them, we will eat them, we will group them, count them. Tell students that by the end of the lesson, they will find out how the pretzels relate to our learning objective for the day. Tell students that in today’s lesson, we will learn how fractions can represent parts of a group of objects.

Exploration: Tell students that their learning objectives for today are: “I can describe the shares using the words halves, thirds, half of, a third of” “I can describe the whole as two halves, three thirds, four fourths.” “I can recognize that equal shares of identical wholes need not have the same shape.”



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Review with students the idea of halves, thirds, and fourths of a whole. Hold up two pictures of a square, one divided in half and the other in 2 unequal parts.

Teacher: “Do both of these squares show halves? “Turn and talk with a partner about your thoughts.”

Some students may think both pictures show half, while others do not.

Teacher: “Those who think both pictures show halves of a pie, tell me why.”

Possible response: because they each have two parts. Accept any answer.

Teacher: “Those who do not think that both pictures show halves, tell me why.”

Possible response: because the one square has unequal parts.

Teacher: “So what you are telling me is that the parts have to be equal to be halves?”

Teacher to the group who thought both pictures showed halves: “what do you think of their reasoning?”

Possible responses: students do not agree, students now see Clarify any misconceptions about halves. They MUST be equal. Show students a set of pictures of a rectangle divided into three parts. One picture has thirds and the other picture has unequal parts of 3. Go through the same questioning (bulleted dialogue) as with the previous pictures. Repeat for the set of circles. The set of circles might be trickier since one picture is not cut into pie wedges. Clarify any misconceptions about a circle divided in this manner. It would be possible for a circle to be divided into thirds this way, but it would take a lot of multiplication and division to do it accurately. Now move onto the new topic of fractions representing groups of objects. Teacher: “We know that we can divide an object into equal parts, I wonder if we can divide groups of objects into equal parts?” Have eight students volunteer to be part of a group at the front of the room.

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Tell the students that you would like to divide this group in half. “How many parts do we need to create? Use your fingers to show me.” Model counting off: person 1 stand on the left, person 2 stand on the right, next person on the left, etc. Teacher: “How do we know we have two-halves?” Possible response: The groups have an equal number of people. Teacher: “Now I want to divide this group into fourths. How should I do that?” Possible responses: count by fours, guess and then rearrange, count off 1, 2, 3, 4, 1, 2, 3, 4… Accept all responses and write them on the board. Model counting off and grouping: 1, 2, 3, 4, 1, 2, 3, 4 Teacher: “How many groups do we have? (4) Teacher: “How many people in each group?” (2) Teacher: “How do we know that we successfully divided this group into fourths?” (the groups are equal) Tell students that you now want to divide the class into thirds (deliberately make the groups unequal, but don’t students this). Note, if students are absent, divide the class into groups that will eventually be evenly divided - ex: if 25 students are present, make 5 unequal groups. After the class is grouped by “thirds,” ask them: “Would you please make sure that our group is divided into thirds?” Some students will say yes it is, while others may disagree. Ask students for reasoning for their answers. The intent of this activity is for students to determine that their class or “group” can be divided into thirds - 3 equal parts. Have students rearrange themselves so that they are in 3 equal groups. Teacher: “Yes! You just used fractions to show parts of our whole group!” Thank the students and invite them to be seated.

Explanation:

We just saw that we can use fractions to divide groups of objects or people into parts.

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What one thing is very important when using fractions to show parts of a group? Tease out the word “equal” parts. Ask students if it would be “equal parts” if the numbers in each group were different. How do you think this concept of using fractions to show parts of a group of objects could apply to things that happen in our everyday lives? Possible responses: when we bring a treat and want to share it, when we want to split up a pile of rubber bands between friends, when we have candy to share with a friend.

Extension:

Tell students that in this next activity, we will be working in groups of three to answer some the questions on a stack of activity cards. Students will use manipulatives such as counters, to help find the answers to these questions. It is important that each student is engaged in helping to find the answers to these questions. Ask for 3 students to come to the front to model this activity. On the document camera, display 12 counters. Place the activity cards near them, face down. Have one student draw the top card and read it to the group. Students should work together to find a solution to the question. One person records the answer on the card. Assign groups and hand out counters and activity cards. Circulate around room answering questions and checking for understanding (asking groups how they got their answers). Students done early should make up their own story problem similar to the questions they just had. Exchange questions with members of their group. After groups have finished the activity, go over answers with the class. Visually assess student success with questions by asking for a thumbs-up or down after each question. Evaluation:

Ask students if they figured out what the pretzel rods had to do with today’s math lesson. (They are to share) How will we figure out how to divide this set of pretzels evenly? (Pass them out one at a time). How many pretzels did you each get? (2) Did anyone get more? (no) Did anyone get less? (no) So do each of you have a fraction of the whole group of pretzels? There were 52 pretzels in the group. What is the fraction of pretzels that you have? (2/52)

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Formative assessments: Have students chorus read the learning objectives with teacher. Ask students to rate their own knowledge of our learning objectives on a scale of 1-4. Students should keep their eyes closed as they hold up 1, 2, 3, or 4 fingers. Time permitting, give students the individual practice sheet. Otherwise, ask students for to hold up fingers (1-4) to represent their level of understanding for today’s objective which was to demonstrate how fractions can show equal parts of a group.

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Grade Level

2nd

Time Needed

45-60 minutes

Materials Needed

Internet access to: Which is Your Flag?

http://www.youtube.com/watch?v=L9SPiZ_54rc

Flags of all Countries of the World: http://www.youtube.com

/watch?v=PwGc35XoKNc

World Flags: http://www.youtube.com/watch?v=QPBQC7jAJt4

C.O.W.

30 half sheets of paper 27 summative

assessments

Books:

Flags of the World by

Sylvie Bednar

Complete Flags of the

World by DK

Flags by Jason Cooper

Flags of the Fifty States

by Randy Howe

The World Encyclopedia of Flags by Alfred

Znamierowski

Unit Lesson 7: Fraction Flags

Introduction: Students will examine and analyze state and

world flags to look for fractional patterns.

Background: Students have learned how to identify objects

divided into halves, thirds, and fourths. They will use this knowledge to explore, identify, and make state and country flags with colors that display these patterns.

GLCE(s):


Engagement: Inform students that we will watch a short video which shows many country flags from around the world. They should be using their prior knowledge about halves, thirds, and fourths, to identify flags with colors that display these attributes. Watch flags video: Which is Your Flag? http://www.youtube.com/watch?v=L9SPiZ_54rc

Exploration: Tell students that their learning objectives for today are: “I can partition rectangles into two, three, or four shares using the words halves, thirds, half of, a third of, a fourth of” “I can describe the whole as two halves, three thirds, four fourths.”




http://www.youtube.com/watch?v=PwGc35XoKNc


http://www.youtube.com/watch?v=QPBQC7jAJt4




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Last week’s newsletter informed parents that we would be exploring state and country flag colors that display patterns of halves, thirds, and fourths. In order to engage students more fully, it would help for them to have a personal connection to the flag they choose to illustrate. Some students may come from other states or countries, have relatives from other countries, or they may be interested in finding out more information about a particular state or country. Tell students that we will be making a Fraction Flag bulletin board. They will be illustrating one flag to put on this board. There are many resources around the room with state and world flags. Students will work as partners and should look through these items to:

Identify 3 flags with patterns of half, thirds, fourths, or some other fractional pattern

Identify 3 flags without a fractional pattern Each student should record these flags and state or country names in their journal, showing a pencil illustration of that flag. Students should identify if the flag pattern is halves, thirds, fourths, or another fractional pattern (they must be able to identify the fraction). Optional: computers to investigate state and country flags. During this time, videos will be displayed for students to look at during their investigation: http://www.youtube.com/watch?v=QPBQC7jAJt4 http://www.youtube.com/watch?v=PwGc35XoKNc As students finish early, they can help other students identify flags that meet the requirements.

Explanation:

Students share their findings. Teacher: “Let’s share flags with patterns of half.” Ask for volunteers to tell which state or country and what the pattern looked like. How do we know that this flag has a pattern of half? (Two EQUAL parts) Ask if anyone else recorded that country. Continue to ask for volunteer until all half patterns have been spoken for. In a quadruple-T-chart (halves, thirds, fourths, other), keep track of countries on the board. Record student name next to the country name. Teacher: “Now we will share flags with patterns of thirds.” Ask for volunteers to tell which state or country and what the pattern looked like. How do we know that this flag has a pattern of thirds? (Three EQUAL parts) Ask if anyone else recorded that country.



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Continue to ask for volunteer until all half patterns have been spoken for. Record findings on board. Teacher: “Next we will share flags with patterns of fourths.” Ask for volunteers to tell which state or country and what the pattern looked like. How do we know that this flag has a pattern of fourths? (Four EQUAL parts) Ask if anyone else recorded that country. Continue to ask for volunteer until all half patterns have been spoken for. Record findings on board. Teacher: “Did anyone find a different fractional pattern?” Ask for volunteers to tell which state or country and what the pattern looked like. How do we know that this flag has a fractional pattern? (EQUAL parts) Ask if anyone else recorded that country. Continue to ask for volunteer until all half patterns have been spoken for. Record findings on board. Review all the t-chart with the class. Assign students to a particular flag to replicate on a half piece of paper.

Extension:

Hand out half sheets of paper. Invite students to make their assigned country flags. Drawings should reflect halves, thirds, fourths, and other fractions appropriately. Ask students if they remember the very important detail about fractions: Equal parts. If they finish early, they can get a computer out to research information about their chosen country. They should write this information on the back of their flag.

Evaluation:

Have students chorus read the learning objectives with teacher. Ask students to rate their own knowledge of our learning objectives on a scale of 1-4. Students should keep their eyes closed as they hold up 1, 2, 3, or 4 fingers. Give students the following summative assessment that addresses all CCSS standards.

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K-12 Student Performance Assessment: Unit Level 2

All Initial Endorsement Candidates are required to gather evidence on how well their K-12 students performed during a Candidate-created unit. The data from the assessment will be shared with the university field coordinator. The data will be used

primarily to assist the College of Education in assessing its program and will not be used as a means of assigning the Candidates’ semester grades.

Candidate’s Name_____________________________________________________________________

Grade Level _______________________ Number of Students Enrolled ______________________

ELEMENT or INDICATORS

(0) UNSATISFACTORY

(1) PROGRESSING

(2) PROFICIENT

(3) DISTINGUISHED

Totals

Knowledge of Content

The student does not have a basic knowledge of the content.

The student displays a basic knowledge of the content.

The student displays solid content knowledge.

The student displays extensive content knowledge and continues to pursue further knowledge.

Student Interaction

Student interactions are characterized by conflict, sarcasm, or put-downs.

Students do not demonstrate negative behavior toward one another.

Student interactions are generally polite and respectful.

Students demonstrate genuine caring for one another as individuals and as students.

Student Pride in Work

Students demonstrate little or no pride in their work. They rush through to get the “task” completed and do not focus on high quality work.

Students complete most of the “tasks,” but invest little of their energy in the quality of the work.

Students complete the “tasks” and demonstrate pride in their completed work.

Students take obvious pride in their work and initiate improvements in it (i.e. by revising drafts on their own initiative, helping peers, and ensuring that high-quality work is displayed).

Student Participation

Limited engagement in the activity.

Somewhat engaged in the activity.

Actively engaged during the activity.

Highly engaged and enthusiastic during the activity.

Be sure that each row’s total is equal to the number of students you have in your class. (e. g. if there are 25 students enrolled then each row should total 25)

Types of evidence used to assess student learning

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

________________________________________________________________________________

Candidate’s response to lesson experience and student learning

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

____________________________________________________________________________________________________

(McCrea & Patterson, 2004) McCrea Revised 2008

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Bibliography Lesson 1: Alder, D. A. (1996). Fraction fun. New York, NY: Holiday House. Bell, M., Bell, J., Bretzlauf, J., Dillard, A., Hartfield, R., Isaacs, A., McBride, J., Moran,

C.G., Pitvorec, K.,& Saecker. P. (2012). Everyday mathematics teacher lesson guide (Common Core State Standard ed., Vol. 2, pp. 592-643). Chicago, IL: McGraw-Hill Companies, Inc.

Dodds, D.A. (2007) Full house an invitation to fractions. Sommerville, MA: Candlewick

Press Miller, M., & Lee, M. (2002). Mega-fun fractions. In Common Core Georgia State

Standards. Retrieved November 1, 2013, from http://ccgpsmathematicsk-5.wikispaces.com/file/view/Mega-Fun%2BFractions.pdf

Understanding fractions (2012, April 10). In Pearson Education, Inc.. Retrieved

November 2, 2013. Retrieved from http://www.youtube.com/watch?v=x8VXW1GakB8

Lesson 2: Bell, M., Bell, J., Bretzlauf, J., Dillard, A., Hartfield, R., Isaacs, A., McBride, J., Moran,


Miller, M., & Lee, M. (2002). Mega-fun fractions. In Common Core Georgia State


Mr. R's fractions-fractions song (n.d.). In Mr. R's World of Math and Science. Retrieved

November 1, 2013, from http://www.youtube.com/watch?v=DnFrOetuUKg

http://ccgpsmathematicsk-5.wikispaces.com/file/view/Mega-Fun%2BFractions.pdf





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Lesson 3: Murphy, Stuart J. Give me half! New York: HarperCollins, 1996. Print. Bell, M., Bell, J., Bretzlauf, J., Dillard, A., Hartfield, R., Isaacs, A., McBride, J., Moran,




Lesson 4: Allen-Stokes, T. (2011, March 29). Equivalent fractions. In You Tube. Retrieved October

25, 2013, from http://www.youtube.com/watch?v=wL4hICyMLKU Bell, M., Bell, J., Bretzlauf, J., Dillard, A., Hartfield, R., Isaacs, A., McBride, J., Moran,


Comparing fractions and equivalent fractions (2011, February 21). In Promethean

Planet. Retrieved November 2, 2013, from http://www.prometheanplanet.com/en/Resources/Item/76426/comparing-fractions-and-equivalent-fractions#.UnVQ3Pkqhni

Equivalent fractions shoot (n.d.). In Shepphard Software. Retrieved October 2, 2013,

from http://www.sheppardsoftware.com/mathgames/fractions/equivalent_fractions_shoot.htm

Lanius, C. (2008). Who wants pizza?. In Rice University Department of Mathematics.

Retrieved November 2, 2013, from http://math.rice.edu/~lanius/fractions/index.html







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Comparing fractions and equivalent fractions (2011, February 21). In Promethean

Planet. Retrieved November 2, 2013, from http://www.prometheanplanet.com/en/Resources/Item/76426/comparing-fractions-and-equivalent-fractions#.UnVQ3Pkqhni

Fraction monkeys (n.d.). In SUMS Online. Retrieved November 2, 2013, from

http://www.fractionmonkeys.co.uk/activity/ Hester, S. (n.d.). Making a cake. In Georgia Department of Education. Retrieved

November 2, 2013, from http://gadoe.georgiastandards.org/mathframework.aspx?PageReq=MathCake

Visual fractions worksheets: Compare (n.d.). In Visual Fractions. Retrieved November 2,

2013, from http://www.visualfractions.com/worksheets/compare/compareworksheets.pdf



Feaman, M. (2008). 2nd grade number sense lesson plan: Fractions - #2. In Juab

School District. Retrieved October 26, 2013, from https://www.juab.k12.ut.us/index.php?option=com_content&view=article&id=1168:2nd-grade-math-lesson-plan-fractions&catid=66:grammar&Itemid=58

http://gadoe.georgiastandards.org/mathframework.aspx?PageReq=MathCake

http://www.visualfractions.com/worksheets/compare/compareworksheets.pdf

https://www.juab.k12.ut.us/index.php?option=com_content&view=article&id=1168:2nd-grade-math-lesson-plan-fractions&catid=66:grammar&Itemid=58

https://www.juab.k12.ut.us/index.php?option=com_content&view=article&id=1168:2nd-grade-math-lesson-plan-fractions&catid=66:grammar&Itemid=58

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Lesson 7: Bednar, S. (2009). Flags of the world. New York, NY: Abrams. Complete flags of the world. (2008). New York, NY: DK Publishing. Cooper, J. (1997). Flags. Vero Beach, FL: Rourke Publishing. Hosein, A. (2010). Flags of all countries of the world. In You Tube. Retrieved November

3, 2013, from http://www.youtube.com/watch?v=PwGc35XoKNc Howe, R. (2009). Flags of the Fifty States (2nd ed.). Guilford, CT: Lyons Press. Kids. (2012). World flags: Learning flags of countries. In You Tube. Retrieved

November 3, 2013, from http://www.youtube.com/watch?v=QPBQC7jAJt4 Miller, M., & Lee, M. (2002). Mega-fun fractions. In Common Core Georgia State


Znamierowski, A. (2013). The World Encyclopedia of Flags. Wigston, Leicestershire,

England: Lorenz Books.



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