15 partition a number line in this lesson, students are ... · chapter 10, lesson 6 engage ny...

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13 | Page 15 Partition a number line into the given fractional units, and then label the number line. Express 0 and 1 as fractions on the number line according to the given fractional unit. In this lesson, students are briefly introduced to the term equivalence, but this will be revisited later in the unit. Number bonds may help students distinguish between the labels on the number line and the intervals of the fractional unit. Sample PARCC EOY assessment question: Adapted from EngageNY Module 5, Lessons 14 & 24 Exit Tickets and Homework: 1. Partition the fraction strip into sixths and label the number line. Be sure to label 0 and 1 using the same fractional units. 2. The fraction 1/4 is shown on the number line below. Which of the points on the number line is closest to where 1 should be? Explain your reasoning. 3. How can one whole be represented as a fraction? Use words, an example, and pictures to support your answer. Engage NY Module 5 Lessons 14 & 24 (Appendix C) My Math Chapter 10, Lesson 7 “Make ONE” (Appendix C) 16 Place non-unit fractions on a number line with endpoints 0 and 1. This lesson is designed to give students additional practice with partitioning and labeling number lines. They should not have to label each tic mark on the number line (as they did in Lesson #14) in order to answer the questions in the problem set or the exit tickets. Adapted from EngageNY Module 5, Lesson 15 Exit Ticket: 1. Estimate to label the fraction 3/5 on the number line below. 2. Partition the number line, then label each of the following fractions on the number line: 3/6, 1/6, 5/6: 3. Mrs. Rivera is planting flowers in her 1- meter long rectangular plant box. She divides the plant box into sections 1/4 meter in length, and plants 1 seed in each section. a. Use the fraction strip below to represent the plant box from 0 meters to 1 meter. Engage NY Module 5, Lesson 15 (Appendix C)

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15 Partition a number line into the given fractional units, and then label the number line. Express 0 and 1 as fractions on the number line according to the given fractional unit.

In this lesson, students are briefly introduced to the term equivalence, but this will be revisited later in the unit. Number bonds may help students distinguish between the labels on the number line and the intervals of the fractional unit. Sample PARCC EOY assessment question:

Adapted from EngageNY Module 5, Lessons 14 & 24 Exit Tickets and Homework:

1. Partition the fraction strip into sixths and label the number line. Be sure to label 0 and 1 using the same fractional units.

2. The fraction 1/4 is shown on the number

line below. Which of the points on the number line is closest to where 1 should be? Explain your reasoning.

3. How can one whole be represented as a

fraction? Use words, an example, and pictures to support your answer.

Engage NY Module 5 Lessons 14 & 24 (Appendix C) My Math Chapter 10, Lesson 7 “Make ONE” (Appendix C)

16 Place non-unit fractions on a number line with endpoints 0 and 1.

This lesson is designed to give students additional practice with partitioning and labeling number lines. They should not have to label each tic mark on the number line (as they did in Lesson #14) in order to answer the questions in the problem set or the exit tickets.

Adapted from EngageNY Module 5, Lesson 15 Exit Ticket:

1. Estimate to label the fraction 3/5 on the number line below.

2. Partition the number line, then label each of

the following fractions on the number line: 3/6, 1/6, 5/6:

3. Mrs. Rivera is planting flowers in her 1-

meter long rectangular plant box. She divides the plant box into sections 1/4 meter in length, and plants 1 seed in each section.

a. Use the fraction strip below to represent the plant box from 0 meters to 1 meter.

Engage NY Module 5, Lesson 15 (Appendix C)

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b. How many seeds will she be able to

plant in 1 box? c. Mrs. Rivera places a pretty rock at

3/4 meter. Draw the rock in your fraction strip. Label the number line to support your answer.

17

Flex Day (Instruction Based on Data) Recommended Resources:

“Using Fraction Strips to Explore the Number Line” (Appendix C)

18 Use unit fractions to build and write fractions greater than one whole.

Students must be able to recognize that the fractional unit refers to the number of equal parts in the identified whole, not necessarily in the entire picture. When asked to create their own visual model, students must remember that the denominator defines the fractional unit, or the number of equal parts. When presented with the fraction in word form, students may benefit from first writing it in numeral form (or vice versa).

Adapted from EngageNY Module 5, Lesson 9 Exit Ticket:

1. Each shape represents 1 whole. Fill in the chart:

2. Estimate to draw and shade units on the

fraction strips. a. 4 thirds:

b. 10/4

3. What do you notice about the relationship

between the numerator and denominator of fractions that are greater than one whole? Why is this true?

Engage NY Module 5, Lesson 9 (Appendix C)

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19 Identify a shaded fractional part in different ways depending on the designation of the whole.

Students must understand that the size of a fractional part depends on what is identified as the whole. They will benefit from multiple real-world examples during the mini-lesson. Students should remember for future lessons that they must specify the whole. This will be useful when they must partition more than one whole into the given fractional units on a number line. For example, in the sample PARCC EOY assessment questions shown below, students should specify that whole from 0-1 instead of 0-2:

From the unpacked standards guide:

Adapted from EngageNY Module 5, Lesson 13 Exit Ticket and Homework:

1. Complete the table below:

2. Ms. Silverstein asked the class to draw a

model showing 2/3 shaded. Karol and Deb drew the models below. Which is correct. Explain how you know.

Engage NY Module 5, Lesson 13 (Appendix C)

20 Express whole numbers as fractions when the unit interval is 1.

Some students may benefit from following a procedure or a list of guiding questions in order to complete the problem set: 1.) How many parts is one whole divided into? 2.) How many of those parts are shaded? Again, equivalence may be briefly discussed, but will be revisited later in the unit.

1. Express the whole number 4 as a fraction. 2. Fill in the blank below:

3. Explain in words and pictures the

difference between these two fractions: 3/1 and 3/3.

Engage NY Module 5, Lesson 25 (Appendix C)

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21 Express whole numbers greater than 1 as fractions on the number line according to the given fractional unit.

Students should begin to notice that the numerator divided by the denominator equals the whole number, and may use this as a way to check their work. Again, equivalence may be briefly discussed, but will be revisited later in the unit.

Adapted from EngageNY Module 5, Lesson 26 Exit Ticket & Homework:

1. Partition the number line to show the unit fractions. Then draw number bonds with copies of 1 whole for the circled whole numbers.

2. Irene has 2 yards of fabric. Draw a number

line to represent the total length of Irene’s fabric.

a. Irene cuts her fabric into pieces 1/6 yard in length. Partition the number line to show her cuts.

b. How many 1/6-yard pieces does she cut altogether?

c. Use your answer to b. to fill in the blank:

2 = ____ sixths 3. What pattern do you notice about whole

numbers represented as fractions?

Engage NY Module 5, Lesson 26 (Appendix C)

22 Place whole number fractions and fractions between whole numbers on the number line.

Students must be careful to express the whole number as a fraction when presented with a number line that does not start at 0.

1. Estimate to equally partition the number line below into fifths. Label the number line, including expressing the wholes as fractions.

2. Draw a number line with endpoints 0 and 2.

Label the wholes. Estimate to partition each whole into 6 unit fractions and label them on the number line.

3. Macy labeled the top of the number line below. Did Macy label the number line

Engage NY Module 5, Lesson 16 (Appendix C) My Math Chapter 10, Lesson 7

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correctly? Why or why not? If not, correct her mistakes.

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Flex Day (Instruction Based on Data) Recommended Resources:

Engage NY Module 5, Lesson 17 (Appendix C) “Fraction Number Lines” (Appendix C)

“Exploring Fractions Further with Pattern Blocks” (Appendix C) “Make a Hexagon Game” (Appendix C)

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Mid-Unit Assessment Recommended Resources:

EngageNY Module 5 Mid-Module and End-of-Module Assessment My Math Chapter 10 Check My Progress

25 Compare fractions and whole numbers on the number line by reasoning about their distance from 0.

Teachers may revisit Lessons #5 and #9 about comparing fractions and pull additional problems from those resources.

Adapted from EngageNY Module 5, Lesson 18 Exit Ticket: Place the two fractions on the number line. Circle the fraction with the distance closest to 0. Then compare using <, >, or =.

1.

2.

Engage NY Module 5, Lesson 18 (Appendix C)

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3. Mr. Brady draws a fraction on the board. Ken says it’s 2/3 and Dan says it’s 3/2. Do both of these fractions mean the same thing? If not, which fraction is larger? Draw a number line to model 2/3 and 3/2. Use words, pictures, and numbers to explain your comparison.

26 Use manipulatives to model and explore equivalent fractions.

This lesson is designed to give students opportunities to explore equivalent fractions on their own and to draw their own conclusions about equivalence and fractional values.

1. Choose one pair of equivalent fractions that you found and write them in the blanks below:

______ = ______ 2. Attending to precision, use the rectangle

below to model the fractions you chose:

3. Use your example and your picture to

explain what it means for two fractions to be equivalent.

“Comparing Fractions” “Cuisenaire Equivalent Fractions” (Appendix C)

27 Recognize that equivalent fractions refer to the same point on the number line.

Teachers should refer back to Lessons #14, #18, and #19 to identify expressing whole numbers as fractions as a matter of equivalence.

Adapted from EngageNY Module 5, Lesson 21 Homework:

1. Use the unit fractions on the left to count up on the number line. Label the missing fractions:

Use the number line above to fill in the blanks:

a. 2/3 = ___/6 b. 6/3 = 12/___ c. 3/3 = ___/6 d. 4/3 = ___/6

2. Choose a. or b. to explain using a number line and words:

a. 1 = 2/2 = 6/6 b. 2 = 4/2

Engage NY Module 5, Lesson 21 (Appendix C)

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28 Create, identify, and explain equivalent pairs using visual models and number lines.

Students should be see equivalent fractions in other pictorial area models, aside from just fraction strips (i.e. rectangles partitioned both vertically and horizontally and circles). According to the unpacked standards guide, “students should only explore equivalent fractions using models, rather than using algorithms and procedures.” Therefore, students must attend to precision when creating models to identify equivalent fraction pairs. A common error is to draw unequal parts (as shown below), which might lead a student to believe that 1/3 = 2/4.

This lesson is allocated two days in order to give students time to work with visual models, manipulatives, and number lines, and to situate fractional equivalence in word problems.

1. Shade Rectangle B below to show equivalent fractions, then complete the number sentence:

1/4 = _______

Sample PARCC EOY assessment question:

2. Which three comparisons are true? q 1/3 = 3/6 q 3/4 = 6/8 q 4/8 = 1/2 q 1/4 = 4/8 q 4/6 = 2/3

a. For one comparison that you selected above, draw a picture to support your reasoning.

b. For a comparison that you did not select above, draw a number line to support your reasoning.

EngageNY Module 5, Lesson 23 Exit Ticket: 3. Henry and Maddie were in a pie-eating

contest. The pies were cut either into thirds or sixths. Henry picked up a pie cut into sixths, and ate 4/6 of it in 1 minute. Maddie picked up a pie cut into thirds. What fraction of pie does Maddie have to eat in 1 minute to tie with Henry? Justify your reasoning.

My Math Chapter 10, Lesson 6 Engage NY Module 5, Lessons 22 & 23 (Appendix C)

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30 Explain equivalence by manipulating units and reasoning about their size.

This lesson is divided into 2 objectives to give students time to develop strategies other than a direct visual comparison to identify equivalent fractions. Students should recognize that with equivalent fractions, the shaded/otherwise represented area or distance stays the same, but the number of equal parts changes. Notice on the SBAC question (Exit Ticket #1) and the first PARCC sample question below that the number lines are not lined up for students to make a straightforward assessment of which points fall on the same line. Additionally, the wholes represented in the PARCC question are different sizes. Sample PARCC EOY assessment questions: A fraction is shown on the number line.

Plot a point on this number line to show a fraction that is equivalent to the fraction shown on the other number line.

From the Smarter Balanced Assessment Consortium:

1. Look at point P on the number line. Then look at the number lines in the box. Is the point on each number line equal to the number shown by P? Choose Yes or No.

2. Choose one of your “Yes” answers from #1

and use that to answer the following questions:

a. What happened to the size of the whole?

Engage NY Module 5, Lesson 27 (Appendix C)

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31 Julia wants to plant flowers in a second* garden, but she has not planned it yet. Write the letter for a different tile in each of the four spaces in this second garden so that 1/2 of the garden will be covered with flowers.

*Presumably this question is a second part of Exit Ticket #3.

b. What happened to the distance of P from 0?

c. What happened to the number of equal parts?

3. Julia is planting flowers. She wants to cover 3/4 of her garden with flowers. The picture below shows Julia’s garden and the parts of it she has already planned:

Which of the following tiles should you place in the empty space to complete the plan for her garden?

a. b. c. d.

32 Construct fraction models to represent fractions as fair sharing.

In addition to solving fair sharing problems, students may also create stories that require fair sharing and solve each other’s problems.

1. Anna divides a pan of brownies into six equal pieces. Four children share the entire pan fairly. What fraction of the brownies did each child receive? Explain your reasoning using words, pictures, and/or numbers.

2. Anna divides a second pan of brownies into four equal pieces. This time, six children share the entire pan fairly. What fraction of the brownies did each child receive? Explain your reasoning using words, pictures, and/or numbers.

3. Why are your answers to #1 and #2 different, even though you used the same numbers?

“Their Fair Share” (Appendix C)

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33 2 Flex Days (Instruction Based on Data) Recommended Resources:

“Cuisenaire Fractions” (Appendix C) “Pizza for Dinner” (Appendix C)

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35 Create a ruler with 1-inch, 1/2-inch, and 1/4-inch intervals and generate measurement data.

Students should be able to identify unit fractions and mixed numbers on their rulers. Students should rely on estimation strategies to measure to the nearest whole, half, or quarter inch.

Adapted from EngageNY Module 6, Lesson 5 Exit Ticket:

1. Davon marks a 4-inch paper strip into equal parts as shown below.

Label the whole and quarter inches on the paper strip.

2. Label 2½ inches. What is an equivalent fraction?

3. Davon tells his teacher that his paper strip measures 4 inches. Sandra says it measures 16 quarter inches. Who is correct? Use words, pictures, or numbers to explain your reasoning.

Engage NY Module 6, Lesson 5 (Appendix C) My Math Chapter 12, Lesson 6

36 Interpret measurement data from line plots.

Students must be able to answer questions about line plots on the following topics:

• The most common or frequent measurement

• The total number of objects/people • The total number of objects/people with a

certain measurement (students may be required to combine)

• The total number of objects/people with a measurement greater than or less than a given measurement

• How many more/How many less? • The difference between the longest and

shortest measurement

EngageNY Module 6, Lesson 6 Exit Ticket: Ms. Bravo measures the lengths of her third-grade students’ hands in inches. The lengths are shown on the line plot below.

1. How many students are in Ms. Bravo’s

class? How do you know? 2. How many students’ hands are longer than

4-2/4 inches? 3. Darren says that more students’ hands are

4-2/4 inches long than 4 and 5-1/4 inches combined. Is he right? Explain your answer.

EngageNY Module 6, Lesson 6 (Appendix C) My Math Chapter 12, Lesson 7

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37 Represent measurement data with line plots, given a scale.

Students must be aware of equivalent fractions when plotting data. Sample PARCC EOY assessment question:

Adapted from EngageNY Module 6, Lesson 7 Exit Ticket: Scientists measure the growth in inches of mice. The scientists measure the length of the mice to the nearest ¼ inch and record the measurements as shown below:

1. Label each tick mark. Then record the data

on the line plot below.

2. Explain how you knew where to place 4-1/2

on the number line. 3. How many mice were longer than 3-1/2

inches?

Engage NY Module 6, Lesson 7 (Appendix C) My Math Chapter 12, Lesson 7

38 Represent measurement data on a line plot by determining an appropriate scale.

According to the unpacked standards guide, “To make a line plot from the data in the table, the student can determine the greatest and least values in the data: 13½ inches and 14¾ inches. The student can draw a segment of a number line diagram that includes these extremes, with tick marks indicating specific values on the measurement scale.” This suggests that students must be able to create their own number line diagrams by choosing the appropriate scale before plotting the data.

Adapted from EngageNY Module 6, Lesson 8 Homework: Mrs. Leah’s class uses what they have learned about simple machines to build marshmallow launchers. They record the distances their marshmallows travel in the chart below:

Engage NY Module 6, Lesson 8 (Appendix C) My Math Chapter 12, Lesson 7

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1. Use the data to draw a line plot below. 2. Explain the steps you took to create the line

plot. 3. Come up with 3 different types of questions

that a classmate could answer using the data on this line plot. Include an answer key.

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Flex Day (Instruction Based on Data) Recommended Resources:

“Measuring to the Half and Quarter Inch” (Appendix C) “Peter’s Garden” (Appendix C)

EngageNY Module 5 Mid-Module and End-of-Module Assessment (Appendix C)

MCLASS Beacon End of Unit Assessment Appendix B

*Note: This assessment will be administered online