3-5 Formative Instructional and Assessment Tasks

Formative Instructional and Assessment Tasks

NC DEPARTMENT OF PUBLIC INSTRUCTION FOURTH GRADE

Equivalent Pizzas 4.NF.1 - Task 1

Domain Number & Operations- Fractions Cluster Extend understanding of fraction equivalence and ordering. Standard(s) 4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual

fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

Materials Paper and pencil, Graph paper (optional) Task There is two-thirds of a pizza left.

How many pieces of pizza are left if the original pizza had a total of 3 slices? 6 slices? 12 slices? Write a sentence to explain your thinking.

Rubric

Level I Level II Level III Limited Performance • The student has not shown a

clear understanding about how to find equivalent fractions.

Not Yet Proficient • Answer is correct, but the

explanation is unclear OR work is logically shown but the student has made a calculation error.

Proficient in Performance • Solutions: A 3 slice pizza

would have 2 slices left. A 6 slice pizza would have 4 slices left. A 9 slice pizza would have 6 slices left.

• The sentence includes a clear explanation about finding equivalent fractions.

Standards for Mathematical Practice

1. Makes sense and perseveres in solving problems. 2. Reasons abstractly and quantitatively. 3. Constructs viable arguments and critiques the reasoning of others. 4. Models with mathematics. 5. Uses appropriate tools strategically. 6. Attends to precision. 7. Looks for and makes use of structure. 8. Looks for and expresses regularity in repeated reasoning.



Equivalent Pizzas

There is two-thirds of a pizza left. How many pieces of pizza are left if the original pizza had a total of 3 slices? How many pieces of pizza are left if the original pizza had a total of 6 slices? How many pieces of pizza are left if the original pizza had a total of 12 slices? Write a sentence to explain your thinking.



Comparing Ropes

4.NF.1- Task 2 Domain Number & Operations- Fractions Cluster Extend understanding of fraction equivalence and ordering. Standard(s) 4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual


Materials Paper and pencil, Graph paper (optional) Task Sally has a piece of rope that is 3/4 of a foot long. Tomas has a piece of rope that is 1/2 of

a foot long. Mitch has a piece of a rope that is 1/3 of a foot long. How many inches is each piece of rope? Write a sentence explaining your thinking.

Rubric





Proficient in Performance • Solutions: Sally- 9 inches.

Tomas- 6 inches. Mitch- 4 inches.

• The sentence includes a clear explanation about finding equivalent fractions.





Comparing Ropes

Sally has a piece of rope that is 3/4 of a foot long. Tomas has a piece of rope that is 1/2 of a foot long. Mitch has a piece of a rope that is 1/3 of a foot long. How many inches is each piece of rope? Write a sentence explaining your thinking.



Trading Blocks 4.NF.1 - Task 3



Materials Pattern blocks, Paper, Pencil, Activity sheet *Computer-based pattern blocks can be found here- http://illuminations.nctm.org/ActivityDetail.aspx?ID=27

Task Task sheet (below). The 2 pattern blocks below have a value of 1 whole.

Part One:

• If the 2 pattern blocks above have a value of 1 whole, then what is the fractional value of 3 trapezoids? What is the fractional value of 1 trapezoid?

• If you have 3 trapezoids, how many green triangles would it take to cover the same area? If the 2 hexagons have a value of 1 whole, what is the fractional value of all the green triangles? What is the fractional value of one triangle?

• Since the number of trapezoids and the number of green triangles covers the same space, they are equal. Write an equivalent fraction expressing the number of trapezoids and the number of green triangles.

Part Two: • If 2 hexagons have a value of 1 whole, what is the value of 4 blue rhombuses?

What is the value of 1 blue rhombus? • If you have 4 rhombuses how many green triangles would it take to cover the same

area? If the 2 hexagons have a value of 1 whole, what is the fractional value of all the green triangles? What is the value of 1 green triangle?

• Write an equivalent fraction expressing the number of rhombuses and the number of green triangles.

Conclusion: Write a sentence explaining how you found equivalent fractions.



Rubric Level I Level II Level III

Limited Performance • The student has not shown a




Proficient in Performance • Accurate solutions: Part One-

Trapezoids: 3/4, 1/4. Triangles 9/12, 1/12. Fraction: 3/4 = 9/12. Part Two: Rhombuses: 2/3, 1/3. Triangles: 8/12, 1/12. Fraction: 2/3 = 8/12. AND

• Clearly and accurately explains their strategy.





Trading Blocks

The 2 pattern blocks below have a value of 1 whole.

Part One: If the 2 pattern blocks above has a value of 1 whole then what is the fractional value of 3 trapezoids? What is the fractional value of 1 trapezoid? If you have 3 trapezoids, how many green triangles would it take to cover the same area? If the 2 hexagons has a value of 1 whole, what is the fractional value of all the green triangles? What is the fractional value of one triangle? Since the number of trapezoids and the number of green triangles covers the same space, they are equal. Write an equivalent fraction expressing the number of trapezoids and the number of green triangles.



Part Two: If 2 hexagons have a value of 1 whole, what is the value of 4 blue rhombuses? What is the value of 1 blue rhombus? If you have 4 rhombuses how many green triangles would it take to cover the same area? If the 2 hexagons have a value of 1 whole, what is the fractional value of all the green triangles? What is the value of 1 green triangle? Write an equivalent fraction expressing the number of rhombuses and the number of green triangles. Conclusion: Write a sentence explaining how you found equivalent fractions.



Splitting to Make Equivalent Fractions

4.NF.1-Task 4 Domain Number and Operation- Fractions Cluster Extend understanding of fraction equivalence and ordering. Standard(s) 4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n x a)/ (n x b) by using visual


Materials Paper and pencil Task This standard addresses the idea that equivalent fractions can be made by multiplying the

numerator and the denominator by the same number. It also introduces the idea that dividing or splitting the numerator and denominator by the same number results in an equivalent fraction. Students will make models to show that splitting the number in the whole also splits the number in a part of the whole. The resulting fraction is the same. Task 1: Jenna ate 1/3 of a cake and had 2/3 leftover for her friends. She split each of the remaining thirds into four pieces. How many pieces of cake did she have? What fraction of the whole was each piece? Each of her friends ate the same amount of cake as Jenna. How many pieces would each friend get to eat 1/3 of the whole cake? Write or draw this fraction in two different ways. Solution: There are 8 pieces of cake leftover, each piece is 1/12 of the whole, so 8/12 is leftover. Each friend will need to eat 4/12 to eat the same amount as Jenna (1/3). 1/3 = 4/12. Task 2: Ronoldo ate ¼ of a pizza for dinner and had ¾ of the pizza leftover. He cut the leftover pizza into 6 equal slices for his friends. What fraction of the whole pizza was each piece? Each of his friends ate the same amount of pizza as Ronoldo. How many pieces would each friend get in order to eat ¼ of the whole pizza? Represent (write or draw) the solution (fraction) in two different ways. Solution: There are 6 pieces leftover, each piece is 1/8 of the whole. If each friend ate ¼ of the whole, that would be 2 pieces that are eighths, or 2/8, so 2/8 = ¼. Task 3: 4/12 = 1/3 2/8 = ¼ Look at the equivalent fractions from the story problems. What relationships do you notice between the numerators and denominators in each equation? What is happening to the numbers? We see the numbers being split. How can we see this idea happening in the models that you drew? Can you think of additional examples that show the numerator and denominator of fractions being split by the same number? What is the result?



Rubric

Level I Level II Level III Limited Performance • Students are unable to show

with numbers or models that a/b = (𝑎 ÷ 𝑛)/(𝑏 ÷ 𝑛), or to explain why dividing the numerator and denominator of a fraction by the same number yields an equivalent fraction.

Not Yet Proficient • Students can show with

numbers or models that a/b = (𝑎 ÷ 𝑛)/(𝑏 ÷ 𝑛), but are unable to explain why dividing the numerator and denominator of a fraction by the same number yields an equivalent fraction.

Proficient in Performance • Students can show with

numbers or models that a/b = (𝑎 ÷ 𝑛)/(𝑏 ÷ 𝑛), and are able to explain why dividing the numerator and denominator of a fraction by the same number yields an equivalent fraction.





Splitting to Make Equivalent Fractions

Task 1: Jenna ate 1/3 of a cake and had 2/3 leftover for her friends. She split each of the remaining thirds into four pieces. How many pieces of cake did she have? What fraction of the whole was each piece? Each of her friends ate the same amount of cake as Jenna. How many pieces would each friend get to eat 1/3 of the whole cake? Write or draw this fraction in two different ways.



Splitting to Make Equivalent Fractions Task 2: Ronoldo ate ¼ of a pizza for dinner and had ¾ of the pizza leftover. He cut the leftover pizza into 6 equal slices for his friends. What fraction of the whole pizza was each piece? Each of his friends ate the same amount of pizza as Ronoldo. How many pieces would each friend get in order to eat ¼ of the whole pizza? Represent (write or draw) the solution (fraction) in two different ways.



Splitting to Make Equivalent Fractions Task 3:

4/12 = 1/3 2/8 = 1/4 Look at the equivalent fractions from the story problems. What relationships do you notice between the numerators and denominators in each equation? What is happening to the numbers? We see the numbers being split. How can we see this idea happening in the models that you drew? Can you think of additional examples that show the numerator and denominator of fractions being split by the same number? What is the result?



Fraction Rectangles 4.NF.1-Task 5

Domain Number and Operation- Fractions Cluster Extend understanding of fraction equivalence and ordering. Standard(s) 4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n x a)/ (n x b) by using visual


Materials Paper and pencil, color tiles Task This standard addresses the idea that equivalent fractions can be made by multiplying the

numerator and the denominator by the same number. Students will make models to show that doubling the number in the whole also doubles the number in a part of the whole. The resulting fraction is the same. Task 1: Use color tiles to make a rectangle or square that is one half red and one half blue. Students will make several different representations of one half. By looking at them in order, they can see that the denominator and numerator are being multiplied by the same number. Write the equations so that they can see the proper notation. Task 2: Use color tiles to make a rectangle or square that is one third red. Find at least three different ways to represent one third. Using pictures, numbers, and/or words, prove that the three models that you made are all equal to one third. Repeat the task with ¼ and 1/6 for additional practice.



Rubric

Level I Level II Level III Limited Performance • Students are unable to show

with numbers or models that a/b = (n x a)/(n x b), or to explain why multiplying the numerator and denominator of a fraction yields an equivalent fraction.

Not Yet Proficient • Students can show with

numbers or models that a/b = (n x a)/(n x b), but are unable to explain why multiplying the numerator and denominator of a fraction yields an equivalent fraction.

Proficient in Performance • Students can show with

numbers or models that a/b = (n x a)/(n x b), and can explain why multiplying the numerator and denominator of a fraction yields an equivalent fraction.





Fraction Rectangles

Task 1: Use color tiles to make a rectangle or square that is one half red and one half blue.

Task 2: Use color tiles to make a rectangle or square that is one third red. Find at least three different ways to represent one third. Using pictures, numbers, and/or words, prove that the three models that you made are all equal to one third. Repeat the task with ¼ and 1/6 for additional practice.



Tiling the Patio 4.NF.1 - Task 6



Materials Paper, Pencil Task Covering the Patio

Part 1: Cover the patio below with the same kind of tile.

Part 2: Now cover half of the patio. Complete the table below for how many tiles it would take to cover half of the tile.

Part 3: For one of the fractions above explain how multiplication can help you find equivalent fractions.








Proficient in Performance • Accurate solutions: Part 1:

Each region is accurately partitioned into equal sections. Part 2: Tile A: 12, 6, 6/12. Tile B: 6, 3, 3/6. Tile C: 4, 2, 2/4. Tile D: 8, 4, 4/8.

• Part 3: The student writes something about, “Multiplying both the numerator and the denominator by the same number will result in an equivalent fraction.”.





Covering the Patio Cover the patio below with the same kind of tile.

Part 1: Tile A: It takes 12 tiles Tile B: It takes 6 tiles Tile C: It takes 4 tiles Tile D: It takes 8 tiles

Part 2: Cover half of the patio. Complete the table below for how many tiles it would take to cover half of the tile. Tile Tiles needed to

cover the whole patio.

Tiles needed to cover half the patio.

Fraction showing how much of the patio is covered.

Tile A

21 =

126 .

126 of the patio is covered by tiles.

Tile B

=

21

Tile C

=

21

Tile D

=

21

Part 3: For one of the fractions above explain how multiplication can help you find equivalent fractions.



Weird Pieces of Cake

4.NF.1 - Task 7 Domain Number & Operations- Fractions Cluster Extend understanding of fraction equivalence and ordering. Standard(s) 4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual


Materials Paper, Pencil Task Weird Pieces of Cake

Part 1: A baker makes square cakes and decides to cut the pieces different each day of the week. If she wants to make 8 dollars for the whole cake, how much money will each individual piece sell for?

Part 2: While shopping on Wednesday, Martina says to the baker, “Buying 2 pieces of cake today will cost the same as one piece of cake on Monday. Is Martina correct? Explain why or why not.

(Modified from the Unusual Baker, NCTM, 2012)






Proficient in Performance • Accurate solutions: Part 1:

Monday- $4 each. Tuesday- $4 for large piece. Small pieces are $2 each. Wednesday- $2 each. Part 2: The explanation says something about, “Monday’s slices are ½ of the whole cake. Wednesday’s slices are 2/4 of the whole cake. ½ = 2/4.”







Weird Pieces of Cake Part 1: A baker makes square cakes and decides to cut the pieces different each day of the week. If she wants to make 8 dollars for the whole cake, how much money will each individual piece sell for?

Part 2: While shopping on Wednesday, Martina says to the baker, “Buying 2 pieces of cake today will cost the same as one piece of cake on Monday. Is Martina correct? Explain why or why not.

(Modified from the Unusual Baker, NCTM, 2012)



The Whole Matters 4.NF.2-Task 1

Domain Number and Operation- Fractions Cluster Extend understanding of fraction equivalence and ordering. Standard(s) 4.NF.2 Compare two fractions with different numerators and different denominators, e.g.

by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½. Recognize that comparisons are valid only when the two fractions refer to the same size whole. Record the results of comparisons with symbols >, =, or <, and justify conclusions, e.g., by using a visual fraction model.

Materials Paper and pencil Task Task 1:

Two friends each ate ½ of a pizza. Joselin says they must have eaten the same amount, but Donnie says they could have eaten different amounts. Who do you think is correct, and why? Explain your thinking in words, pictures, and numbers. Possible solution: The two friends could have each eaten half of two different size pizzas. Half of a large pizza is more than half of a medium pizza because the wholes are not the same size. Task 2: Mrs. Johnson and Mrs. Black each gave ½ of their students a pencil. Mrs. Johnson handed out 5 more pencils than Mrs. Black. What can we say about the number of students in each class? If Mrs. Johnson handed out 16 pencils and that was 5 more than Mrs. Black, how many students are in each class? Possible solution: Mrs. Black must have 22 students in her class. Mrs. Johnson must have 32 students in her class. Task 3: Jerry made one gallon of sweetened tea and one half gallon of lemonade for a picnic. If he drank ¼ of each container, how many cups of tea did he drink? How many cups of lemonade? *1 gallon = 16 cups If Jerry drank 2 cups of lemonade and 2 cups of tea, what fraction of the tea did he drink? What fraction of the lemonade did he drink? Possible solution: Question 1: Jerry drank 4 cups of tea and 2 cups of lemonade. Question 2: Jerry drank 1/8 of the gallon of tea and ¼ of the half gallon of lemonade. Connect the tasks by discussing with students how the size of the wholes matters in each context.

Rubric

Level I Level II Level III Limited Performance • Students are unable to solve

Task 1, 2, or 3.

Not Yet Proficient • Students can solve 1 or 2 of

the 3 tasks correctly with a complete explanation.

Proficient in Performance • Students can solve and explain

their answers to all three tasks.







The Whole Matters

Task 1: Two friends each ate ½ of a pizza. Joselin says they must have eaten the same amount, but Donnie says they could have eaten different amounts. Who do you think is correct, and why? Explain your thinking in words, pictures, and numbers.

Task 2: Mrs. Johnson and Mrs. Black each gave ½ of their students a pencil. Mrs. Johnson handed out 5 more pencils than Mrs. Black. What can we say about the number of students in each class? If Mrs. Johnson handed out 16 pencils and that was 5 more than Mrs. Black, how many students are in each class?



The Whole Matters Task 3: Jerry made one gallon of sweetened tea and one half gallon of lemonade for a picnic. If he drank ¼ of each container, how many cups of tea did he drink? How many cups of lemonade? *1 gallon = 16 cups If Jerry drank 2 cups of lemonade and 2 cups of tea, what fraction of the tea did he drink? What fraction of the lemonade did he drink?



Enough Soda

4.NF.2 - Task 2 Domain Number & Operations- Fractions Cluster Extend understanding of fraction equivalence and ordering. Standard(s) 4.NF.2 Compare two fractions with different numerators and different denominators, e.g.,

by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

Materials Paper and pencil, Graph paper (optional) Task You need 3/4 of a Liter of soda to make punch for a party. Which containers have enough

soda in them to make punch? Write a sentence explaining your thinking. Container A- 2/4 of a Liter Container B- 2/3 of a Liter Container C- 5/6 of a Liter Container D- 11/12 of a Liter Container E- 7/12 of a Liter

Rubric





Proficient in Performance • Solutions: Containers C and D. • The sentence shows a clear and

logical explanation of their strategy.





Enough Soda

You need 3/4 of a Liter of soda to make punch for a party. Which containers have enough soda in them to make punch? Write a sentence explaining your thinking.

Container A- 2/4 of a Liter Container B- 2/3 of a Liter Container C- 5/6 of a Liter Container D- 11/12 of a Liter Container E- 7/12 of a Liter



Which is Bigger?

4.NF.2- Task 3 Domain Number & Operations- Fractions Cluster Extend understanding of fraction equivalence and ordering. Standard(s) 4.NF.2. Compare two fractions with different numerators and different denominators, e.g.,


Materials Pattern blocks, Paper and pencil Optional: Graph paper *Computer-based pattern blocks can be found here- http://illuminations.nctm.org/ActivityDetail.aspx?ID=27

Task Which is Bigger? Two joint hexagons have a value of 1 whole. Based on that, draw each fraction in terms of pattern blocks and determine which is bigger:

• 3/4 or 4/6 • 1/2 or 5/12 • 2/4 or 3/6 • 5/6 or 3/4

Write your own comparison question using fourths, sixths, or twelfths. Draw a picture to prove which is easier. Pick one of the questions above and write a sentence explaining how you know that you are correct.

Rubric





Proficient in Performance • Solutions: 4/6, 1/2, they are

equal, 5/6. AND • The sentence shows a clear and

logical explanation of their strategy.





Which is Bigger?

If two hexagons have a value of 1 whole, think about the value of other pattern block. Draw each fraction below in terms of pattern blocks and determine which is bigger:

• 3/4 or 4/6

• 1/2 or 5/12

• 2/4 or 3/6

• 5/6 or 3/4

Write your own comparison question using fourths, sixths, or twelfths. Draw a picture to prove which is easier. Pick one of the questions above and write a sentence explaining how you know that you are correct.



Pattern Blocks 4.NF.2-Task 4

Domain Number and Operation- Fractions Cluster Extend understanding of fraction equivalence and ordering. Standard(s) 4.NF.2 Compare two fractions with different numerators and different denominators, e.g.

by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½. Recognize that comparisons are valid only when the two fractions refer to the same size whole. Record the results of comparisons with symbols >, =, or <, and justify conclusions, e.g., by using a visual fraction model.

Materials Paper and pencil, pattern blocks, grid paper Task Task 1: Use pattern blocks.

• If a hexagon is one whole, which block represents ½? Which block represents 1/3? Which blocks represents 2/3?

• If a trapezoid if one whole, which block represents 1/3? Which block represents 2/3? • If a blue rhombus is one whole, which block represents ½? • If a blue rhombus is ½ of a whole, what would one whole look like? • Find one half of a hexagon and one half of a blue rhombus. Why don't they make one whole

altogether? • If a green triangle is 1/3 of a whole, what would one whole look like? How many these wholes

could you make with 3 hexagons? Task 2: Use grid paper. 1. Justin planted tomatoes in 1/3 of his 6' x 6' garden. Gina planted tomatoes in 1/3 of her 8' x 7'

garden. How many square feet of the garden did each person use for tomatoes? If each person planted 1/3 of their garden with tomatoes, why did they use a different amount of square feet?

2. Deon used a 9 x 9 grid to represent 1 whole and Shawn used a 12 x 12 grid to represent 1. Each boy shaded in squares to show 1/3 of the whole. How many squares did Deon shade? How many squares did Shawn shade? Why did they shade different numbers of squares if they each shaded in 1/3?

Rubric

Level I Level II Level III Limited Performance • Students are unable to solve

Task 1 or 2.

Not Yet Proficient • Students can solve 1 of the 2

tasks correctly with a complete explanation.

Proficient in Performance • Students can solve and explain

their answers to both tasks. Responses indicate that they understand that the size of the whole determines the amount in a fraction of that whole.







Pattern Blocks Task 1: Use pattern blocks. If a hexagon is one whole, which block represents ½? Which block represents 1/3? Which blocks represents 2/3? If a trapezoid if one whole, which block represents 1/3? Which block represents 2/3? If a blue rhombus is one whole,which block represents ½? If a blue rhombus is ½ of a whole, what would one whole look like? Find one half of a hexagon and one half of a blue rhombus. Why don't they make one whole altogether? If a green triangle is 1/3 of a whole, what would one whole look like? How many these wholes could you make with 3 hexagons?



Task 2: Use grid paper. 1. Justin planted tomatoes in 1/3 of his 6' x 6' garden. Gina planted tomatoes in 1/3

of her 8' x 7' garden. How many square feet of the garden did each person use for tomatoes? If each person planted 1/3 of their garden with tomatoes, why did they use a different amount of square feet?

2. Deon used a 9 x 9 grid to represent 1 whole and Shawn used a 12 x 12 grid to

represent 1. Each boy shaded in squares to show 1/3 of the whole. How many squares did Deon shade? How many squares did Shawn shade? Why did they shade different numbers of squares if they each shaded in 1/3?



Who’s on the Bus?

4.NF.2 - Task 5 Domain Number & Operations- Fractions Cluster Extend understanding of fraction equivalence and ordering. Standard(s) 4.NF.2 Compare two fractions with different numerators and different denominators, e.g.,


Materials Paper and pencil, Graph paper (optional) Task There are some children on the bus.

2/6 of the children are wearing tan pants. 6/10 of the children are wearing tennis shoes. 5/12 of the children are wearing a red shirt. 2/3 of the children are wearing a hat. For each item of clothing, are more than half or less than half of the children wearing that item? Write a sentence explaining how you know that you are correct.

Rubric





Proficient in Performance • Solutions: Less than half- tan

pants, red shirt. More than half- tennis shoes, hat.

• The sentence demonstrates a clear understanding of comparing fractions to the benchmark of 1/2.





Who’s On The Bus? There are some children on the bus. • 2/6 of the children are wearing tan pants. • 6/10 of the children are wearing tennis shoes. • 5/12 of the children are wearing a red shirt. • 2/3 of the children are wearing a hat.

For each item of clothing, are more than half or less than half of the children wearing that item? Write a sentence explaining how you know that you are correct.



Who Has More Gum?

4.NF.2- Task 6 Domain Number & Operations- Fractions Cluster Extend understanding of fraction equivalence and ordering. Standard(s) 4.NF.2. Compare two fractions with different numerators and different denominators, e.g.,


Materials Paper, pencil, sentence strips or paper to fold (optional) Task Who has more gum?

A group of friends buys a big long strip of gum and tear it into pieces. Sally has 2/3 of a foot of gum. Josey has 3/4 of a foot of gum. Mitch has 4/6 of a foot of gum. Gary has 3/6 of a foot of gum. Part 1: Draw pictures and write an expression using the >, <, or = signs to show who has more gum between:

Gary or Sally? Mitch or Sally? Josey or Mitch?

Part 2: Taylor comes in and gets ½ of a foot of gum. Gary says, “We have the same amount.” Is Gary correct? Why or why not?

Rubric





Proficient in Performance • Solutions:

Part 1: Sally. 3/6 < 2/3. The same. 4/6 = 2/3. Mitch. ¾ < 4/6. Part 2: Gary is correct. 3/6 = ½.





Who Has More Gum?

A group of friends buys a big long strip of gum and tear it into pieces. Sally has 2/3 of a foot of gum. Josey has 3/4 of a foot of gum. Mitch has 4/6 of a foot of gum. Gary has 3/6 of a foot of gum. Part 1: Draw pictures and write an expression using the >, <, or = signs to show who has more gum between: Gary or Sally? Mitch or Sally? Josey or Mitch? Part 2: Taylor comes in and gets ½ of a foot of gum. Gary says, “We have the same amount.” Is Gary correct? Why or why not?



Sharing Cake 4.NF.3- Task 1

Domain Number & Operations- Fractions Cluster Build fractions from unit fractions. Standard(s) 4.NF.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b.

4.NF.3b Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8. Other Standard: 4.NF.3a Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

Materials Paper, pencil Task At a party you are giving out 8 pieces of cake. People will get different amounts of cake.

Tom and Hal will both get 1 piece of cake. Mary will get 2 pieces of cake. Nancy and Bob share equally the remaining pieces of cake. What fraction of the cake will each person eat? Write an equation to match the situation. Write a sentence explaining the strategy used to solve the problem.

Rubric


clear understanding about how to represent the pieces of cake as fractions.


equation or explanation is incorrect OR work is logically shown but the student has made a calculation error.

Proficient in Performance • Solutions: Tom and Hal: 1/8,

Mary, Nancy and Bob: 2/8 • Equation: 1/8 + 1/8 + 2/8 + 2/8

+ 2/8 = 8/8 AND The sentence clearly describes an accurate strategy.





Sharing Cake At a party you are giving out 8 pieces of cake. People will get different amounts of cake. • Tom and Hal will both get 1 piece of cake. • Mary will get 2 pieces of cake. • Nancy and Bob share equally the remaining pieces of cake.

What fraction of the cake will each person eat? Write an equation to match the situation. Write a sentence explaining the strategy used to solve the problem.



Candy Bucket 4.NF.3 - Task 2

Domain Number & Operations- Fractions Cluster Build fractions from unit fractions. Standard(s) 4.NF.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b.


Materials Paper, pencil Task There are 12 pieces of candy in the bucket. Maria and Sam each get 2 pieces of candy.

Tom gets 5 pieces of candy. Vinny gets the rest of the candy. What fraction does each student get? Write an equation to match this story. Write a sentence to explain the strategy used to solve the problem.

Rubric





Proficient in Performance • Solutions: Maria and Sam:

2/12 or 1/6. Tom: 5/12. Vinny 3/12.

• Equation: 2/12 + 2/12 + 5/12 + 3/12 AND The sentence clearly describes an accurate strategy.





Candy Bucket There are 12 pieces of candy in the bucket. • Maria and Sam each get 2 pieces of candy. • Tom gets 5 pieces of candy. • Vinny gets the rest of the candy.

What fraction does each student get? Write an equation to match this story. Write a sentence to explain the strategy used to solve the problem.



Square Tiles 4.NF.3-Task 3

Domain Number and Operation- Fractions Cluster Build fractions from unit fractions by applying and extending previous

understandings of operations on whole numbers. Standard(s) 4.NF.3c Add and subtract mixed numbers with like denominators, e.g., by replacing each

mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

Materials Pencil, paper, square tiles Task Task 1: Use square tiles to build mixed numbers.

Place 3 color tiles together as a whole on the table or draw on board or display however works best for your classroom. One way to understand mixed numbers is to look at them as groups of unit fractions. Model how to use square tiles to build the number 2 1/3. • If this rectangle is a whole what does one tile represent? (thirds) • How many square tiles does it take to make one whole? (three thirds) • How many thirds will we need to build 2 whole? (six thirds) • Build arrangement below, how many thirds in all did we use? (seven thirds or 1/3 + 1/3 + 1/3 +

1/3 + 1/3 + 1/3 + 1/3) Continue to use the square tiles to connect unit fractions and mixed numbers. Now the square tiles represent ¼. • If we wanted to build the number 3 ¼, how many tiles would we need? How do you know? • Build 2 3/8. How many tiles do you need? How many unit fractions make one whole? • If you have 17 square tiles and each one is an unit of a whole, how many fourths can you

build? Students should make four groups of four fourths with one fourth left over. What mixed number does this make? 4 ¼

Task 2: Use mixed number fractions to compute. In Task 2, some students may be able to transition to drawing the mixed number models while others may continue to need the square tiles to count the unit fractions. Some may draw or build the models and cross out or combine pieces to find answers. One strategy of efficiently adding and subtracting mixed number is to convert them to improper fractions, and some students may be able to do this using models. Allow students to complete the problems and then share their strategies. Addition: Maria needs 6 1/3 feet of string for a solar system mobile. She has 2 2/3 feet of yellow string and 3 2/3 feet of green string. How much string does she have altogether? Will it be enough to complete the project? Explain why or why not. Subtraction: Leland has 5 1/8 pizzas left over from his birthday party. After giving some pizza to his friend, he has 3 3/8 pizzas left. How much pizza did Leland give away to his friend?



Rubric

Level I Level II Level III Limited Performance • Students are unable to convert

mixed numbers to improper fractions, use models to build mixed numbers, or add or subtract mixed numbers with like denominators.

Not Yet Proficient • Students can build and draw

mixed numbers, and can use models to show the equivalence of improper fractions and mixed numbers. Students are unable to solve mixed number word problems by breaking up mixed numbers to facilitate addition and subtraction.

Proficient in Performance • Students can build and use

models and equations with unit fractions to solve the problems. Students are able to use the idea of mixed numbers as groups of unit fractions, or as an improper fraction to solve addition and subtraction problems with like denominators.





Square Tiles

Addition: Maria needs 6 1/3 feet of string for a solar system mobile. She has 2 2/3 feet of yellow string and 3 2/3 feet of green string. How much string does she have altogether? Will it be enough to complete the project? Explain why or why not. Subtraction: Leland has 5 1/8 pizzas left over from his birthday party. After giving some pizza to his friend, he has 3 3/8 pizzas left. How much pizza did Leland give away to his friend?



Pattern Blocks & Unit Fractions

4.NF.3-Task 4 Domain Number and Operation- Fractions Cluster Build fractions from unit fractions by applying and extending previous

understandings of operations on whole numbers. Standard(s) 4.NF.3 Understand a fraction a/b with a> 1 as a sum of fractions 1/b.

4.NF.3a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

Materials Pattern blocks, Pencil, Paper Task Use unit fractions in the equations to show that a fraction can be thought of as the sum of several

unit fractions. Task 1: Use pattern blocks. Establish equivalencies with students. If the yellow hexagon is one whole, what fraction of the whole is each block? If the green triangle is 1/6 of the whole, how many green triangles would we need to build 4/6? Use the pattern blocks to model and solve these problems. Write an equation to represent each situation. Use unit fraction to represent each pattern block in the equation. • Scott and Zachary shared a sub. Scott ate 2/6 of the sub. Zachary ate 1/6 of the sub. How much

of the sub did they eat together? 1/6 + 1/6 + 1/6 = 3/6 • Three students were sharing 2 pies. Each student ate ½ of a pie. How much of the total amount

of pie did they eat together? ½ + ½ + ½ = 3/2 or 1 ½ • Trevor had 1 1/3 pizzas. His dad ate 2/3 of a pizza. How much pizza was left? 1 1/3 = 3/3 +

1/3 or 4/3. 4/3 = 1/3 + 1/3 + 1/3 + 1/3. If you subtract 2/3 from that there will be 2/3 leftover. • Madeline had 7/6 yards of fabric. She cut off one yard to make curtains. How much fabric was

left? 7/6 = 6/6 + 1/6 so she had 1/6 of one yard of fabric left. • Lauren had 7/3 pans of brownies leftover after a party. Her brother ate 2/3 of a pan of

brownies. What part of the total amount of brownies was left? 7/3 = 3/3 + 3/3 + 1/3 or 2 1/3. 2 1/3 = 1 + 1/3 + 1/3 + 1/3 +1/3 and if we subtract 2/3 there will be 1 2/3 pans of brownies leftover.

Task 2: Use unit fractions to solve. Use what you know about unit fractions to solve the problems. Write an equation that includes unit fractions to show the answer for each problem. 2/3 + 2/3 = 4/3 = 1/3 + x 5/7 + y = 12/7 1 ¼ – ¾ = 2 1/5 – 3/5 = 8/9 – 3/9 = ½ x 5 = 1 3/5 + 4/5 = 2/3 x 4 =

Rubric

Level I Level II Level III Limited Performance • Students are unable to use

models or unit fractions to solve the problems in Tasks 1 and 2.

Not Yet Proficient • Students can use models to solve

the problems in Task 1 but have difficulty writing equations with unit fractions in Task 1 and/or 2.

Proficient in Performance • Students can use models and

equations with unit fractions to solve the problems in Tasks 1 & 2.







Pattern Blocks & Unit Fractions Use the pattern blocks to model and solve these problems. Write an equation to represent each situation. Use unit fraction to represent each pattern block in the equation. • Scott and Zachary shared a sub. Scott ate 2/6 of the sub. Zachary ate 1/6 of the

sub. How much of the sub did they eat together? • Three students were sharing 2 pies. Each student ate ½ of a pie. How much of

the total amount of pie did they eat together? • Trevor had 1 1/3 pizzas. His dad ate 2/3 of a pizza. How much pizza was left? • Madeline had 7/6 yards of fabric. She cut off one yard to make curtains. How

much fabric was left? • Lauren had 7/3 pans of brownies leftover after a party. Her brother ate 2/3 of a

pan of brownies. What part of the total amount of brownies was left?



Task 2: Use unit fractions to solve. Use what you know about unit fractions to solve the problems. Write an equation that includes unit fractions to show the answer for each problem. 2/3 + 2/3 = 4/3 = 1/3 + x 5/7 + y = 12/7 1 ¼ – ¾ = 2 1/5 – 3/5 = 8/9 – 3/9 = ½ x 5 = 1 3/5 + 4/5 = 2/3 x 4 =



Dividing Up the Land

4.NF.3- Task 5 Domain Number & Operations- Fractions Cluster Build fractions from unit fractions. Standard(s) 4.NF.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b.


Materials Paper, pencil Pattern blocks Virtual pattern blocks can be found here- http://www.mathplayground.com/patternblocks.html

Task There is a plot of land shaped like the figure below. Each hexagon has a value of 1 whole unit. The plot of land, therefore, has a value of 3 whole units.

Determine how to use pattern blocks to divide the shape up into the following ways. For each way, make a picture and write an equation. Part 1: The land owner will only sell the land in sections that are one-third of a unit. The following people buy land: Taylor: 2 sections

Bill: 1 section Nick: 4 sections

Use your pattern blocks to make a picture of how the land was divided up. Is there any land left? If so, how much? Write an equation to show how the land was split up by the land owner Part 2: The land owner will only sell the land in sections that are one-sixth of a unit. The following people buy land: Tom: 3 sections

Susan: 2 sections Bob: 4 sections Mallory: 1 section Wes: 6 sections

Use your pattern blocks to make a picture of how the land was divided up. Is there any land left? If so, how much? Write an equation to show how the land was split up by the land owner.








Proficient in Performance • Solutions: Part 1: There are 2

sections left or 2/3 of a unit left. 2/3 + 1/3 + 4/3 + 2/3 = 3. Part 2: There are 2 sections left or 2/6 of a unit. 3/6 + 2/6 + 4/6 + 1/6 + 6/6 + 2/6.





Dividing Up the Land

There is a plot of land shaped like the figure below. Each hexagon has a value of 1 whole unit. The plot of land, therefore, has a value of 3 whole units.

Determine how to use pattern blocks to divide the shape up into the following ways. For each way, make a picture and write an equation. Part 1 The land owner will only sell the land in sections that are one-third of a unit. The following people buy land:

Taylor: 2 sections Bill: 1 section Nick: 4 sections

Use your pattern blocks to make a picture of how the land was divided up. Is there any land left? If so, how much? Write an equation to show how the land was split up by the land owner. Include any unsold land.



Part 2 The land owner will only sell the land in sections that are one-sixth of a unit. The following people buy land:

Tom: 3 sections Susan: 2 sections Bob: 4 sections Mallory: 1 section Wes: 6 sections

Use your pattern blocks to make a picture of how the land was divided up. Is there any land left? If so, how much? Write an equation to show how the land was split up by the land owner. Include any unsold land.



How Much Punch is Left?

4.NF.3- Task 6 Domain Number & Operations- Fractions Cluster Build fractions from unit fractions. Standard(s) 4.NF.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b.


Materials Paper, pencil Task Part 1

There are 2 gallons of punch left in the punch bowl. It gets divided between 8 students, with each getting a different amount.

a) Micah takes 1/12 of a gallon of punch. b) Roberta takes three times as much Micah. c) Steve takes twice as much as Roberta. d) Yanni takes 2/12 of a gallon of punch less than Steve. e) Amy takes 1/12 of a gallon of punch less than Yanni. f) The remaining punch is divided between Tom, Jackie, and Henry. g) Tom and Jackie had the same amount of punch. h) Henry had less punch than both Tom and Jackie.

How much punch did each person take? Draw a picture and write an equation to match this context. Part 2 At the next party, the amount of punch doubled to 4 gallons. Each person took the same fraction of the punch. How much would each person get?

Rubric





Proficient in Performance • Solutions: Part 1: Micah: 1/12;

Roberta, 3/12 or ¼; Steve: 6/12 or ½; Yanni: 4/12 or 1/3; Amy: 3/12 or ¼: Henry 1/12 while Tom and Jackie each get 3/12.



Standards for Mathematical Practice 1. Makes sense and perseveres in solving problems. 2. Reasons abstractly and quantitatively. 3. Constructs viable arguments and critiques the reasoning of others. 4. Models with mathematics. 5. Uses appropriate tools strategically. 6. Attends to precision. 7. Looks for and makes use of structure. 8. Looks for and expresses regularity in repeated reasoning.



How Much Punch is Left?

Part 1 There are 2 gallons of punch left in the punch bowl. It gets divided between 8 students, with each getting a different amount.

a) Micah takes 1/12 of a gallon of punch. b) Roberta takes three times as much Micah. c) Steve takes twice as much as Roberta. d) Yanni takes 2/12 of a gallon of punch less than Steve. e) Amy takes 1/12 of a gallon of punch less than Yanni. f) The remaining punch is divided between Tom, Jackie, and Henry. g) Tom and Jackie had the same amount of punch. h) Henry had less punch than both Tom and Jackie.

How much punch did each person take? Draw a picture and write an equation to match this context. Part 2 At the next party, the amount of punch doubled to 4 gallons. Each person took the same fraction of the punch. How much would each person get?



Boxing Up Leftover Brownies

4.NF.3 Task 7 Domain Number and Operations - Fractions Cluster Build fractions from unit fractions. Standard(s) 4.NF3. Understand a fraction a/b with a > 1 as a sum of fractions 1/b.

4.NF.3c. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. 4.NF.3d. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

Materials Activity sheet Task Boxing Up Leftover Brownies

Amaria has brownies at her birthday party. At the end of the party there are the following brownies left over:

• 5 brownies with cream cheese frosting • 4 plain chocolate brownies • 3 chocolate brownies with nuts • 7 brownies with caramel frosting

Part 1: After the party the brownies are put into boxes. A box can hold 8 brownies. If each type of brownie were packed into their own box, what fraction of a box does each type of brownie take up? Draw pictures below to show your work. Part 2: Amaria and her Mom want to use fewer boxes and put different types of brownies into the same box. How many whole boxes do they fill? Will there be a box partially filled? If so what fraction of the box is partially filled? Draw pictures to show your work. Part 3: Write an equation to match the picture that you drew in Part 2. Part 4: Is there space for any more brownies? If so how many more brownies do you have room for? Write an equation that shows your work.



Rubric

Level I Level II Level III Limited Performance • Solutions include many

errors and show limited understanding.

Not Yet Proficient • Solutions will include between

1 to 3 errors in various parts of the task.

Proficient in Performance • Solutions include correct answers

and show a deep understanding of concepts.

• Answers: Part 1: Pictures are correctly drawn and fractions are correctly labeled. Cream cheese: 5/8. Plain: 4/8. Nuts: 3/8. Caramel: 7/8.

• Part 2: Picture is correctly drawn. Answer is 2 and 3/8.

• Part 3: 5/8 + 4/8 + 3/8 + 7/8 = 2 and 3/8.

• Part 4: There is space for 5 more brownies or there is 5/8 of a box empty. Equation: 3 – 2 and 3/8 = 5/8.





Boxing Up Leftover Brownies

Amaria has brownies at her birthday party. At the end of the party there are the following brownies left over:

• 5 brownies with cream cheese frosting • 4 plain chocolate brownies • 3 chocolate brownies with nuts • 7 brownies with caramel frosting

Part 1: After the party the brownies are put into boxes. A box can hold 8 brownies. If each type of brownie were packed into their own box, what fraction of a box does each type of brownie take up? Draw pictures below to show your work. Part 2: Amaria and her Mom want to use fewer boxes and put different types of brownies into the same box. How many whole boxes do they fill? Will there be a box partially filled? If so what fraction of the box is partially filled? Draw pictures to show your work. Part 3: Write an equation to match the picture that you drew in Part 2. Part 4: Is there space for any more brownies? If so how many more brownies do you have room for? Write an equation that shows your work.



Going the Distance

4.NF.3 Task 8 Domain Number and Operations - Fractions Cluster Build fractions from unit fractions. Standard(s) 4.NF3. Understand a fraction a/b with a > 1 as a sum of fractions 1/b.

4.NF.3c. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. 4.NF.3d. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

Materials Activity sheet Task Going the Distance

In order to train for the Girls on the Run 5K Race, the girls’ running team at Lincoln Elementary School runs the following distances: Week Distance Week 1 1 and 1/6 miles Week 2 1 and 3/6 miles Week 3 2 and 4/6 miles Week 4 2 and 5/6 miles

Part 1: Draw a number line to show the distance that the girls ran each week. Part 2: How far did the girls run in all? Write an equation that matches the story. Part 3: The girls at Jefferson Elementary School ran 10 miles total during the same time. How much farther did they run than the girls at Lincoln Elementary School? Use a picture and an equation to find your answer.



Rubric

Level I Level II Level III Limited Performance • Solutions include many

errors and show limited understanding.

Not Yet Proficient • Solutions will include between

1 to 3 errors in various parts of the task.

Proficient in Performance • Solutions include correct answers

and show a deep understanding of concepts.

• Answers: Part 1: The number line matches the distance that the girls ran.

• Part 2: The girls ran 8 and 1/6 miles. Equation: 1 1/6 + 1 3/6 + 2 4/6 + 2 5/6 = 8 1/6.

• Part 3: Picture is correct. Equation: 10 – 8 1/6 = 1 5/6 miles.





Going the Distance

In order to train for the Girls on the Run 5K Race, the girls’ running team at Lincoln Elementary School runs the following distances: Week Distance Week 1 1 and 1/6 miles Week 2 1 and 3/6 miles Week 3 2 and 4/6 miles Week 4 2 and 5/6 miles Part 1: Draw a number line to show the distance that the girls ran each week. Part 2: How far did the girls run in all? Write an equation that matches the story. Part 3: The girls at Jefferson Elementary School ran 10 miles total during the same time. How much farther did they run than the girls at Lincoln Elementary School? Use a picture and an equation to find your answer.



Pasta Party

4.NF.4 - Task 1 Domain Number and Operations - Fractions Cluster Apply and extend previous understandings of multiplication to multiply a fraction by

a whole number. Standard(s) 4.NF.4 Understand a fraction a/b as a multiple of 1/b (i.e., 5/4 = 5 x ¼ = ¼ + ¼ + ¼ + ¼ +

¼ ); be able to express a multiple of a/b as 1/b and use this to multiply a fraction by a whole number (i.e., 3 x 2/5 = (3 x 2)/5 = 6 x 1/5), or generalize that n x a/b = (n x a)/b; Solve word problems involving multiplication of a fraction by a whole number.

Materials Paper and pencil Task Part 1:

Katie makes 1/4 pound of pasta for each person at her dinner party. If seven people attend the party, how many pounds of pasta will be needed for her guests? Write an addition equation to show this situation. Show your answer with a number line or an area model. Use numbers or words to explain how your model shows addition. Part 2: Write a multiplication equation to show this situation. Show your answer with a number line or an area model. Use numbers or words to explain how your model shows multiplication. Part 3 How are your addition and multiplication equations alike? Different? Would you use one over the other? Why or why not? Extension: Students can write their own word problem using ¼ x 7.




Limited Performance • Part 1: Student is unable

to write an addition equation or draw a model.

• Part 2: Student is unable to write a multiplication equation or draw a model.

Not Yet Proficient • Part 1: Student writes a correct

addition equation that totals 7/4 (i.e., ¼ + ¼ + ¼ + ¼ + ¼ + ¼ + ¼ = 7/4), but is unable to show the sum on a number line as seven ‘jumps’ of ¼, or as an area model, and does not clearly explain how the model matches their addition equation.

• Part 2: Student writes a correct multiplication equation (¼ x 7= 7/4), but is unable to show the total 7/4 on a number line or area model, and does not clearly explain how the model matches their multiplication equation.

• Part 3: Students have some idea how they are alike and different.

Proficient in Performance • Part 1: Student writes a correct

addition equation that totals 7/4 (i.e., ¼ + ¼ + ¼ + ¼ + ¼ + ¼ + ¼ = 7/4).They show the sum on a number line as seven ‘jumps’ of ¼, or as an area model, and clearly explain how the model matches their addition equation.

• Part 2: Student writes a correct multiplication equation (¼ x 7= 7/4). They show the total 7/4 on a number line or area model, and clearly explain how the model matches their multiplication equation.

• Part 3: Students understand how they are alike and different and clearly states.




Pasta Party Part 1: Katie makes 1/4 pound of pasta for each person at her dinner party. If seven people attend the party, how many pounds of pasta will be needed for her guests? Write an addition equation to show this situation. Show your answer with a number line or an area model. Use numbers or words to explain how your model shows addition. Part 2: Write a multiplication equation to show this situation. Show your answer with a number line or an area model. Use numbers or words to explain how your model shows multiplication.



Part 3 How are your addition and multiplication equations alike? Different? Would you use one over the other? Why or why not? Extension: Write your own word problem using ¼ x 7.



Drawing a Model

4.NF.4 Task 2 Domain Number and Operations - Fractions Cluster Apply and extend previous understandings of multiplication to multiply a fraction by a

whole number. Standard(s) 4.NF.4 Understand a fraction a/b as a multiple of 1/b (i.e., 5/4 = 5 x ¼ = ¼ + ¼ + ¼ + ¼ + ¼ );

be able to express a multiple of a/b as 1/b and use this to multiply a fraction by a whole number (i.e., 3 x 2/5 = (3 x 2)/5 = 6 x 1/5), or generalize that n x a/b = (n x a)/b; Solve word problems involving multiplication of a fraction by a whole number.

Materials Paper and pencil Task Part 1:

Kelly was making curtains for her living room. She bought four pieces of fabric that were each 2/3 yard long. How many yards of fabric did Kelly buy in all? Draw a picture and write an equation to show the total amount of fabric if each piece is 2/3 yard long. Part 2: With the fabric that she bought in part 1, Kelly cut each piece of fabric into a 1/3 yard long piece. Draw a picture and write an equation to show the total amount of fabric if each piece is 1/3 yard long. Part 3: Is the amount of fabric in Part 1 and Part 2 the same? Use pictures to prove it. Write a sentence to explain how you know that you are correct.

Rubric

Level I Level II Level III Limited Performance • Part 1

Student is unable to create a correct equation and/or picture.

• Part 2 Student is unable to create a correct equation and/or picture.

• Part 3 The student cannot draw a model to show this relationship or explain it in words or numbers.

Not Yet Proficient • Part 1

addition equation 2/3 + 2/3 + 2/3 + 2/3 = 8/3 multiplication equation 4 x 2/3 = 8/3 Picture should show four groups of 2/3.

• Part 2 Addition equation 1/3 + 1/3 + 1/3 + 1/3 + 1/3 +1/3 + 1/3 + 1/3= 8/3 Multiplication equation 8 x 1/3 = 8/3 Picture should show eight groups of 1/3

• Part 3 It is unclear from the student’s picture that they understand the relationship 8/3 = 4 x 2/3.

Proficient in Performance • Part 1

addition equation 2/3 + 2/3 + 2/3 + 2/3 = 8/3 multiplication equation 4 x 2/3 = 8/3 Picture should show four groups of 2/3.

• Part 2 Addition equation 1/3 + 1/3 + 1/3 + 1/3 + 1/3 +1/3 + 1/3 + 1/3= 8/3 Multiplication equation 8 x 1/3 = 8/3 Picture should show eight groups of 1/3

• Part 3 Picture and explanation should show that eight individual copies of one third can be grouped as four groups of two-thirds. Equations: 8 x 1/3 = 4 x 2/3







Drawing a Model Part 1: Kelly was making curtains for her living room. She bought four pieces of fabric that were each 2/3 yard long. How many yards of fabric did Kelly buy in all? Draw a picture and write an equation to show the total amount of fabric if each piece is 2/3 yard long.

Part 2: With the fabric that she bought in part 1, Kelly cut each piece of fabric into a 1/3 yard long piece. Draw a picture and write an equation to show the total amount of fabric if each piece is 1/3 yard long.

Part 3: Is the amount of fabric in Part 1 and Part 2 the same? Use pictures to prove it. Write a sentence to explain how you know that you are correct.



Chris’s Cookies 4.NF.4-Task 3

Domain Number and Operations - Fractions Cluster Apply and extend previous understandings of multiplication to multiply a fraction by



Materials Paper and pencil Task Students will work together or independently to show their solutions to the fraction word

problems. Chris’s Cookies

Chris is making cookies for his friend’s birthday party using the following recipe. Chocolate Chip Cookies: Makes 2 dozen cookies 2 cups flour 1/2 teaspoon baking soda 1 teaspoon salt 3/5 cups butter, softened 3/4 cups sugar 1/2 cup light brown sugar 1 egg 1 teaspoon vanilla extract 1 package (6 ounces) chocolate chips 1/2 cup chopped walnuts From http://www.mccormick.com/ 1. How much butter will he need to make 3 batches of cookies? Write an equation to show your answer. 2. How much butter will Chris need to make 6 batches of cookies? Write an equation to show your answer. 3. How much butter will Chris need to make 9 batches of cookies? Write an equation to show your answer. 4. What patterns do you notice in the amounts of butter needed for 3 batches, 6 batches, and 9 batches of cookies? 5. How can we use these patterns to predict the amount of butter needed for 18 batches? 36 batches?



Rubric

Level I Level II Level III Limited Performance • Students may or may not be

able to correctly compute answers to 1-3. They may still be relying on addition to compute.

Not Yet Proficient • 1. 3 x 3/5 = 9/5 • 2. 6 x 3/5 = 18/5 • 3. 9 x 3/5 = 27/5 • 4. Students may notice

patterns but they have difficulty using them to predict answers.

Proficient in Performance 1. 3 x 3/5 = 9/5 2. 6 x 3/5 = 18/5 3. 9 x 3/5 = 27/5 4. Students may notice patterns such as: · Alternating odd and even totals

(9/5, 18/5, 27/5) · n x a/b = (n x a)/b Multiplying

the numerator times the whole number always yields the answer.

· As the multiplier (3) grows by 3, the amount of butter increases by 9. Students may notice that this is because the numerator is 3.

· To predict the amount of butter for 18 batches, students may notice that they can double 3/5 x 9 since 9 doubled is 18 so that they have (3/5 x 9) x 2 = 27/5 x 2 = 54/2.

· To predict the amount of butter needed for 36 batches, students may double the amount for 18 batches, multiply the amount needed for 9 batches by 4, etc. (3/5 x 3) x 12 = 9/5 x 12 = 108/5 (3/5 x 6) x 6 = 18/5 x 6 = 108/5 (3/5 x 9) x 4 = 27/5 x 4 = 108/5




Chris’s Cookies

Chris is making cookies for his friend’s birthday party using the following recipe.

Chocolate Chip Cookies: Makes 2 dozen cookies 2 cups flour 1/2 teaspoon baking soda 1 teaspoon salt 3/5 cups butter, softened 3/4 cups sugar 1/2 cup light brown sugar 1 egg 1 teaspoon vanilla extract 1 package (6 ounces) chocolate chips 1/2 cup chopped walnuts From http://www.mccormick.com/ 1. How much butter will he need to make 3 batches of cookies? Write an equation to show

your answer. 2. How much butter will Chris need to make 6 batches of cookies? Write an equation to show

your answer. 3. How much butter will Chris need to make 9 batches of cookies? Write an equation to show

your answer. 4. What patterns do you notice in the amounts of butter needed for 3 batches, 6 batches, and 9

batches of cookies? 5. How can we use these patterns to predict the amount of butter needed for 18 batches? 36

batches?



Going the Distance




Materials Paper and pencil Task During her first week of training for the Girls on the Run 5K, Molly runs ¾ of a mile each

day for 6 days. Part 1: Write an addition equation to show this situation. Show your answer with a number line or an area model. Use numbers or words to explain how your model shows addition. Part 2: Write a multiplication equation to show this situation. Show your answer with a number line or an area model. Use numbers or words to explain how your model shows multiplication. Part 3 How are your addition and multiplication equations alike? Different? Would you use one over the other? Why or why not? Part 4 Molly’s friend Tonya ran 1 and 2/4 miles each day for 3 days. Who ran more? Explain your reasoning.




Limited Performance • Part 1: Student is

unable to write an addition equation or draw a model.



addition equation, but is unable to show the sum on a number line as seven ‘jumps’ of ¼, or as an area model, and does not clearly explain how the model matches their addition equation.

• Part 2: Student writes a correct multiplication equation, but is unable to show the total on a number line or area model, and does not clearly explain how the model matches their multiplication equation.

• Part 3: Students communicate unclearly how they are alike and different.

• Part 4: Student does not clearly communicate that they need 4 containers that are 1 cup each.


addition equation that totals 18/4 (3/4+3/4+3/4+3/4+3/4+3/4= 18/4). They show the sum on a number line as five ‘jumps’ of 3/4 or as an area model, and clearly explain how the model matches their addition equation.

• Part 2: Student writes a correct multiplication equation ¾ x 6 = 18/4). They show the total 18/4 on a number line or area model, and clearly explain how the model matches their multiplication equation.

• Part 3: Student understands how they are alike and different and clearly states.

• Part 4: Student communicates that Molly and Tanya have run the same amount.




Going the Distance

During her first week of training for the Girls on the Run 5K, Molly runs ¾ of a mile each day for 6 days. Part 1: Write an addition equation to show this situation. Show your answer with a number line or an area model. Use numbers or words to explain how your model shows addition. Part 2: Write a multiplication equation to show this situation. Show your answer with a number line or an area model. Use numbers or words to explain how your model shows multiplication. Part 3 How are your addition and multiplication equations alike? Different? Would you use one over the other? Why or why not? Part 4 Molly’s friend Tonya ran 1 and 2/4 miles each day for 3 days. Who ran more? Explain your reasoning.



Serving Ice Cream




Materials Paper and pencil Task Katie uses 2/3 of a cup of ice cream for each ice cream sundae that she makes. For a party

she makes 5 sundaes. Part 1: Write an addition equation to show this situation. Show your answer with a number line or an area model. Use numbers or words to explain how your model shows addition. Part 2: Write a multiplication equation to show this situation. Show your answer with a number line or an area model. Use numbers or words to explain how your model shows multiplication. Part 3 How are your addition and multiplication equations alike? Different? Would you use one over the other? Why or why not? Part 4 If ice cream were sold in 1 cup containers how many containers does she need to buy for her party?




Limited Performance • Part 1: Student is

unable to write an addition equation or draw a model.



addition equation, but is unable to show the sum on a number line as seven ‘jumps’ of ¼, or as an area model, and does not clearly explain how the model matches their addition equation.

• Part 2: Student writes a correct multiplication equation, but is unable to show the total on a number line or area model, and does not clearly explain how the model matches their multiplication equation.

• Part 3: Students communicate unclearly how they are alike and different.

• Part 4: Student does not clearly communicate that they need 4 containers that are 1 cup each.


addition equation that totals 10/3 (2/3 + 2/3+2/3+2/3+2/3).They show the sum on a number line as five ‘jumps’ of 2/3 or as an area model, and clearly explain how the model matches their addition equation.

• Part 2: Student writes a correct multiplication equation 2/3 x 5 = 10/3). They show the total 10/3 on a number line or area model, and clearly explain how the model matches their multiplication equation.

• Part 3: Student understand how they are alike and different and clearly states.

• Part 4: Student communicates that in order to buy 10/3 cups of ice cream they must buy 4 containers that are 1 cup each.




Serving Ice Cream

Katie uses 2/3 of a cup of ice cream for each ice cream sundae that she makes. For a party she makes 5 sundaes. Part 1: Write an addition equation to show this situation. Show your answer with a number line or an area model. Use numbers or words to explain how your model shows addition. Part 2: Write a multiplication equation to show this situation. Show your answer with a number line or an area model. Use numbers or words to explain how your model shows multiplication. Part 3 How are your addition and multiplication equations alike? Different? Would you use one over the other? Why or why not? Part 4 If ice cream were sold in 1 cup containers how many containers does she need to buy for her party? Write a sentence explaining your reasoning.



Karen’s Garden

4.NF.5 Task 1 Domain Number and Operations - Fractions Cluster Understand decimal notation for fractions, and compare decimal fractions. Standard(s) 4.NF.5 Express a fraction with a denominator of 10 as an equivalent fraction with a

denominator of 100, and use this technique to add two fractions with respective denominators 10 and 100. Express 3/10 as 30/100 and add 3/10 + 4/100 =34/100.

Materials Decimal grids (hundredths grids), base ten blocks (optional), paper and pencil Task In this task, students will be using decimal grids (hundredths) to shade in tenths and

hundredths as decimals and fractions, and find totals and differences. Introduce the manipulatives and task with the following practice problem. Karen is planting vegetables in her 10’ x 10’ garden. She wants 3/10 of the garden to be tomatoes. If Karen has already planted peas in 0.25 of the garden, how much space will she have left for other vegetables? Some students may be comfortable using hundredths grids while others may need the additional support of using base ten blocks (flat = 1 whole, ten stick = 1/10, unit cube = 1/100). Students may work on the Karen’s Garden sheet independently or in pairs if they need support. As they work, they should shade in hundredths grids or use base ten blocks to solve the addition or subtraction.

Rubric

Level I Level II Level III Limited Performance • Solutions will

include many errors in conversions and equivalencies, as well as addition and subtraction errors. Students may struggle to choose appropriate numbers from the problems for computation.

Not Yet Proficient • Students should be able to

convert decimals (tenths and hundredths) to fractions with 10 or 100 as a denominator. Their solutions should show that they can work flexibly with fractions and decimals.

• At this level, their solutions will include errors in several conversions and equivalencies.

Proficient in Performance • At this level, their solutions will include few

or no errors in conversions and equivalencies.

Possible solutions: 1. 76/100 + 24/100 = 100/100 2. 0.6 + 0.23 = 0.83

6/10 + 23/100 = 83/100 60/100 + 23/100 = 83/100

3. 0.5 – 0.14 = 0.36 0.14 + 0.36 = 0.50 14/100 + 36/100 = 5/10 or 50/100

4. 2/10 + 0.2 + 20/100 = 0.6 or 6/10 or 60/100 5. Students should figure out that 0.6 + 0.36 =

0.96 of the original grid, so 0.04 would be leftover for radishes. If radishes are now taking up 22/100 of the garden, 0.22 – 0.04 = 0.18. The deer ate peas in 0.18 of the garden.







Karen’s Garden

Use 10 x 10 grids to shade in your solutions to these problems.

1. Karen planted squash and watermelon in her 10’ x 10’ garden. She planted squash in 0.4 of her garden, but it grew so much that it took up 76/100 of the garden. How much space is left for watermelon?

2. Six tenths of the garden is planted with green beans. Twenty-three hundredths is planted with radishes. How much of the garden is planted?

3. Karen wants half of her garden to be planted with tomatoes. She has planted 0.14 of the garden with tomatoes so far. How much of the garden does she still need to plant with tomatoes?

4. Karen planted lettuce in 2/10 of her garden, peas in 0.2 of her garden, and peppers in 20/100 of the garden. How much of the garden is planted?

5. Six tenths of the garden was planted with peppers. Thirty six hundredths of the garden was planted with peas, but some of them were eaten by deer. Karen planted radishes in the leftover space and the empty space where the peas were eaten by deer. If radishes now take up 22/100 of the garden, how much of the garden did the deer eat?



Filling the Jar 4.NF.5 Task 2

Domain Number and Operations - Fractions Cluster Understand decimal notation for fractions, and compare decimal fractions. Standard(s) 4.NF.5 Express a fraction with a denominator of 10 as an equivalent fraction with a


Materials Decimal grids (hundredths grids), base ten blocks (optional), paper and pencil Task In this task, students will be using decimal grids (hundredths) to shade in tenths and

hundredths as decimals and fractions, and find totals and differences. Part 1: A jar can hold 100 marbles. For each of the situations below, find the amount for the various colors of marbles.

Jar A: The jar contains 103 blue,

102 white, and

10019 red marbles. The rest are yellow.

What fraction represents the number of yellow marbles? _____

Jar B: 107 green,

101 purple, and

1004 brown. The rest are white. What fraction represents

the number of white marbles? ______

Jar C: 103 gray and

10051 black. The rest are pink or yellow. There are more pink than

yellow marbles. What fraction represents the number of pink and yellow marbles? ____ pink, ____ yellow.

Jar D: 102 clear and

10018 orange. The rest are red and blue. There are 2 more red marbles

than blue marbles. What fraction represents the number of red and blue marbles? ___ red, ____ blue. Part 2: Pick one of the tasks above. Explain how you worked with the different denominators to find your answer. Some students may be comfortable using hundredths grids while others may need the additional support of using base ten blocks (flat = 1 whole, ten stick = 1/10, unit cube = 1/100).




Limited Performance • Solutions will include many

errors in conversions and equivalencies, as well as addition and subtraction errors. Students may struggle to choose appropriate numbers from the problems for computation.




Proficient in Performance • Students correctly find the

answer to each problem. Jar A: 31/100 yellow. Jar B: 16/100 white. Jar C: Multiple possible answers. Both fractions must add up to 19/100 and the fraction for pink must be greater than yellow. Jar D: Red: 32/100, Blue: 30/100.

• Part 2: The answer discusses that tenths can also be written as hundredths by multiplying the numerator and denominator both by 10.




Filling the Jar A jar can hold 100 marbles. For each of the situations below, find the amount for the various colors of marbles. Jar A: The jar contains

103 blue,

102 white, and

10019 red marbles. The rest are yellow.

What fraction represents the number of yellow marbles? _____ Jar B:

107 green,

101 purple, and

1004 brown. The rest are white. What fraction represents

the number of white marbles? ______ Jar C:

103 gray and

10051 black. The rest are pink or yellow. There are more pink than

yellow marbles. What fraction represents the number of pink and yellow marbles? ____ pink, ____ yellow. Jar D:

102 clear and

10018 orange. The rest are red and blue. There are 2 more red marbles

than blue marbles. What fraction represents the number of red and blue marbles? ___ red, ____ blue. Part 2: Pick one of the tasks above. Explain how you worked with the different denominators to find your answer.





Children’s Shirts

4.NF.5 Task 3 Domain Number and Operations - Fractions Cluster Understand decimal notation for fractions, and compare decimal fractions. Standard(s) 4.NF.5 Express a fraction with a denominator of 10 as an equivalent fraction with a


Materials Decimal grids (hundredths grids), base ten blocks (optional), paper and pencil Task Part 1:

A group of 100 fourth graders are on the playground. 102 of the group are wearing black

shirts. 10011 of the group are wearing blue shirts.

103 of the group are wearing white shirts.

The rest of the class is wearing green or yellow shirts. There are more children wearing yellow shirts than green shirts. What fraction of the group is wearing yellow shirts? Green shirts? Find at least three different correct solutions. Part 2: Describe your process for solving the task above.

Rubric

Level I Level II Level III Limited Performance • Solutions will include

many errors in conversions and equivalencies, as well as addition and subtraction errors. Students may struggle to choose appropriate numbers from the problems for computation.




Proficient in Performance • There are 39 students wearing a green

or yellow shirt. Students should be able to find three correct solutions that show a that there are more yellow than green shirts and that add up to 39 of the 100 students.

• Students should be able to explain the process for finding solutions.





Children’s Shirts

A group of 100 fourth graders are on the playground. 102 of the group are

wearing black shirts. 10011 of the group are wearing blue shirts.

103 of the group

are wearing white shirts. The rest of the class is wearing green or yellow shirts. There are more children wearing yellow shirts than green shirts. What fraction of the group is wearing yellow shirts? What fraction of the group is wearing green shirts? Find at least three different correct solutions.

Part 2: Describe how you used equivalent fractions to solve the task above.





Where am I now? How much farther?

4.NF.6 Task 1 Domain Number and Operations - Fractions Cluster Understand decimal notation for fractions, and compare decimal fractions. Standard(s) 4.NF.6. Use decimal notation for fractions with denominators 10 or 100. For example,

rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.

Materials Decimal grids (hundredths grids), base ten blocks (optional), paper and pencil Task Where am I now? How much farther?

Part 1: You have walked 0.32 of the way from your house to the school. A) What is that distance as a fraction?

B) If you walk another 17/100 of the way to the school how far have you gone now in

terms of both a fraction and a decimal?

C) If you walk another 3/10 of the way to the school how far have you gone now in terms of both of a fraction and a decimal?

D) Draw a number line from 0 to 1 and label each tenth on the number line. Plot the three

distances above as both fractions and decimals. Part 2: Write an explanation explaining how you worked with equivalent fractions and decimals to solve this task.


Limited Performance • Solutions will include





Proficient in Performance • Students correctly find the answer to

each problem. A) 32/100. B) 49/100, C) 79/100, D) all 3 fractions and decimals are correctly plotted on a number line.

• Part 2: The answer discusses that tenths can also be written as hundredths by multiplying the numerator and denominator both by 10, and that decimals are equivalent to fractions that have either a 10 or 100 in the denominator.






Where Am I Now? How Much Farther?

Part 1: You have walked 0.32 of the way from your house to the school. A) What is that distance as a fraction?

B) If you walk another 17/100 of the way to the school how far have you gone now in terms of both a fraction and a decimal?

C) If you walk another 3/10 of the way to the school how far have you gone now in terms of both of a fraction and a decimal?

D) Draw a number line from 0 to 1 and label each tenth on the number line. Plot the three distances above as both fractions and decimals.

Part 2: Write an explanation explaining how you worked with equivalent fractions and decimals to solve this task.



Is the Tire Full Yet?

4.NF.6 Task 2 Domain Number and Operations - Fractions Cluster Understand decimal notation for fractions, and compare decimal fractions. Standard(s) 4.NF.6. Use decimal notation for fractions with denominators 10 or 100. For example,

rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.

Materials Decimal grids (hundredths grids), base ten blocks (optional), paper and pencil Task Is the tire full?

Part 1: You are about to go on vacation with your family. Your tire is 78/100 full of air. If you add air so that it 0.93 full, what fraction of the tire did you just fill with air? What fraction (and decimal) of the tire still needs to be filled with air? Part 2: Write an explanation explaining how you worked with equivalent fractions and decimals to solve this task.

Rubric

Level I Level II Level III Limited Performance • Solutions will include





Proficient in Performance • Students correctly find the answer

to each problem. A) 15/100 or 0.15. B) 7/100 or 0.07.

• Part 2: The answer discusses that tenths can also be written as hundredths by multiplying the numerator and denominator both by 10, and that decimals are equivalent to fractions that have either a 10 or 100 in the denominator.





Is the Tire Full?

Part 1: You are about to go on vacation with your family. Your tire is 78/100 full of air. If you add air so that it 0.93 full, what fraction of the tire did you just fill with air? What fraction (and decimal) of the tire still needs to be filled with air? Part 2: Write an explanation explaining how you worked with equivalent fractions and decimals to solve this task.



Who Jumped Farther?

4.NF.7-Task 1 Domain Number and Operations – Fractions Cluster Understand decimal notation for fractions, and compare decimal fractions. Standard(s) 4.NF.7 Compare two decimals to hundredths by reasoning about their size. Recognize that

comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.

Materials Decimal grids (hundredths grids), base ten blocks (optional), paper and pencil Who Jumped Farther?

Part 1: Tom, Steve, and Peter each jump in a jumping contest. They measure their jumps and then discuss who jumped farther.

Tom said, “I jumped 1 and 34 hundredths of a meter.” Steve said, “I jumped 1 and 43 hundredths of a meter.” Peter said, “I jumped 1 and 4 tenths of a meter.”

For each ingredient, shade in the decimal grid and write a comparison statement using >, <, or =.

Which boy jumped farther between Tom and Steve? How do you know? Which boy jumped farther between Tom and Peter? How do you know? Which boy jumped farther between Steve and Peter? How do you know?

Part 2: Mitch jumped a distance between Steve and Peter. How far could he have jumped? Alex jumped a distance between Tom and Peter. How far could he have jumped?

Rubric

Level I Level II Level III Limited Performance • Students are unable to

accurately compare decimals.

Not Yet Proficient • Students make 1 or 2 errors

comparing decimals. OR students get correct answers but do not provide clear and accurate explanations.

Proficient in Performance • The student provides correct answers.

Part 1: 1.2 > 1.02, 1.2<1.23, 1.02<1.23. Part 2: You need either 1.21 or 1.22 Liters of fruit juice.

• All explanations are clear and accurate.





Who Jumped Farther? Part 1: Tom, Steve, and Peter each jump in a jumping contest. They measure their jumps and then discuss who jumped farther.

Tom said, “I jumped 1 and 34 hundredths of a meter.” Steve said, “I jumped 1 and 43 hundredths of a meter.” Peter said, “I jumped 1 and 4 tenths of a meter.”

Shade in the decimal grids for each of the boys’ distances. Which boy jumped farther between Tom and Steve? How do you know? Which boy jumped farther between Tom and Peter? How do you know? Which boy jumped farther between Steve and Peter? How do you know? Part 2: Mitch jumped a distance between Steve and Peter. How far could he have jumped? Alex jumped a distance between Tom and Peter. How far could he have jumped?





Making Punch 4.NF.7-Task 2

Domain Number and Operations – Fractions Cluster Understand decimal notation for fractions, and compare decimal fractions. Standard(s) 4.NF.7 Compare two decimals to hundredths by reasoning about their size. Recognize that

comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.

Materials Decimal grids (hundredths grids), base ten blocks (optional), paper and pencil Making Punch

Part 1: While making punch for a party the following ingredients are needed:

1.2 Liters of Ginger Ale 1.02 Liters of Sprite 1.23 Liters of Fruit Juice

For each ingredient, shade in the decimal grid and write a comparison statement using >, <, or =.

Do you need more Ginger Ale or Sprite? Explain your reasoning. Do you need more Ginger Ale or Fruit Juice? Explain your reasoning. Do you need more Sprite or Fruit Juice? Explain your reasoning.

Part 2: For a different recipe, frozen yogurt can be added. The amount of frozen yogurt is between the amount of Ginger Ale and Fruit Juice. How much frozen yogurt is needed? Explain how you found your answer.

Rubric

Level I Level II Level III Limited Performance • Students are unable

to accurately compare decimals.

Not Yet Proficient • Students make 1 or 2 errors

comparing decimals. OR students get correct answers but do not provide clear and accurate explanations.

Proficient in Performance • The student provides correct answers.

Part 1: 1.2 > 1.02, 1.2<1.23, 1.02<1.23. Part 2: You need either 1.21 or 1.22 Liters of fruit juice.

• All explanations are clear and accurate.





Making Punch Part 1: While making punch for a party the following ingredients are needed:

1.2 Liters of Ginger Ale 1.02 Liters of Sprite 1.23 Liters of Fruit Juice

For each ingredient, shade in the decimal grid. Do you need more Ginger Ale or Sprite? Explain your reasoning. Do you need more Ginger Ale or Fruit Juice? Explain your reasoning. Do you need more Sprite or Fruit Juice? Explain your reasoning. Part 2: For a different recipe, frozen yogurt can be added. The amount of frozen yogurt is between the amount of Ginger Ale and Fruit Juice. How much frozen yogurt is needed? Explain how you found your answer.



Documents

3-5 Formative Instructional and Assessment Tasks