Use the four operations with whole numbers to solve problems.3-5cctask.ncdpi.wikispaces.net/file/view/4.OA Tasks.do… · Web viewMultiply or divide to solve word ... The fourth

Formative Instructional and Assessment TasksDonut Shop

4.OA.1 Task 1Domain Operations and Algebraic ThinkingCluster Use the four operations with whole numbers to solve problems.Standard(s) 4.OA.1. Interpret a multiplication equation as a comparison and represent verbal

statements of multiplicative comparisons as multiplication equations.Materials Paper and pencil, chart paper or white boardTask Present the following problem to students:

A donut shop makes three times as many donuts as pastries. If the shop makes 186 donuts per day, how many pastries do they make?How can we compare the amount of donuts to the amount of pastries?

Using Think-Pair-Share, ask students to think independently about how they might use multiplication to compare the numbers. Give them a brief time to talk with a partner, then ask them to share their thoughts.Record their statements on chart paper or a white board as sentences and/or equations.

Examples:There are three times as many donuts as pastries. 3 x pastries = donuts 3p = d 186 = 3 x pastries 186 ÷ 3 = 62 62 x 3 = 186

There are one third as many pastries as donuts. 1/3 x donuts = pastries 1/3d = p

Also, draw a comparison model to show the amounts:186 donuts

1/3 1/3 1/3

Ask students to generate additional examples of multiplicative comparisons, and see if they can state the inverse and/or the equations.

Examples: I have five times as many toes as feet. I have one fifth as many feet as toes.5 x feet = toes 1/5 x toes = feet

There are half as many boys in our class as girls. There are twice as many girls in our class as boys. boys x 2 = girls ½ x girls = boys

Use the Activity Sheet Donut Shop for additional practice.

NC DEPARTMENT OF PUBLIC INSTRUCTION FOURTH GRADE

Formative Instructional and Assessment TasksRubric

Level I Level II Level IIILimited Performance The student has difficulty

restating the comparison situation in his or her own words. They might struggle to determine which amount is more or less.

They may be able to generate one equation to compare amounts but will have difficulty stating its inverse. This student will rely on models to make sense of the situations and may need assistance creating models as a tool for writing the appropriate equations.

Not Yet Proficient The student can create a model

to compare the amounts multiplicatively and can use the model to generate a multiplication equation, but is not consistently correct.

Proficient in Performance With consistency and accuracy,

the student is able to state the comparison situations in his or her own words and can generate multiplication equations to describe them. They can draw a model that clearly compares two or more amounts multiplicatively.

Standards for Mathematical Practice1. 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.

Additional Resource: http://www.mathplayground.com/thinkingblocks.html (multiplication link)


http://www.mathplayground.com/thinkingblocks.html

Formative Instructional and Assessment TasksDonut Shop

Show your thinking using pictures, numbers, or words.

1. At the party, Emile ate 2 donuts. Lucas ate four times as many donuts as Emile. How many donuts did they eat altogether?

2. Frank ordered 24 cookies from the donut shop. That is three times as many cookies as Jenny ordered and six times as many cookies as Barb ordered. How many cookies did they order altogether?

How many more cookies did Frank order than Jenny and Barb together?

3. The donut shop made 28 chocolate donuts. That is 7 times as many strawberry donuts as they made. How many more chocolate donuts did the shop make than strawberry donuts?

4. Students in Mr. Juarez’s class predicted the number of donuts they could eat. The chart below shows their predictions.

Rosa Jeremy Frank Jill Emile Troy Sandy

Lucas Shante Molly

2 18 4 6 3 14 9 12 36 8

Compare these numbers in as many ways as you can.Example: Shante said he could eat three times as many donuts as Lucas.


Formative Instructional and Assessment TasksANSWER KEY for Donut Shop

1. Emile: 2 donutsLucas: 8 donuts 4 x 2 = 8 Altogether: 10 donuts 8 + 2 = 10 or (4 x 2) + 2 = 10

2. Frank: 24 cookiesJenny: 24 ÷ 3 = 8 8 x 3 = 24 1/3 x 24 = 8Barb: 24 ÷ 6 = 4 6 x 4 = 24 1/6 x 24 = 4Altogether: 24 + 8 + 4 = 36 Frank ordered 24 cookies and together, Jenny and Barb ordered 12 cookies. 24 - 12 = 12 Frank ordered 12 more cookies than Jenny and Barb together.

3. 28 = 7 x s s = 4 (strawberry donuts)28-4 = 24 The shop made 24 mode chocolate donuts than strawberry donuts.

4. Answers will vary but should use multiplicative relationships between the numbers in the chart.

Rosa Jeremy Frank Jill Emile Troy Sandy

Lucas Shante Molly

2 18 4 6 3 14 9 12 36 8

Possible answers: Jeremy said he could eat nine times as many donuts as Rosa, and she said she could eat one ninth as much as him.Jill said she could eat twice as much as Emile, three times as much as Rosa, half as much as Lucas, one third as much as Jeremy, and one sixth as much as Shante.Emile will eat one third as much as Sandy. Sandy will eat three times as much as Emile. *Frank will eat two thirds as much as Jill.*Sandy will eat ¾ as much as Lucas.


Formative Instructional and Assessment Tasks Three Times as Much

4.OA.1-Task 2Domain Operations and Algebraic ThinkingCluster Use the four operations with whole numbers to solve problems.Standard(s) 4.OA.1. Interpret a multiplication equation as a comparison and represent verbal

statements of multiplicative comparisons as multiplication equations.Materials Paper and pencilTask Task 1: 24 = 8 x 3 24 = 3 x 8

24 is three times as many as 8. Draw a model to show what this means.

24 is eight times as many as 3. Draw a model to show what this means.

Label your models with words or numbers.

Task 2:Explain the relationship between the models. How is 3 x 8= 24 related to 8 x 3= 24?

Task 3:Describe a real life situation that this model could represent. Explain how multiplication is used in this situation to compare the amounts.ORThink of a situation in real life where one amount is three times as much as another. What kind of situation might this describe?

RubricLevel I Level II Level III

Limited Performance Tasks 1 & 2:

This student may or may not be able to draw appropriate models for 3 x 8 = 24 and 8 x 3 = 24 (i.e., array model), and label them correctly.

Task 3:The task is not attempted or the student’s response shows that they cannot generate a real life example of a multiplicative comparison.

Not Yet Proficient Tasks 1 & 2: The student can create

appropriate models for 3 x 8 = 24 and 8 x 3 = 24 (i.e., array model), and label them correctly. The student’s models show that 3 groups of 8 make 24 and that 8 groups of 3 make 24. The student understands that 24 is being grouped in different ways. We say 24 is 8 times as much as 3 because it takes 8 threes to make 24. We say 24 is 3 times as much as 8 because it takes 3 eights to make 24.

Task 3: The student is unable to generate a real life example of a multiplicative comparison and/or explain how the numbers are related using multiplication.

Proficient in Performance Tasks 1 & 2: With

consistency and accuracy, the student is able to create models, label them, and explain their relationship.

Task 3: The student explains a real life situation in which a multiplicative comparison exists, naming the numbers and how they are related multiplicatively.


Formative Instructional and Assessment TasksStandards 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.


Formative Instructional and Assessment TasksThree Times As Much

Task 1: 24 = 8 x 3 24 = 3 x 8

24 is three times as many as 8. Draw a model to show what this means.

24 is eight times as many as 3. Draw a model to show what this means.

Label your models with words or numbers.

Task 2: Explain the relationship between the models. How is 3 x 8= 24 related to 8 x 3= 24?

Task 3: Describe a real life situation that this model could represent. Explain how multiplication is used in this situation to compare the amounts. ORThink of a situation in real life where one amount is three times as much as another. What kind of situation might this describe?


Formative Instructional and Assessment TasksSelling Candy4.OA.2- Task 1

Domain Operations and Algebraic ThinkingCluster Use the four operations with whole numbers to solve problems.Standard(s) 4.OA.2 Multiply or divide to solve word problems involving multiplicative comparison,

e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.

Materials Paper and pencilTask Sarah and Jose are both selling candy for a school fundraiser. Sarah’s total amount of

money is 7 times greater than the number of days that they have sold candy. Jose’s total amount of money is $3 more than the number of days that they have sold candy. Complete the table below showing the amount of money that they have earned for all 7 days selling candy.

Part 2:For both Sarah and Jose calculate how much money would be made on the tenth day. Write an equation to explain your reasoning.

Part 3:Write a sentence comparing how to calculate how much Sarah and Jose each made on the tenth day.

Sarah JoseDays Total Days Total

1 7 1 42 14 2 53 34 45 56 67 7


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: Sarah- 7, 14, 21, 28, 35,

42, 49. Jose- 4, 5, 6, 7, 8, 9, 10. AND The equation in Part 2 is correct.

AND The written explanation discusses that Sarah was found by multiplying, while Jose’s total was found by adding.





Formative Instructional and Assessment TasksSelling Candy

Sarah and Jose are both selling candy for a school fundraiser. Sarah’s total amount of money is 7 times greater than the number of days that they have sold candy. Jose’s total amount of money is $3 more than the number of days that they have sold candy. Complete the table below showing the amount of money that they have earned for all 7 days selling candy.

Sarah JoseDays Total Days Total

1 7 1 42 14 2 53 34 45 56 67 7

Part 2: For both Sarah and Jose calculate how much money would be made on the tenth day. Write an equation to explain your reasoning.

Part 3: Write a sentence comparing how to calculate how much Sarah and Jose each made on the tenth day.


Formative Instructional and Assessment TasksClothing Prices4.OA.2- Task 2

Domain Operations and Algebraic ThinkingCluster Use the four operations with whole numbers to solve problems.Standard(s) 4.OA.2 Multiply or divide to solve word problems involving multiplicative comparison,

e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.

Materials Paper and pencilTask Part 1:

Two stores in Greensboro sell shirts and pants together in matching outfits. In Store A, pants are half the cost of shirts. In Store B, pants are $4 less than the cost of shirts. For each Store complete the table below.

Part 2:If a shirt costs $30 how much will the matching pants cost in each store? For each store, write an equation to show your work. Write a sentence explaining your strategy for finding the cost of the pants.

Store A Store BShirts Pants Shirts Pants

10 106 8

14 1416 16

9 1820 20


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: Store A: 5, 12, 7, 8, 18,

10. Store B: 6, 12, 10, 12, 14, 16.AND

If shirts cost $30, pants would cost $15 in Store A and $26 in Store B.

AND The equation is correct and the

sentence includes that Store A can be found by dividing and Store B can be found by subtracting.





Formative Instructional and Assessment TasksClothing Prices

Part 1: Two stores in Greensboro sell shirts and pants together in matching outfits. In Store A, pants are half the cost of shirts. In Store B, pants are $4 less than the cost of shirts. For each Store complete the table below.

Store A Store BShirts Pants Shirts Pants

10 106 8

14 1416 16

9 1820 20

Part 2: If a shirt costs $30 how much will the matching pants cost in each store? For each store, write an equation to show your work. Write a sentence explaining your strategy for finding the cost of the pants.


Formative Instructional and Assessment Tasks Fund Raiser

4.OA.2-Task 3Domain Operations and Algebraic ThinkingCluster Use the four operations with whole numbers to solve problems.Standard(s) 4.OA.2. Multiply or divide to solve word problems involving multiplicative comparisons

(e.g., by using drawings and equations with a symbol for the unknown number to represent the problem); distinguishing multiplicative comparisons from additive comparisons.

Materials Paper and pencil, chart paper or white boardTask Review multiplicative comparisons with the practice problem below.

Ask students to write a multiplication equation and a division equation, and to draw a picture or model to solve the problem.

The fourth graders collected 210 cans of food this week during their canned food drive for the community center. On Monday, they collected 70 cans. On Wednesday, twice as many cans were collected as on Monday. How many cans did the students collect on Wednesday?

Ask students to model/explain their solutions.Possible responses:

210 cans in all 70 cans

onMonday

70 = 210 ÷ 3 The amount of cans collected on Monday was one third as much as they70 = 210 x 1/3 collected all week. Seventy is one third of 210. Seventy times 3 is 210.70 x 3 = 210

210 = 70 + c The total amount of cans is equal to 70 cans plus the amount collected on Wednesday (unknown).

70 x 2 = 140 The amount of cans collected on Monday was half as much as the number140 ÷ 2 = 70 of cans collected on Wednesday. The amount collected on Wednesday140 x ½ = 70 was twice as much as the amount of cans collected on Monday.

2M = 140 The amount of cans collected on Wednesday was twice the amount onM = 70 Monday. If M = Monday, 2M is Wednesday’s amount.

210 = M + 2M210 = 3MM = 70

Use the attached Activity Sheet Fund Raiser Fun for additional practice and discussion.


Wednesday ? cans


Level I Level II Level IIILimited Performance The student struggles to

generate one or more equations to compare amounts, and has difficulty understanding or representing inverse equations. The student does not recognize the multiplicative relationship between 70 and 210, and may need to work with smaller numbers. The student relies on models to make sense of the situations and may need assistance creating models as a tool for writing the appropriate equations.


to compare the amounts multiplicatively and can use the model to generate a multiplication equation, but is not consistently correct. The student is still working on using variables as unknowns in equations, and does not yet have the numerical fluency to see how various equations can describe the same comparison.

Proficient in Performance They can draw a model that

clearly compares two or more amounts multiplicatively. With consistency and accuracy, the student is able to generate multiplication and division equations and use variables to describe comparisons. The student is able to explain how the various equations are related.



Formative Instructional and Assessment TasksFund Raiser Fun

DIRECTIONS: For each problem, write at least one multiplication equation and one division equation to compare the amounts. Draw a model to show how the amounts can be compared with multiplication.

1. The fourth graders are raising money for a community center by collecting coins. The goal for each class is to collect $50.00. Mrs. Yang’s class has collected one fifth of the money needed to reach their goal. How much money has the class collected?

How much more do they need to collect to reach their goal?

2. During week 1 of the fund raiser, 75 children donated coins. During week 2, four times as many children donated coins. How many children donated coins during week 2?

How many more children donated coins during week 2 than week 1?


Formative Instructional and Assessment Tasks

3. Complete the chart based on the clues:

The fourth grade class raised $356.00 in all. The fifth grade class raised half as much as the fourth graders. The sixth graders raised three times as much as the 5th graders. How much money did each grade level raise? How much money did they raise altogether?


Grade level Amount of money raised

4th $356.005th6th

Formative Instructional and Assessment TasksANSWER KEY

1. Mrs. Yang’s class raised $10.00. They need to raise $40.00 more to meet their goal.

10 x 5 = 50 1/5 x 50 = 10 50 ÷ 5 = 10 50-10 = 40

2. During week two, 300 children donated coins. During week two, 225 more children donated coins than week one.

Week Two$75.00Week One

$75.00 $75.00 $75.00

$75.00 x 4 = c $75.00 x 4 = $300.00

¼ x $300 = $75 $300 - $75 = $225

3. Fifth grade ½ x $356 = $178 or ½ x $356 = fSixth grade 3 x $178 = $534 or 3 x $178 = sAltogether $356 + $178 + $534 = $1,068


Goal $50.00 $10 $10 $10 $10 $10

Formative Instructional and Assessment TasksBuying Music4.OA.2-Task 4

Domain Operations and Algebraic ThinkingCluster Use the four operations with whole numbers to solve problems.Standard(s) 4.OA.2. Multiply or divide to solve word problems involving multiplicative comparisons

(e.g., by using drawings and equations with a symbol for the unknown number to represent the problem); distinguishing multiplicative comparisons from additive comparisons.

Materials Paper and pencil, chart paper or white boardTask Review the difference between additive comparisons and multiplicative comparisons with

the following task.

Problem 1:The cost to download one song is $1.99, and the cost to download an album is $12.99. How much more will you pay to download the album than just one song?What is the relationship between the numbers in this problem?

Problem 2:An album will cost three times as much to download as one song. If one album costs $12, how much does it cost to download one song?What is the relationship between the numbers in this problem?

Compare the relationships between the numbers in the first problem to the numbers in the second problem.What equations can we write to show these relationships?

In problem 1, the numbers $1.99 and $12.99 are related additively because we can ask How much more is $12.99 than $1.99?

In problem 2, the numbers are related multiplicatively because we can ask How many times more than $3 is $12? Or What factor would we multiply three times to get $12?

Let s equal the cost of one song and a equal the cost of one album. d is the difference in cost between an album and a song in problem 1.

Problem 1 Problem 2

a – s = d 3 x s = aa ÷ 3 = s



Level I Level II Level IIILimited Performance The student struggles to

generate one or more equations to compare amounts, and has difficulty understanding or representing inverse equations. The student does not recognize the multiplicative relationship between 70 and 210, and may need to work with smaller numbers. The student relies on models to make sense of the situations and may need assistance creating models as a tool for writing the appropriate equations.


to compare the amounts multiplicatively and can use the model to generate a multiplication equation, but is not consistently correct. The student is still working on using variables as unknowns in equations, and does not yet have the numerical fluency to see how various equations can describe the same comparison.

Proficient in Performance They can draw a model that

clearly compares two or more amounts multiplicatively. With consistency and accuracy, the student is able to generate multiplication and division equations and use variables to describe comparisons. The student is able to explain how the various equations are related.



Formative Instructional and Assessment TasksBuying Music

Problem 1: The cost to download one song is $1.99, and the cost to download an album is $12.99. How much more will you pay to download the album than just one song?

What is the relationship between the numbers in this problem?

Problem 2:An album will cost three times as much to download as one song. If one album costs $12, how much does it cost to download one song?

What is the relationship between the numbers in this problem?

Compare the relationships between the numbers in the first problem to the numbers in the second problem.

What equations can we write to show these relationships?


Formative Instructional and Assessment Tasksv

Remainders4.OA.3-Task 1

Domain Operations and Algebraic ThinkingCluster Use the four operations with whole numbers to solve problems.Standard(s) 4.OA.3 Solve multistep word problems posed with whole numbers and having whole-

number answers using the four operations, including problems in which remainders must be interpreted.

Materials Paper and pencilTask This standard involves interpreting remainders. Remainders should be interpreted in story

contexts so students can make sense of how to deal with them. Ways to address remainders include: Remain as a left over Partitioned into fractions or decimals Discarded leaving only the whole number answer Increase the whole number answer up one Round to the nearest whole number for an approximate resultThe example below came from the 4th grade Mathematics Unpacked Content Document http://maccss.ncdpi.wikispaces.net/Fourth+Grade

Give students the problem 53÷ 7 = ? and discuss situations in which each answer would be correct:

Problem A: 7Problem B: 7 r 2Problem C: 8Problem D: 7 or 8

Problem E: 7 47

possible solutions: Problem A: 7 Josh had 53 cookies. Seven cookies fit into his snack size bag. How

many bags did he fill? 53 ÷ 7 = p; p = 7 r 4. Josh can fill 7 bags completely. Problem B: 7 r 4 Josh had 53 cookies. Seven cookies fit into each of his snack bags.

How many snack bags could he fill and how many cookies would he have left? 53 ÷ 7 = p; p = 7 r 4; Josh can fill 7 bags and have 4 left over.

Problem C: 8 Josh had 53 cookies. Seven cookies fit into each of his snack bags. What would be the fewest number of bags he would need in order to hold all of his cookies?

53 ÷ 7 = p; p = 7 r 4; Josh needs 8 bags to hold all of the cookies. Problem D: 7 or 8 Josh had 53 cookies. He divided them equally among his friends.

Then, he gave the leftovers away, one each to some of his friends. How many cookies could his friends have received? 53 ÷ 7 = p; p = 7 r 4; Some of his friends received 7 cookies. Four friends received 8 cookies.

Problem E: 7 47 Josh had 53 cookies and put seven cookies in each bag. What

fraction represents the number of bags that he filled? 53 ÷ 7 = p; p = 7 47


Formative Instructional and Assessment TasksAfter whole class discussion:Ask students to generate additional examples of situations in which the remainder would be dealt with differently. Choose one scenario and try to apply it to each treatment of the remainder. Would it make sense to interpret the remainder as a decimal or fraction in all situations?Through discussion and examples, make a list of generalizations or rules about how the remainder should be dealt with in certain situations.


Limited Performance The student is unable to use

invented strategies or algorithms to divide. The student has limited or no strategies for interpreting or solving word problems, and is unable to explain how the remainder should be dealt with in a real life example.

Not Yet Proficient The student may or may not be

able to use invented strategies or algorithms to divide. The student has at least one strategy for interpreting or solving word problems, such as drawing a picture or diagram, and can explain at least two different ways the remainder might be dealt with in a real life example.

Proficient in Performance The student can find the

answer to division word problems and division computation problems in at least one way. The student has at least two strategies for interpreting or solving word problems, and can explain at least three different ways the remainder might be dealt with in a real life example.

Standards for Mathematical Practice1. 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


Formative Instructional and Assessment TasksRemainders

Using the problem 53÷ 7 = ?, find situations in which each of the following answers would be correct:

Problem A: 7

Problem B: 7 r 2

Problem C: 8

Problem D: 7 or 8

Problem E: 7 47


Formative Instructional and Assessment TasksHow Many Teams?

4.OA.3-Task 2Domain Operations and Algebraic ThinkingCluster Use the four operations with whole numbers to solve problems.Standard(s) 4.OA.3 Solve multistep word problems posed with whole numbers and having whole-


Materials Activity sheetTask How Many Teams?

In eastern North Carolina there are 3,277 fourth graders signed up for basketball. In western North Carolina there are 2,981 fourth graders signed up for basketball. In the Piedmont region there are 1,512 players signed up. Every player will get placed on a team in their region of the state.Part 1:The league wants to place 9 players on each team. Leftover players will be added to teams, so some teams will have ten players. How many teams will have 9 players? How many teams will have 10 players? Explain your reasoning.Part 2:In order to maximize playing time, the league decides to only place 7 players on each team. If there are extra players, some teams will have 8 players. How many teams will have 7 players? How many teams will have 8 players? Explain your reasoning.


Limited Performance The student is

unable to use strategies to find correct answers to any aspect of the task.

Not Yet Proficient The student has

between two to four incorrect answers.

Proficient in Performance The answers are correct. Explanations are clear and

accurate. Part 1: East: 363 teams have 9 players. 1 team has 10

players. West: 329 teams have 9 players. 2 teams have 10 players. Piedmont: 168 teams have 9 players. No teams have 10 players.

Part 2: East: 467 teams have 7 players. 1 team has 8 players. West: 419 teams have 7 players. 6 teams have 8 players. Piedmont: 216 teams have 7 players. No teams have 8 players.



How Many Teams?

In eastern North Carolina there are 3,277 fourth graders signed up for basketball. In western North Carolina there are 2,981 fourth graders signed up for basketball. In the Piedmont region there are 1,512 players signed up. Every player will get placed on a team in their region of the state.

Part 1: The league wants to place 9 players on each team? Leftover players will be added to teams, so some teams will have ten players. How many teams will have 9 players in each region of the state? How many teams will have 10 players in each region of the statewide? Statewide, how many teams have 9 players and how many teams have 10 players? Explain your reasoning.

Part 2:In order to maximize playing time, the league decides to only place 7 players on each team. If there are extra players, some teams will have 8 players. How many teams will have 7 players in each region of the state? How many teams will have 8 players in each region of the state? Statewide, how many teams have 7 players and



Formative Instructional and Assessment Taskshow many teams have 8 players? Explain your reasoning.


Formative Instructional and Assessment TasksMaking Gift Bags

4.OA.3-Task 3Domain Operations and Algebraic ThinkingCluster Use the four operations with whole numbers to solve problems.Standard(s) 4.OA.3 Solve multistep word problems posed with whole numbers and having whole-


Materials Activity sheetTask Making Gift Bags

Mrs. Turner’s fourth grade class is making gift bags for their parent volunteers. They have collected bite sized candy bars which they are distributing equally among each bag.Here is a list of the candy: 27 Dark Chocolate bars, 12 Milky Way bars, 19 Three Musketeer Bars.Part 1:How much candy will be in each bag if they have 7 parent volunteers? How much leftover candy will they have?Part 2:The class changes their mind and decides to also make gift bags for their Teacher, their Principal and Assistant Principal. How much candy will be in each bag now? How much leftover candy will they have?


Limited Performance The student is unable

to use strategies to find correct answers to any aspect of the task.

Not Yet Proficient The student has between

two to four incorrect answers.

Proficient in Performance The answers are correct. Explanations are clear

and accurate. Part 1: 58 divided by 7 = 8 with a remainder of

2. There will be 8 candy bars in each bag with 2 candy bars leftover.

Part 2: 58 divided by 10 = 5 with a remainder of 8. There will be 5 candy bars in each bag. There will be 2 candy bars leftover.



Formative Instructional and Assessment TasksMaking Gift Bags

Mrs. Turner’s fourth grade class is making gift bags for their parent volunteers. They have collected bite sized candy bars which they are distributing equally among each bag.

Here is a list of the candy: 27 Dark Chocolate bars 12 Milky Way bars, 19 Three Musketeer Bars

Part 1: How much candy will be in each bag if they have 7 parent volunteers? How much leftover candy will they have?

Part 2:The class changes their mind and decides to also make gift bags for their Teacher, their Principal and Assistant Principal. How much candy will be in each bag now? How much leftover candy will they have?


Formative Instructional and Assessment TasksEnlarging the Yard

4.OA.3 - Task 4Domain Operations and Algebraic ThinkingCluster Use the four operations with whole numbers to solve problems.Standard(s) 4.OA.3 Solve multistep word problems posed with whole numbers and having whole-


Materials Activity sheet, Graph paper (optional)Task Enlarging the Yard

Currently, you have a rectangular yard that has perimeter of 72 meters. The current area is between 300 and 350 meters.Part 1:What are the dimensions of your current fenced-in space?Part 2:In order to have more space to play your parents decide that they want to lengthen both sides by 5 meters. What are the new dimensions of your yard? What is the new perimeter? What is the new area?Part 3:Explain how you found the answer to Part 2.




Not Yet Proficient The student has between

two to four incorrect answers.

Proficient in Performance The answers are correct. Part 1: The 2 dimensions must add up to 36.

The two dimensions must have a product between 300 and 350. Possible answers: 18x18, 19x17, 20x16, 21x15, 22x14.

Part 2: The dimensions from Part 1 have been increased by 5. The new perimeter and the area are correct.

Part 3: The explanation is clear and accurate.



Formative Instructional and Assessment TasksEnlarging the Yard

Currently, you have a rectangular yard that has perimeter of 72 meters. The current area is between 300 and 350 meters.

Part 1:What are the dimensions of your current fenced-in space?

Part 2: In order to have more space to play your parents decide that they want to lengthen both sides by 5 meters. What are the new dimensions of your yard? What is the new perimeter? What is the new area?

Part 3: Explain how you found the answer to Part 2.


Formative Instructional and Assessment TasksA Ride on the Bus

4.OA.4-Task 1Domain Operations and Algebraic ThinkingCluster Gain familiarity with factors and multiplesStandard(s) 4.OA.4 Find all factor pairs for a whole number in the range 1-100.Materials Paper and pencilTask Part 1:

Eighty fourth grade students at Andrews Elementary School are going on a field trip. Their teachers need to put between 3 and 25 students in each group to visit the shark tank. How many different ways can the teachers group their students so that each group has the same number of students?

Example: 4 students in a group, 20 groups

Part 2:If four groups of eight students ride bus 1, how many students will ride bus 2?How many different ways can the teacher group the students on bus 2 so that each group has the same number of students? Explain your reasoning using pictures, numbers or words.


Limited Performance Student has minimal solutions

and incomplete explanation

Not Yet Proficient Student has most of the

possible solutions and has partial explanation of reasoning

Proficient in Performance Task 1: 5 x16 and 8 x 10 Task 2: Bus 2 has a total of 48

students, possible groupings 1 x 48, 2 x 24, 3 x16, 4 x 12, 6

x 8 Student has all the possible

solutions and has explained reasoning.



Formative Instructional and Assessment TasksA Ride On A Bus

Part 1:Eighty fourth grade students at Andrews Elementary School are going on a field trip. Their teachers need to put between 3 and 25 students in each group to visit the shark tank. How many different ways can the teachers group their students so that each group has the same number of students?

Part 2:If four groups of eight students ride bus 1, how many students will ride bus 2? How many different ways can the teacher group the students on bus 2 so that each group has the same number of students? Explain your reasoning using pictures, numbers or words.


Formative Instructional and Assessment TasksArranging Chairs

4.OA.4 - Task 2Domain Operations and Algebraic ThinkingCluster Gain familiarity with factors and multiples.Standard(s) 4.OA.4 Find all factor pairs for a whole number in the range 1–100. Recognize that a

whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite.

Materials Activity sheet,Task Arranging Chairs

Part 1:There are 24 chairs in the art room. What are the different ways that the chairs can be arranged into equal groups if you want at least 2 groups and want at least 2 chairs in each group? How do you know that you have found every arrangement? Write division equations to show your answers.Part 2:There are 48 chairs in the multi-purpose room. What are the different ways that the chairs can be arranged into equal groups if you want at least 2 groups and want at least 2 chairs in each group? How do you know that you have found every arrangement? Write division equations to show your answers.Part 3:What relationship do you notice about the size of the groups if the chairs were arranged in 4 groups in both Part 1 and Part 2? What about if the chairs were arranged in 8 groups? Explain why you think this relationship exists.






Proficient in Performance The answers are correct. Part 1: 2 groups of 12; 3 groups of 8; 4 groups of 6;

6 groups of 4; 8 groups of 3; 12 groups of 2. Part 2: 2 groups of 24; 3 groups of 16; 4 groups of

12; 6 groups of 8; 8 groups of 6; 12 groups of 4; 16 groups of 3; 24 groups of 2.

Part 3: 24 chairs can be put into 4 groups of 6. 48 chairs can be put into 4 groups of 12. 24 chairs can be put into 8 groups of 3. 48 chairs can be put into 8 groups of 6. The explanation should reference that 48 is double 24, which means that when one factor remains constant, the other factor is doubled.

Standards for Mathematical Practice1. Makes sense and perseveres in solving problems.


Formative Instructional and Assessment Tasks2. 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


Formative Instructional and Assessment TasksArranging Chairs

Part 1: There are 24 chairs in the art room. What are the different ways that the chairs can be arranged into equal groups if you want at least 2 groups and want at least 2 chairs in each group? How do you know that you have found every arrangement? Write division equations to show your answers.

Part 2:There are 48 chairs in the multi-purpose room. What are the different ways that the chairs can be arranged into equal groups if you want at least 2 groups and want at least 2 chairs in each group? How do you know that you have found every arrangement? Write division equations to show your answers.

Part 3:What relationship do you notice about the size of the groups if the chairs were arranged in 4 groups in both Part 1 and Part 2? What about if the chairs were arranged in 8 groups? Explain why you think this relationship exists.



Tiling the Patio4.OA.4 - Task 3

Domain Operations and Algebraic ThinkingCluster Gain familiarity with factors and multiples.Standard(s) 4.OA.4 Find all factor pairs for a whole number in the range 1–100. Recognize that a

whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite.

Materials Activity sheet, plastic square tiles (optional), graph paper (optional)Task Tiling the Patio

A landscaping company visits the school to talk about the possible ways to tile a patio and picnic area near the playground. The school can afford between 24 and 30 square tiles.Part 1:For each of the proposed number of tiles (24-30), determine all of the possible dimensions of rectangles you could make.Part 2:The space for the patio is configured so that there cannot be any more than 10 tiles in a row. For the proposed number of tiles (24-30), determine which numbers would work as the total number of tiles.Part 3:Which number of tiles provides the most flexibility in terms of the possible ways that the tiles could be arranged? Explain your reasoning.






Proficient in Performance The answers are correct. Part 1: 24: 24x1, 12x2, 8x3, 6x4; 25: 25x1, 5x5; 26:

26x1, 13x2; 27: 27x1, 9x3; 28: 28x1, 14x2, 7x4; 29: 29x1; 30: 30x1, 15x2, 10x3, 6x5

Part 2: 24, 25, 27, 28, 30 Part 3: 24 has the most possible ways to arrange the

tiles. The explanation is clear and accurate.



Formative Instructional and Assessment TasksTiling the Patio

A landscaping company visits the school to talk about the possible ways to tile a patio and picnic area near the playground. The school can afford between 24 and 30 square tiles.

Part 1:For each of the proposed number of tiles (24-30), determine all of the possible dimensions of rectangles you could make.

Part 2: The space for the patio is configured so that there cannot be any more than 10 tiles in a row. For the proposed number of tiles (24-30), determine which numbers would work as the total number of tiles.

Part 3:Which number of tiles provides the most flexibility in terms of the possible ways that the tiles could be arranged? Explain your reasoning.


Formative Instructional and Assessment Tasks Table Dilemma4.OA.5-Task 1

Domain Operations and Algebraic ThinkingCluster Generate and analyze patterns.Standard(s) 4.OA.5 Generate a number pattern that follows a given rule.Materials Square tiles (optional), Paper, PencilTask Square tables at Giovanni’s Pizza seat 4 people each. For bigger groups, square tables can

be joined. Tables can be pushed together so that they share a side.Part 1:One square table seats 4 people.Two square tables seat 8 people.How many people can sit at 3 tables? 4 tables? 5 tables?Make a chart to show how many people can be seated at five tables that are not pushed together. Find a rule that helps you predict the number of people that can be seated at n tables.Part 2:Two tables pushed together seat 6 people.How many people can sit at three tables pushed together? 4 tables pushed together?5 tables pushed together?Make a chart to show how many people can be seated at five tables that are pushed together. Find a rule that helps you predict the number of people that can be seated at n tables.Part 3:Compare the patterns that you see on your charts. What pattern do you notice for each chart?



Level I Level II Level IIILimited Performance Students are unable to

complete both Part 1 and Part 2.

Not Yet Proficient Students have the correct

answer but do not have a clear explanation of the pattern for each chart OR Students show a logical approach to solving each part of the task, but have made calculation errors. OR Students are able to complete either Part 1 or Part 2 accurately.

Proficient in Performance Part 1: Students will create a

chart to show tables: people (perimeter)1 table: 4 people2 tables: 8 people3 tables: 12 people4 tables: 16 people5 tables: 20 peopleThey will identify the rule as n x 4.

Part 2:Students will create a chart to show tables: people (perimeter)1 table: 4 people2 tables: 6 people3 tables: 8 people4 tables: 10 people5 tables: 12 peopleThey will identify the rule as n x 2 + 2.

Observations may include:Numbers in chart 1 increase by 4 vertically while numbers in chart 2 increase by 2 vertically. All numbers (of seats) are even. AND Students write a clear and accurate explanation of both patterns in Part 3.



Formative Instructional and Assessment TasksTable Dilemma

Square tables at Giovanni’s Pizza seat 4 people each. For bigger groups, square tables can be joined. Tables can be pushed together so that they share a side.

Part 1:One square table seats 4 people. Two square tables seat 8 people.How many people can sit at 3 tables? 4 tables? 5 tables?

Make a chart to show how many people can be seated at five tables that are not pushed together. Find a rule that helps you predict the number of people that can be seated at n tables.

Part 2:Two tables pushed together seat 6 people. How many people can sit at three tables pushed together? 4 tables pushed together?5 tables pushed together?

Make a chart to show how many people can be seated at five tables that are pushed together. Find a rule that helps you predict the number of people that can be seated at n tables.

Part 3: Compare the patterns that you see on your charts. What pattern do you notice for each chart?


Formative Instructional and Assessment TasksArranging Tables4.OA.5 - Task 2

Domain Operations and Algebraic ThinkingCluster Generate and analyze patterns.Standard(s) 4.OA.5 Generate a number or shape pattern that follows a given rule. Identify apparent

features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.

Materials Task handout, pattern blocks (optional)Task Arranging Tables

A banquet company provides options for table arrangements: triangular tables, square tables, and hexagonal tables. For each type of table you can fit 1 person on each side of the table. For their parties they want to put all of the tables together so that every table shares at least one side with another table.Part 1:Based on this proposed arrangement, how many people could you sit at 1 triangular table? 2 connected triangular tables? 3 connected triangular tables? 4 connected triangular tables?Part 2:Based on this proposed arrangement, how many people could you sit at 1 square table? 2 connected square tables? 3 connected square tables? 4 connected square tables?Part 3:Based on this proposed arrangement, how many people could you sit at 1 hexagonal table? 2 connected hexagonal tables? 3 connected hexagonal tables? 4 connected hexagonal tables?Part 4:For each type of table, write a sentence explaining how many more seats get added every time you add a new table. Explain how you found your answer.



Limited Performance The student is

unable to use strategies to find correct answers to any aspect of the task.



Proficient in Performance The answers are correct. Part 1: Triangular: 1 table: 3 people, 2 tables: 4 people, 3

tables: 5 people: 4 tables: 6 people; Part 2: Square : 1 table: 4 people, 2 tables: 6 people: 3 tables:

8 people; 4 tables: 10 people; Part 3: Hexagonal: 1 table: 6 people: 2 tables: 10 people: 3

tables: 14 people; 4 tables: 18 people Part 4: Triangular: Each table adds 1 more seat; Square: Each

table adds 2 more seats; Hexagonal: Each table adds 4 more seats.




Formative Instructional and Assessment TasksArranging Tables

A banquet company provides options for table arrangements: triangular tables, square tables, and hexagonal tables. For each type of table, you can fit 1 person on each side of the table. For their parties they want to put all of the tables together so that every table shares at least one side with another table.

Part 1:Based on this proposed arrangement, how many people could you sit at 1 triangular table? 2 connected triangular tables? 3 connected triangular tables? 4 connected triangular tables?

Part 2: Based on this proposed arrangement, how many people could you sit at 1 square table? 2 connected square tables? 3 connected square tables? 4 connected square tables?

Part 3: Based on this proposed arrangement, how many people could you sit at 1 hexagonal table? 2 connected hexagonal tables? 3 connected hexagonal tables? 4 connected hexagonal tables?

Part 4: For each type of table, write a sentence explaining how many more seats get added every time you add a new table. Explain how you found your answer.


Formative Instructional and Assessment TasksLawn Mowing Business

4.OA.5 - Task 3Domain Operations and Algebraic ThinkingCluster Generate and analyze patterns.Standard(s) 4.OA.5 Generate a number or shape pattern that follows a given rule. Identify apparent

features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.

Materials Activity sheetTask Lawn Mowing Business

Ted and Nancy both mow lawns during the summer to earn money.Ted charges $10 per lawn and $2 per hour.Nancy charges $4 per lawn and $4 per hour.

Part 1:Complete the table to show how much Ted and Nancy would each earn based on the amount of time that it took to mow a lawn.

Ted Nancy½ hour1 hour

1 and ½ hours2 hours



Part 2:Explain how you found the amount for both Ted and Nancy in the table.

Part 3:Last week, Ted and Nancy each mowed 3 lawns that took 1 and ½ hours each, and 7 lawns that took 3 hours each. How much money did they each earn? Write an equation to show your work.



Level I Level II Level IIILimited Performance The student

is unable to use strategies to find correct answers to any aspect of the task.



Proficient in Performance The answers are correct. Part 1:

Ted Nancy½ hour 11 61 hour 12 81 and ½ hours 13 102 hours 14 122 and ½ hours 15 143 hours 16 163 and ½ hours 17 184 hours 18 20

Part 2:The explanation is clear and accurate.

Part 3:Ted: 3*$13 + 7*$16 = $151Nancy: 3*10 + 7*$16 = $142



Formative Instructional and Assessment TasksLawn Mowing Business

Ted and Nancy both mow lawns during the summer to earn money.Ted charges $10 per lawn and $2 per hour.Nancy charges $4 per lawn and $4 per hour.

Part 1: Complete the table to show how much Ted and Nancy would each earn based on the amount of time that it took to mow a lawn.

Ted Nancy½ hour1 hour




Part 2: Explain how you found the amount for both Ted and Nancy in the table.

Part 3:Last week, Ted and Nancy each mowed 3 lawns that took 1 and ½ hours each, and 7 lawns that took 3 hours each. How much money did they each earn? Write an equation to show your work.


Documents

Use the four operations with whole numbers to solve problems.3-5cctask.ncdpi.wikispaces.net/file/view/4.OA Tasks.do… · Web viewMultiply or divide to solve word ... The fourth