3-5cctask.ncdpi.wikispaces.net3-5cctask.ncdpi.wikispaces.net/file/view/4.NBT... · Web viewRecognize that in a multi-digit whole number, ... Answers: 1) 400 students; 2) 330 students;

Formative Instructional and Assessment Tasks Coin Collection4.NBT.1 - Task 1

Domain Number and Operations in Base TenCluster Generalize place value understanding for multi-digit whole numbers.Standard(s) 4.NBT.1 Recognize that in a multi-digit whole number, a digit in one place represents ten

times what it represents in the place to its right.Materials Paper and pencilTask Part 1:

You have a collection of 826 coins. If the coins are pennies, what would be the value of your collection? If the coins are dimes, what would be the value of your collection? If they were dollars instead of coins, what would be the value of your collection? If they were ten dollar bills what would be the value of your collection?

Part 2: Look at the four values that you wrote for Part 1. What do you notice about the value of your collections? What pattern do you notice about the value of your collections? Explain your thinking in words, pictures, or numbers.

RubricLevel I Level II Level III

Limited Performance Part 1: Student correctly

identifies values for 0-2 coins.

Part 2: Explanation does not show consistent understanding of place value patterns.

Not Yet Proficient Part 1: Student correctly

identifies values for 3-4 coins. Part 2: Explanation shows a

developing understanding of place value patterns.

Proficient in Performance Part 1: Student correctly

identifies values for each coin.Value in pennies: $8.26Value in dimes: $82.60Value in dollars: $826.00Value in ten dollars: $8,260.00

Part 2: Explanation demonstrates conceptual understanding of place value patterns.

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.

NC DEPARTMENT OF PUBLIC INSTRUCTION FOURTH GRADE

Formative Instructional and Assessment TasksCoin Collection

Part 1:You have a collection of 826 coins.

If the coins are pennies, what would be the value of your collection?

If the coins are dimes, what would be the value of your collection?

If they were dollars instead of coins, what would be the value of your collection?

If they were ten dollar bills what would be the value of your collection?

Part 2: Look at the four values that you wrote for Part 1.

What do you notice about the value of your collections?

What pattern do you notice about the value of your collections?

Explain your thinking in words, pictures, or numbers.


Formative Instructional and Assessment TasksAdding Zeros

4.NBT.1 Task 2Domain Numbers and Operations in Base TenCluster Generalize place value understanding for multi-digit whole numbers.Standard(s) 4.NBT.1 Recognize that in a multi-digit whole number, a digit in one place represents ten

times what it represents in the place to its right.Materials Paper and pencilTask Give students the following writing prompt:

Gina said, “Forty-six multiplied by 10 is 460 because when you multiply a number by ten, you add a zero on to the end of it.” Do you agree or disagree with Gina? Explain your reasoning. Give at least one example to support your reason.


Limited Performance Students think that multiplying

by ten is like adding a zero on to a number. They do not understand the relationship between multiplying by ten and the place value shift that digits make.

Not Yet Proficient The student may agree or

disagree, but cannot clearly articulate that 46 x 10 = 460 because each digit is ten times as much and shifts place value one place to the left. The student cannot generate an example to support this idea.

Proficient in Performance The student may agree or

disagree, and can clearly articulate that 46 x 10 = 460 because each digit is ten times as much and shifts place value one place to the left. The student is able to generate an example to support this idea.



Formative Instructional and Assessment TasksAdding Zeroes

Gina said, “Forty-six multiplied by 10 is 460 because when you multiply a number by ten, you add a zero on to the end of it.”

Do you agree or disagree with Gina? Explain your reasoning. Give at least one example to support your reason.


Formative Instructional and Assessment TasksPackaging Soup Cans

4.NBT.1-Task 3Domain Numbers and Operations in Base TenCluster Generalize place value understanding for multi-digit whole numbers.Standard(s) 4.NBT.1 Recognize that in a multi-digit whole number, a digit in one place represents ten

times what it represents in the place to its right.Materials Paper and pencil, activity sheet, base 10 blocks (optional) , Virtual base ten blocks can be

found here: http://nlvm.usu.edu/en/nav/frames_asid_152_g_1_t_1.htmlTask Packaging Soup Cans

There are 202 soup cans are in the factory. A crate will hold 200 cans. A case will hold 20 cans. The rest of the cans go into individual boxes. The factory wants to use as few packages as possible.

1. How many crates, cases, and individual boxes will you need to hold the 202 soup cans?2. If you only had cases and individual boxes, how many of each would you need?3. If you only had individual boxes, how many would you need?4. What did you notice about the number of crates and cases in Part A compared to Part

B? Explain your reasoning.


Limited Performance Students provide

correct answers on two or fewer of the parts above.

Not Yet Proficient Students provide correct

answers on all but one of the parts above.

Proficient in Performance Students provide correct answers to all problems. Solutions: 1) 1 crate, 0 cases and 2 individual

boxes, 2) 10 cases and 2 individual boxes, 3) 202 individual boxes,4) The explanation says something about the trading of 1 crate for 10 cases. In Part A we needed 1 crate and 0 cases. In Part B, there we needed 10 cases.



http://nlvm.usu.edu/en/nav/frames_asid_152_g_1_t_1.html

Formative Instructional and Assessment TasksPackaging Soup Cans

There are 202 soup cans are in the factory. A crate will hold 200 cans. A case will hold 20 cans. The rest of the cans go into individual boxes. The factory wants to use as few packages as possible.

1. How many crates, cases, and individual boxes will you need to hold the 202 soup cans?

2. If you only had cases and individual boxes, how many of each would you need?

3. If you only had individual boxes, how many would you need?

4. What did you notice about the number of cases in Part A compared to Part B? Explain your reasoning.


Formative Instructional and Assessment TasksValue of the Bills4.NBT.1-Task 4

Domain Numbers and Operations in Base TenCluster Generalize place value understanding for multi-digit whole numbers.Standard(s) 4.NBT.1 Recognize that in a multi-digit whole number, a digit in one place represents ten

times what it represents in the place to its right.Materials Paper and pencil, Activity sheetTask Part 1:

Gina said, “In my pocket I have 25 of the same amount of dollar bills. What is the value of Gina’s money if she has:

a) 25 one dollar billsb) 25 ten dollar billsc) 25 hundred dollar bills

Part 2:Gina reasoned, “The value of the 2 when I have ten dollar bills is 200, but the value of the 2 when I have one dollar bills is only 20.” Is Gina correct? Why or why not?

Part 3:Consider Parts A, B, and C above if you had 260 of the same amount of dollar bills. What would the value of the bills be? Explain how you found your answer.


Limited Performance Students get

incorrect answers on all parts of the task.

Not Yet Proficient The student is successful in

2 of the 3 parts of the task.

Proficient in Performance Answers: Part 1: 25; 250, 2,500; Part 2: Gina is

correct. The explanation should talk about the idea that there are 25 groups of 1, 25 groups of 10, or 25 groups of 100.

Part 3: 260; 2,600; 26,000. Explanation discusses the idea that the value of each digit is multiplied by 10 when the value of the dollar bills increases by 10.



Formative Instructional and Assessment TasksValue of the Bills

Part 1: Gina said, “In my pocket I have 25 of the same amount of dollar bills. What is the value of Gina’s money if she has:

a) 25 one dollar bills

b) 25 ten dollar bills

c) 25 hundred dollar bills

Part 2: Gina reasoned, “The value of the 2 when I have ten dollar bills is 200, but the value of the 2 when I have one dollar bills is only 20.” Is Gina correct? Why or why not?

Part 3: Consider Parts A, B, and C above if you had 260 of the same amount of dollar bills. What would the value of the bills be? Explain how you found your answer.


Formative Instructional and Assessment TasksArranging Students

4.NBT.2-Task 1Domain Numbers and Operations in Base TenCluster Generalize place value understanding for multi-digit whole numbers.Standard(s) 4.NBT.2 Read and write multi-digit whole numbers using numerals, number names and

expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons.

Materials Paper and pencil, Activity sheet, Base ten blocks, Virtual base ten blocks can be found here: http://nlvm.usu.edu/en/nav/frames_asid_152_g_1_t_1.html

Task Arranging Students

For a field trip, 4th grade students will visit North Carolina State University’s Millennial Campus. Students are in groups of 10. Each building can accommodate 10 groups at a time. Based on this information:1) How many students would be in 4 buildings?2) All of the students in 2 buildings and 13 other groups on the field trip visit the electron

microscope before lunch. How many students saw the microscope?3) There were 346 students from Hickory Elementary School. If they all were sent to the

same buildings how many buildings were completely full of students from Hickory School? How many whole groups would go to another building? How many students from that school would be leftover without a group?

4) Students from New Hanover Elementary School take up 2 whole buildings, 14 whole groups in other buildings, and 9 students in different groups. Do they have more or less students than Hickory Elementary? How do you know?


Limited Performance Students do not provide

correct answers to more than 2 parts.

Not Yet Proficient Students do not

provide correct answers to 1 or 2 parts.

Proficient in Performance Students provide correct answers for

parts 1 through 4. Answers: 1) 400 students; 2) 330 students; 3) 3 whole buildings, 4 whole groups in another building, and 6 left over students; 4) New Hanover- 349 students. New Hanover has more students than Hickory.



http://nlvm.usu.edu/en/nav/frames_asid_152_g_1_t_1.html

Formative Instructional and Assessment TasksArranging Students

For a field trip, 5th grade students will visit North Carolina State University’s Millennial Campus. Students are in groups of 10. Each building can accommodate 10 groups at a time. Based on this information:

1) How many students would be in 4 buildings?

2) All of the students in 2 buildings and 13 other groups on the field trip visit the electron microscope before lunch. How many students saw the microscope?

3) There were 346 students from Hickory Elementary School. If they all were sent to the same buildings how many buildings were completely full of students from Hickory School? How many whole groups would go to another building? How many students from that school would be leftover without a group?

4) Students from New Hanover Elementary School take up 2 whole buildings, 14 whole groups in other buildings, and 9 students in different groups. Do they have more or less students than Hickory Elementary? How do you know?


Formative Instructional and Assessment TasksJuice Pouches

4.NBT.2-Task 2Domain Numbers and Operations in Base TenCluster Generalize place value understanding for multi-digit whole numbers.Standard(s) 4.NBT.2 Read and write multi-digit whole numbers using numerals, number names and

expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, = and < symbols to record the results of comparisons.

Materials Paper and pencil, Activity sheetTask Juice Pouches

Juice pouches are packaged in different ways. A box holds 10 pouches. A case holds 10 boxes. A crate holds 10 cases.

Some students bring in juice boxes for Field Day. The information is below.Miguel- 1 crates, 12 cases, 3 boxes and 6 pouches.Aaron- 1 crates, 13 cases, 17 boxes, and 2 pouches.Sarah- 1 crates, 12 cases, 2 boxes and 17 pouches.Vicky- 1 crates, 14 cases, 6 boxes, and 9 pouches.

1) If each person were going to reorganize their drink pouches to use as many of the larger containers as possible, and so that there are no more than 10 of each type of container, how many of each container would each of them need?

2) How many total drink pouches does each student have? Explain how you found your answer.

3) List in order from the student who had the most juice pouches to the student with the smallest number of juice pouches.

Extension (4.NBT.6)If all of the boxes were going to be split evenly among the 6 grades at the school how many boxes would each grade get? Would there be any leftovers?


Formative Instructional and Assessment TasksRubric

Level I Level II Level IIILimited Performance Students are unable to create

different representations of the numbers and does not use place value as a strategy to compare them.

Not Yet Proficient Students are able to

create different representations of the numbers, but does not use place value as a strategy to compare them.

Proficient in Performance Students provide correct answers for

parts 1, 2, and 3. Solutions: Part 1: Miguel- 2 crates, 2 cases, 3 boxes, and 6 pouches; Aaron- 2 crates, 4 cases, 7 boxes, and 2 pouches. Sarah- 2 crates, 2 cases, 3 boxes, and 7 pouches; Vicky- 2 crates, 4 cases, 6 boxes and 9 pouches;

Part 2- Miguel- 2,236 pouches; Aaron- 2,472 pouches Sarah- 2,237 pouches; Vicky- 2,469.Explanation discusses adding up the number of pouches.

Part 3- Aaron, Vicky, Sarah, Miguel.*Extension- 1,569 pouches per grade with no left overs.



Formative Instructional and Assessment TasksJuice Pouches

Juice pouches are packaged in different ways. A box holds 10 pouches. A case holds 10 boxes. A crate holds 10 cases.

Some students bring in juice boxes for Field Day. The information is below.Miguel- 1 crates, 12 cases, 3 boxes and 6 pouches.Aaron- 1 crates, 13 cases, 17 boxes, and 2 pouches.Sarah- 1 crates, 12 cases, 2 boxes and 17 pouches.Vicky- 1 crates, 14 cases, 6 boxes, and 9 pouches.

1) If each person were going to reorganize their drink pouches to use as many of the larger containers as possible, how many of each container would each of them need?

2) How many total drink pouches does each student have?

3) List in order from the student who had the most juice pouches to the student with the smallest number of juice pouches.

Extension: If all of the boxes were going to be split evenly among the 6 grades at the school how many boxes would each grade get? Would there be any leftovers?


Formative Instructional and Assessment TasksOpen Number Lines

4.NBT.3-Task 1Domain Numbers and Operations in Base TenCluster Generalize place value understanding for multi-digit whole numbers.Standard(s) 4.NBT.3 Use place value understanding to round multi-digit numbers to any place.Materials Paper and pencilTask Activity 1: Estimating sums and differences using an open number line.

Specified as a tool for estimating by the CCSSM, an open number line is simply a blank number line. One way that it can be used as an estimation tool is by counting up from a given number to reach benchmark numbers, and then totaling the 'jumps.' For example, to find the difference between 46 and 100, you can jump 4 (from 46 to 50) and then 50 (from 50 to 100) to get a difference of 54. It is not necessary to draw ticks on the number line for each unit.Model using the open number line to find distances between numbers for each scenario. Molly needs to save $128 for a tablet. She received $47 for her birthday. About how

much more does she need to save?I know that 47 is about 50. I'm trying to get to about 130. From 50 to 100 is 50. Then I need to go 30 more to 130. So 50 plus 30 is 80. She needs to save about 80 more dollars. Mr. Smart's class read 362 books in the Read A Thon. Mrs. Walter's class read 275

books. About how many more books did Mr. Smart's class read?I know that 362 is about 400 and 275 is about 300. That's a difference of about 100. Mrs. Collins' class read 446 books in the Read A Thon. That was about 100 more books

than Mrs. White's class. How many books could Mrs. White's class have read? What are some exact numbers of books that would make sense?

Since 446 is closer to 400 than 500, we can round 446 to 400 and Mrs. White's class could have read about 300 books. It would make sense to guess that Mrs. White's class could have read exactly 326 books since that rounds to 300. If you round 446 to 450, Mrs. White's class cold have read about 350 books.

Activity 2Give students the following problems to practice using open number lines. Ask them to use open number lines in at least two different ways for each problem.

Find the difference between 429 and 216. Find the difference between 89 and 501. Find the difference between 350 and 1,050. Find the sum of 48 and 299. Find the sum of 12 and 372.

After students have had time to think about their solutions, allow time for them to share their ideas, noticing similarities and differences in how they thought about the numbers and how they used the open number lines to find the sums or differences.



Level I Level II Level IIILimited Performance Students do not understand

how to round a number to a given place value. They are unable to estimate sums and differences using benchmark numbers and/or open number lines as a tool for computation. They are unable to make reasonable estimates of sums or differences and explain why an estimate can include a range of exact numbers depending on the place value to which a number is rounded.

Not Yet Proficient Students understand how to

round a number to a given place value. They are able to estimate sums and differences using benchmark numbers and/or open number lines as a tool for computation, but may not be able to report more than one possible solution or way to find an answer. They are unable to explain why an estimate can include a range of exact numbers depending on the place value to which a number is rounded.

Proficient in Performance Students understand how to

round a number to a given place value. They are able to estimate sums and differences using benchmark numbers and/or open number lines as a tool for computation, and can to report more than one possible solution for finding each sum or difference. They are able to explain why an estimate can include a range of exact numbers, and can justify their estimates using place value.



Formative Instructional and Assessment TasksPlanning a Pizza Party

4.NBT.3-Task 2Domain Numbers and Operations in Base TenCluster Generalize place value understanding for multi-digit whole numbers.Standard(s) 4.NBT.3 Use place value understanding to round multi-digit numbers to any place.Materials Pencil, paper, Activity sheetTask Planning a Pizza Party

The following classes are having an end of the quarter pizza party for their good behavior.Teacher # of students participating

Mr. Thomas 23Mrs. Little 24Mrs. Jones 17

Mrs. Gordon 24

Part 1:1) About how many students are participating in the pizza party?2) How close was your estimate in question 1 to the actual answer?3) Explain why your estimate was different from your actual answer.

Part 2:4) One pizza will feed 4 students. How many pizzas are needed for all of the students?5) If each pizza costs $12.75 about how much money will be spent on pizza?6) About $324 is spent on the cost of pizza and drinks. Based on your estimate in question

4, about how much money will be spent on drinks? Explain how you found your answer.


Limited Performance Students cannot

provide correct answers on more than two questions.

Not Yet Proficient Students cannot

provide correct answers on one or two questions.

Proficient in Performance Students provide correct answers on all

questions. Answers: 1) 20+20+20+20= 80. 2) Actual: 88 students. 3) Possible answers could include: “When we rounded to the tens place and added the rounded numbers we got 80 for the answer.” 4) 88 divided by 4 is 22 pizzas. 5) We could round both numbers: 20x$13 = 260. We could round only the pizza 22x13 = 286. Either is acceptable. 6) 324 minus the answer to number 5. Answers could be 64 or 38.


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 TasksPlanning a Pizza Party

The following classes are having an end of the quarter pizza party for their good behavior:

Teacher # of students participatingMr. Thomas 23Mrs. Little 25Mrs. Jones 16

Mrs. Gordon 24Part 1: 1) About how many students are participating in the pizza party?

2) How close was your estimate in question 1 to the actual answer?

3) Explain why your estimate was different from your actual answer.

Part 2: 4) One pizza will feed 4 students. How many pizzas are needed for all of the

students?

5) If each pizza costs $12.75 about how much money will be spent on pizza?

6) About $324 is spent on the cost of pizza and drinks. Based on your estimate in question 4, about how much money will be spent on drinks? Explain how you found your answer.


Formative Instructional and Assessment TasksFilling the Auditorium

4.NBT.4 - Task 1Domain Number and Operations-Base TenCluster Use place value understanding and properties of operations to perform multi-digit

arithmetic.Standard(s) 4.NBT.4 Fluently add and subtract multi-digit whole numbers using the standard

algorithm.Materials Activity sheetTask Filling the Auditorium

On a field trip, three different schools send their fourth graders across town to the high school for a math competition. Each school sends between 120 and 170 students each. There are 417 students total.

Part 1:How many students could have come from each school? Show your thinking.

Part 2:Find another possible solution to this task. Show your thinking.

Part 3:If the number of students from each school was the same, how many students came from each school? Explain how you found your solution.

RubricLevel I d) Level II Level III

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.

Part 1: All three numbers add up to 417.Part 2: All three numbers add up to 417.Part 3: Each school had 139 fourth graders. The explanation is clear and accurate.

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 TasksFilling the Auditorium

On a field trip, three different schools send their fourth graders across town to the high school cafeteria. Each school sends between 120 and 170 students each. There are 417 students total.

Part 1:How many students could have come from each school? Show your thinking.

Part 2: Find another possible solution to this task. Show your thinking.

Part 3:If the number of students from each school was the same, how many students came from each school? Explain how you found your solution.


Formative Instructional and Assessment TasksHow Much Liquid?

4.NBT.4 - Task 2Domain Number and Operations-Base TenCluster Use place value understanding and properties of operations to perform multi-digit

arithmetic.Standard(s) 4.NBT.4 Fluently add and subtract multi-digit whole numbers using the standard

algorithm.Materials Task handoutTask How Much Liquid?

The following amounts of juice were in separate containers after the school’s parent breakfast.

Container 1: 750 ml Container 2: 1,450 ml Container 3: 2 L Container 4: 299 mL Container 5: 476 mL

Part 1:If all of the liquid was put into one large container how much liquid would be in the large container?

Part 2:The large container can hold 5 Liters. How much room is left in the container? Write an equation and an explanation about how you solved this problem.


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

1 and 2 errors.


Part 1: 4,975 ml. The equation is correct.Part 2: 5,000 ml – 4,975 ml = 25 ml.

The explanation is clear and accurate.



Formative Instructional and Assessment TasksHow Much Liquid?

The following amounts of juice were in separate containers after the school’s parent breakfast.

Container 1: 750 ml Container 2: 1,450 ml Container 3: 2 L Container 4: 299 mL Container 5: 476 mL

Part 1:If all of the liquid was put into one large container how much liquid would be in the large container?

Part 2:The large container can hold 5 Liters. How much room is left in the container? Write an equation and an explanation about how you solved this problem.


Formative Instructional and Assessment TasksMultiplication Strategies

4.NBT.5-Task 1Domain Numbers and Operations in Base TenCluster Generalize place value understanding for multi-digit whole numbers.Standard(s) 4.NBT.5 Multiply a whole number of up to 4 digits by a one digit whole number, and

multiply two two-digit numbers, using strategies based on place value and the properties of operations.

Materials Paper and pencilTask This standard calls for students to understand and use a variety of strategies for multiplying multi-

digit numbers. Strategies include the distributive property, doubling and halving, and drawing array area models.

Part 1: Solve this word problem in at least three different ways. Show your thinking with pictures, numbers, and words.

In the cafeteria, each row seats 22 students. There are 12 rows. How many students can be seated?

As students work in pairs or groups, decide which strategies you would like them to share, and in which order. You may start with students who drew array models, and then move to those who used the distributive property in different ways.

Possible strategies:Area array model:

20 x 10= 200 20 x 2 = 40

2 x 10 = 20 2 x 2 = 4

Distributive Property: I broke 22 into 20 and 2. I multiplied 20 x 12 and that is 200 + 40 or 240. Then I multiplied 2 x

12 to get 24. I added 240 + 24 to get 264. I broke 22 into 11 and 11. I multiplied 11 x 12 to get 132, and then doubled it to get 264. I broke 12 into 10 and 2. I multiplied 10 x 22 to get 220 and 2 x 22 to get 44. I added 220 + 44

to get 264. I broke 12 into 6 and 6. I multiplied 6 x 22 to get 132 and then doubled it to get 264.

Part 2: Connect the algorithm to student strategiesModel using the standard algorithm for multiplication to solve 22 x 12. Ask students to explain how their strategies are the same as the algorithm.Look at your numbers and pictures and look at the way we solved this problem with the algorithm. What parts look the same? What parts look different?How are they related?Which strategy do you understand best, and why?What questions do you still have about any of these strategies?



Level I Level II Level IIILimited Performance Students are unable to use a

strategy to solve the multiplication problem. They may be able to use the algorithm to find an answer but cannot explain why it works.

Not Yet Proficient Students can solve the multi-

digit multiplication problem accurately in one way, but do not provide a clear explanation of why it works or how it is related to the standard algorithm for multiplication.

Proficient in Performance Students can solve the multi-

digit multiplication problem accurately in at least two ways, and can provide a clear explanation of why each strategy works and how it is related to the standard algorithm for multiplication.



Formative Instructional and Assessment TasksMultiplication Strategies

Part 1: Solve this word problem in at least three different ways. Show your thinking with pictures, numbers, and words.

In the cafeteria, each row seats 22 students. There are 12 rows. How many students can be seated?

Part 2: Look at your numbers and pictures and look at the way we solved this problem with the algorithm.

What parts look the same?

What parts look different?

How are they related?

Which strategy do you understand best, and why?

What questions do you still have about any of these strategies?


Formative Instructional and Assessment TasksWho Has a Bigger Garden?

4.NBT.5- Task 2Domain Number and Operations-Base TenCluster Use place value understanding and properties of operations to perform multi-digit

arithmetic.Standard(s) 4.NBT.5 Multiply a whole number of up to four digits by a one-digit whole number, and

multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Materials Task handoutTask Who Has a Bigger Garden?

In eastern North Carolina, three farmers are having a discussion about who has the largest garden.Mr. Sanchez: My garden is 87 yards long and its width is 1/3 of its length.Mrs. Thompson: My garden’s width is 18 yards less than the width of Mr. Sanchez’ garden. Its length is 8 yards longer than the length of Mr. Sanchez’ garden.Mr. Peterson: My garden is square and has a perimeter of 204 yards.Part 1:What are the dimensions of each garden?Part 2:List the gardens in order from smallest to largest area.

RubricLevel I e) Level II Level III



Not Yet Proficient The student has

between 1 and 2 errors.

Proficient in Performance The answers are correct. Part 1: Mr. Sanchez: 87x29,

Mrs. Thompson: 95 x 11Mr. Peterson: 51x51.

Part 2: Mrs. Thompson: 1,045 square yards; Mr. Sanchez: 2,523 square yards; Mr. Peterson: 2,601 square yards.



Formative Instructional and Assessment TasksWho Has a Bigger Garden?

In eastern North Carolina, three farmers are having a discussion about who has the largest garden.

Mr. Sanchez: My garden is 87 yards long and its width is 1/3 of its length.Mrs. Thompson: My garden’s width is 18 yards less than the width of Mr. Sanchez’

garden. Its length is 8 yards longer than the length of Mr. Sanchez’ garden.

Mr. Peterson: My garden is square and has a perimeter of 204 yards.

Part 1:What are the dimensions of each garden?

Part 2:List the gardens in order from smallest to largest area.


Formative Instructional and Assessment TasksCollege Basketball Attendance


arithmetic.Standard(s) 4.NBT.5 Multiply a whole number of up to four digits by a one-digit whole number, and

multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Materials Activity sheetTask College Basketball Attendance

Part 1:The college student sections at college basketball games vary UNC Chapel Hill has 1,197 seats reserve for their Carolina students. If students are only allowed to go to 1 game per season, how many different students can go to 6 games?Part 2:Meanwhile, UNC Charlotte only has 874 seats reserved for college students. If students are only allowed to go to 1 game per season, how many different students can go to 6 games?Part 3:How many more students can go to Caroline games than UNC Charlotte games? Explain how you found your answer.

RubricLevel I f) Level II Level III

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 1

and 2 errors.


Part 1:1,197 x 6 = 7,182Part 2: 874 x 6= 5,244Part 3: 7,182- 5,244 = 1,938



Formative Instructional and Assessment TasksCollege Basketball Attendance

Part 1: The college student sections at college basketball games vary. UNC Chapel Hill has 1,197 seats reserved for their Carolina students. If students are only allowed to go to 1 game per season, how many different students can go to 6 games?

Part 2:Meanwhile, UNC Charlotte only has 874 seats reserved for college students. If students are only allowed to go to 1 game per season, how many different students can go to 6 games?

Part 3:How many more students can go to Carolina games than UNC Charlotte games? Explain how you found your answer.


Formative Instructional and Assessment TasksDividing by Multiples of Ten

4.NBT.6 Task 1Domain Numbers and Operations in Base TenCluster Generalize place value understanding for multi-digit whole numbers.Standard(s) 4.NBT.6 Find whole number quotients and remainders with up to four digit dividends and

one digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Materials Paper and pencilTask One component of understanding the relationship between multiplication and division is

understanding how multiples of 10, 100, or 1000 affect products and quotients. In these explorations, students work with multiples of 10 as divisors to understand how they relate to the quotient.

Part 1: Use pictures and numbers to explain how 27 divided by 3 is related to 270 divided by 3 and 2,700 divided by 3.

Part 2: Prove that 23 divided by 4 is the same as 230 divided by 40.


Limited Performance Students are unable to divide

multi-digit numbers using the standard algorithm or invented strategies.

Not Yet Proficient Students can divide multi-digit

numbers using one or more strategies, but they are not consistently accurate. They are unable to explain how multiples of 10, 100, or 1000 affect products and quotients.

Proficient in Performance Students use at least two

different ways to divide multi-digit numbers accurately. They are able to explain how multiples of 10, 100, or 1000 affect products and quotients.



Formative Instructional and Assessment TasksDividing by Multiples of Ten

Part 1: Use pictures and numbers to explain how 27 divided by 3 is related to 270 divided by 3 and 2,700 divided by 3.

Part 2: Prove that 23 divided by 4 is the same as 230 divided by 40.


Formative Instructional and Assessment TasksPackaging Cupcakes


arithmetic.Standard(s) 4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and

one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Materials Activity sheetTask Packaging Cupcakes

The cupcake factory packages cupcakes into packages of 3, 6, and 9 cupcakes each.Part 1:They have 1,782 cupcakes to package. The company’s leaders want to divide the cupcakes so that an equal number of cupcakes will be put into the 3 different types of packages. How many cupcakes will go into each type of package?Part 2:How many packs of cupcakes will have 3 cupcakes in each pack? How many packs of cupcakes will have 6 cupcakes in each pack? How many packs of cupcakes will have 9 cupcakes in each pack?Part 3:Explain how you got your answer to Part 2 above.

RubricLevel I g) Level II Level III



Not Yet Proficient The student has

between 1 and 2 errors.

Proficient in Performance The answers are correct. Part 1:1,782 divided by 3 = 594 cupcakes per

type of package. Part 2: 3 packs: 594 divided by 3 = 198 packs;

6 packs: 594 divided by 6: 99 packs; 594 divided by 9: 66 packs.

Part 3: The explanation is clear and accurate.


Formative Instructional and Assessment Tasks

Packaging Cupcakes

The cupcake factory packages cupcakes into packages of 3, 6, and 9 cupcakes each.

Part 1:They have 1,782 cupcakes to package. The company’s leaders want to divide the cupcakes so that an equal number of cupcakes will be put into the 3 different types of packages. How many cupcakes will go into each type of package?

Part 2:How many packs of cupcakes will have 3 cupcakes in each pack? How many packs of cupcakes will have 6 cupcakes in each pack? How many packs of cupcakes will have 9 cupcakes in each pack?



Formative Instructional and Assessment TasksPart 3: Explain how you got your answer to Part 2 above.


Formative Instructional and Assessment TasksDividing Resources


arithmetic.Standard(s) 4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and

one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Materials Task handoutTask Dividing Resources

The school’s Parent Teacher Organization raised $7,326 through a fund raiser.Part 1:They divide the money evenly between the 6 grades at your school (Kindergarten through 5th Grade). How much will each grade receive?Part 2:With the amount of money that the fourth grade teachers received, they want to spend one-third of it on field trip fees. They will spend the rest on school supplies. How much money was spent on field trip fees? How much was spent on school supplies?Part 3:Explain how you found your answer to Part 2 above.




Not Yet ProficientThe student has between 1

and 2 errors.

Proficient in Performance The answers are correct. Part 1:7326 divided by 6 = $1,221 Part 2: One-third of $1,221 is $1,221

divided by 3 = $407. $407 was spent on field trip fees. The remaining $814 was spent on school supplies.

Part 3: The explanation is clear and accurate.



Dividing Resources

The school’s Parent Teacher Organization raised $7,326 through a fund raiser.

Part 1:They divide the money evenly between the 6 grades at your school (Kindergarten through 5th Grade). How much will each grade receive?

Part 2: With the amount of money that the fourth grade teachers received, they want to spend one-third of it on field trip fees. They will spend the rest on school supplies. How much money was spent on field trip fees? How much was spent on school supplies?




Part 3: Explain how you found your answer to Part 2 above.


Documents

3-5cctask.ncdpi.wikispaces.net3-5cctask.ncdpi.wikispaces.net/file/view/4.NBT... · Web viewRecognize that in a multi-digit whole number, ... Answers: 1) 400 students; 2) 330 students;