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Formative Instructional and Assessment TasksMeasuring the Jump Ropes

4.MD.1-Task 1Domain Measurement and DataCluster Solve problems involving measurement and conversion of measurements from a

larger unit to a smaller unit.Standard(s) 4.MD.1 Know relative sizes of measurement units within one system of units including

km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...

Materials Paper and pencilMeasuring the Jump Ropes

There are some jump ropes in a container in the gym. The students need to sort them by length.Sally picks all the ropes that are 40 inches or shorterMary picks all the ropes between 41 and 50 inches long.Tanya picks all the ropes that are between 51 and 62 inches long.Jose picks all the ropes that are between 63 and 74 inches long.Lebron picks all the ropes that are 75 inches or longer.

Part 1:Based on the data below, how many jump ropes does each person pick up?

3 ft 2 ft 5 ft 4 ft 4 ft 3 ft 5 ft7 ft 6 ft 6 ft 6 ft 3 ft 5 ft 4 ft

Part 2:Another bin is found. After students add the ropes below to their pile, how many do they each have?6 ft 2 in 4 ft 3 in 2 ft 11 in 3 ft 4 in 3 ft 5 in 3 ft 11 in 6 ft 8 in5 ft 11 in 5 ft 2 in 5 ft 3 in 3 ft 1 in 2 ft 3 in 3 ft 6 in 4 ft 2 in

Part 3:Describe how you solved the tasks in Part Two.

RubricLevel I Level II Level III

Limited Performance Students make

more than 2 errors.

Not Yet Proficient Students make 1 or 2

errors OR their explanation in Part 3 is not accurate.

Proficient in Performance The student provides correct answers. Part 1:

Sally: 4 ropes, Mary: 3 ropes, Tanya: 3 ropes, Jose: 2 ropes, Lebron: 1 rope.

Part 2: Sally: 4 ropes. Mary: 4 ropes, Tanya: 2 ropes, Jose: 3 ropes, Lebron: 1 rope.

Part 3: Student discusses multiplying the number of feet by 12 and adding the number of inches.

NC DEPARTMENT OF PUBLIC INSTRUCTION FOURTH GRADE

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 TasksMeasuring the Jump Rope

There are some jump ropes in a container in the gym. The students need to sort them by length.

Sally picks all the ropes that are shorter than 40 inches.Mary picks all the ropes between 41 and 50 inches long.Tanya picks all the ropes that are between 51 and 62 inches long.Jose picks all the ropes that are between 63 and 74 inches long.Lebron picks all the ropes that are longer than 75 inches.

Part 1: Based on the data below, how many jump ropes does each person pick up?

3 ft 2 ft 5 ft 4 ft 4 ft 3 ft 5 ft7 ft 6 ft 6 ft 6 ft 3 ft 5 ft 4 ft

Part 2: Another bin is found. After students add the ropes below to their pile, how many do they each have?

6 ft 2 in 4 ft 3 in 2 ft 11 in 3 ft 4 in 3 ft 5 in 3 ft 11 in 6 ft 8 in5 ft 11 in 5 ft 2 in 5 ft 3 in 3 ft 1 in 2 ft 3 in 3 ft 6 in 4 ft 2 in

Part 3: Describe how you solved the tasks in Part Two.


Formative Instructional and Assessment Tasks How Long Did I Jump?

4.MD.1-Task 2Domain Measurement and DataCluster Solve problems involving measurement and conversion of measurements from a larger unit

to a smaller unit.Standard(s) 4.MD.1 Know relative sizes of measurement units within one system of units including km, m, cm;

kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...

Materials Paper and pencilHow Long Did I Jump?

At school three students are have a jumping competition to see who can jump the farthest.Miguel, Nancy, and Sarah both jump between 3 and 4 feet.

Part 1:A. If Nancy jumps farther than Miguel but shorter than Sarah, what are possible

distances that each person jumped in inches?B. If all 3 people jumped farther than 3 feet 6 inches, what are the possible distances

that each person could have jumped in inches?C. If all 3 people jumped between 3 feet 7 inches and 3 feet 11 inches, how long did

each person jump?Part 2:Write a sentence describing how you found the distances that each person jumped in inches.



more than 2 errors.

Not Yet Proficient

Students make 1 or 2 errors OR their explanation in Part 3 is not accurate.

Proficient in Performance The student provides correct answers. Part 1: A- Distances

must be between 37 and 47 inches. Miguel must have the smallest distance, Nancy must have the 2nd longest, and Sarah must have the longest distance. B- Same as A, but the distances must be between 43 and 47 inches. C- Miguel- 44 inches, Nancy- 45 inches, Sarah- 46 inches.

AND there is a clear and accurate explanation about how they found the distances in inches.

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 TasksHow Long Did I Jump?

At school three students are have a jumping competition to see who can jump the farthest?

Miguel, Nancy, and Sarah both jump between 3 and 4 feet.

Part 1: A. If Nancy jumps farther than Miguel but shorter than Sarah, what are

possible distances that each person jumped in inches?

B. If all 3 people jumped farther than 3 feet 6 inches, what are the possible distances that each person could have jumped in inches?

C. If all 3 people jumped between 3 feet 7 inches and 3 feet 11 inches, how long did each person jump?

Part 2: Write a sentence describing how you found the distances that each person jumped in inches.


Formative Instructional and Assessment TasksBaby Weights4.MD.1-Task 3

Domain Measurement and DataCluster Solve problems involving measurement and conversion of measurements from a larger unit



Materials Paper and pencil, activity sheet (attached)Baby Weights

Using the table below, answer the following questions:

Baby Gender WeightSamuel Boy 7 and 2/4 poundsNicole Girl 7 and 7/8 poundsTJ Boy 1 and 3/4 pounds heavier than SamuelTyrette Girl 1 and 4/8 of a pound heavier than Nicole

Part 1:What is the weight of each baby in pounds?What is the weight of each baby in ounces?Part 2:How many pounds do the boys weigh? How many ounces do the boys weigh?How many pounds do the girls weigh? How many ounces do the girls weigh?Part 3:What was the total weight of all of the babies in pounds?What was the total weight of all of the babies in ounces?Part 4:Write a sentence about a strategy that you used to convert the babies’ weights from pounds to ounces.



more than 2 errors.


errors OR their explanation is not accurate.

Proficient in Performance Part 1: Samuel- 7 and 2/4 pounds, 120 ounces;

Nicole- 7 and 7/8 pounds, 126 ounces; TJ- 9 and 1/4 pounds, 148 ounces; Tyrette- 9 and 3/8 pounds, 150 ounces

Part 2: Boys- 16 and 3/4 pounds, 268 ounces; Girls- 17 and 2/8 or 17 and 1/4 pounds; 276 ounces.

Part 3: Ounces: 34 pounds; 544 ounces Part 4: The sentence includes a logical and

accurate approach of converting units.


Formative Instructional and Assessment TasksBaby Weights

Using the table below, answer the following questions: Baby Gender WeightSamuel Boy 7 and 2/4 poundsNicole Girl 7 and 7/8 poundsTJ Boy 1 and 3/4 pounds heavier than SamuelTyrette Girl 1 and 4/8 of a pound heavier than Nicole

Part 1: What is the weight of each baby in pounds?

What is the weight of each baby in ounces?

Part 2: How many pounds do the boys weigh? How many ounces do the boys weigh?

How many pounds do the girls weigh? How many ounces do the girls weigh?

Part 3: What was the total weight of all of the babies in pounds?

What was the total weight of all of the babies in ounces?

Part 4: Write a sentence about a strategy that you used to convert the babies’ weights from pounds to ounces.


Formative Instructional and Assessment TasksShipping Packages




Materials Paper and pencil, activity sheet (attached)Shipping Packages

Four friends are each sending packages . Use the table below to answer the following questions:

Package WeightSarah’s box 25 and 6/8 poundsKaren’s box 24 and 5/8 poundsTim’s box 29 and 7/8 poundsSteve’s box 24 and 2/8 pounds

Part 1:What is the weight of each person’s box in ounces?

Part 2:What is the combined weight of each person’s box in pounds?What is the combined weight of each person’s box in ounces?

Part 3:Boxes cost a flat rate of $10 if they are between 300 and 400 ounces, and $15 if they are between 400 and 500 ounces. How much does each package cost?

Part 4:If Sarah has 3 boxes that weigh the same amount and Steve has 4 boxes that weigh the same amount, how much do all of those boxes weigh in pounds? Write a sentence explaining how you found your answer.


Formative Instructional and Assessment TasksRubric

Level I Level II Level IIILimited Performance Students make more

than 2 errors.

Not Yet Proficient Students make 1 or 2 errors

OR their explanation is not accurate.

Proficient in Performance Part 1: Sarah: 412 ounces; Karen: 394

ounces; Tim: 478 ounces; Steve: 388 ounces. Part 2: 104 and 4/8 pounds; 1,672 ounces Part 3: Karen and Steve will have to pay $10.

Sarah and Tim will have to pay $15. Part 4: Sarah’s 3 boxes would weigh 77 and

1/4 pounds. Tim’s 4 boxes would weigh 119 and 2/4 pounds. The combined weight would be 196 and 3/4 pounds.



Formative Instructional and Assessment TasksShipping Packages

Four friends are each sending packages . Use the table below to answer the following questions:

Package WeightSarah’s box 25 and 6/8 poundsPrecious’ box 24 and 5/8 poundsTim’s box 29 and 7/8 poundsSteve’s box 24 and 2/8 pounds

Part 1: What is the weight of each person’s box in ounces?

Part 2: What is the combined weight of each person’s box in pounds?

What is the combined weight of each person’s box in ounces?

Part 3: Boxes cost a flat rate of $10 if they are between 300 and 400 ounces, and $15 if they are between 400 and 500 ounces. How much does each package cost?

Part 4: If Sarah has 3 boxes that weigh the same amount and Steve has 4 boxes that weigh the same amount, how much do all of those boxes weigh in pounds? How much do all of the boxes weigh in ounces? Write a sentence explaining how you found your answer.


Formative Instructional and Assessment TasksRelay Running4.MD.1-Task 5




Materials Paper and pencil, activity sheet (attached)Relay Running

The following runners are on the same relay team for the 4,000 meter race. Here are their times:

Runner TimeAlberto 2 minutes and 55 secondsKate 3 minutes and 8 secondsKelly 3 minutes and 17 secondsMatt 2 minutes and 58 seconds

Part 1:What was the time of each runner in terms of only seconds?

Part 2:Write a sentence explaining how you solved the questions in Part 1.


Limited Performance Students make more

than 2 errors.



Proficient in Performance Part 1: Albert-175 seconds, Kate-188

seconds, Kelly-197 seconds, Matt-178 seconds

Part 2: The sentence shows an appropriate way of solving the problems in Part 1.



Formative Instructional and Assessment TasksRelay Running

The following runners are on the same relay team for the 4,000 meter race. Here are their times:

Runner TimeAlberto 2 minutes and 55 secondsKate 3 minutes and 8 secondsKelly 3 minutes and 17 secondsMatt 2 minutes and 58 seconds

Part 1: What was the time of each runner in terms of only seconds?

Part 2: Write a sentence explaining how you solved the questions in Part 1.


Formative Instructional and Assessment TasksOff to the Races4.MD.1-Task 6




Materials Paper and pencil, activity sheet (attached)Off to the Races

The following runners just completed the Seaside Marathon race where they ran 26.2 miles.

Runner TimeAngela 3 hours, 25 minutes, 15 secondsPaul 3 hours, 26 minutes, 30 secondsSandy 3 hours, 41 minutes, 45 secondsJason 3 hours, 39 minutes, 15 seconds

Part 1:What was the time of each runner in terms of only minutes and seconds (e.g., 185 minutes and 15 seconds)?




than 2 errors.



Proficient in Performance Part 1: Angela: 205 min, 15 sec; Paul: 206

min, 30 sec; Sandy: 221 min, 45 sec; Jason: 219 min, 15 sec

Part 2: The sentence shows an appropriate way of solving the problems in Part 1.



Formative Instructional and Assessment TasksOff to the Races

The following runners just completed the Seaside Marathon race where they ran 26.2 miles.

Runner TimeAngela 3 hours, 25 minutes, 15 secondsPaul 3 hours, 26 minutes, 30 secondsSandy 3 hours, 41 minutes, 45 secondsJason 3 hours, 39 minutes, 15 seconds

Part 1: What was the time of each runner in terms of only minutes and seconds (e.g., 185 minutes and 15 seconds)?



Formative Instructional and Assessment TasksMapping My Run




Materials Paper and pencil, activity sheet (attached)Mapping A Run

On her iPhone Molly was able to track how far she ran each day this week. Here are her distances.

Day DistanceMonday 5 km, 430 m, 0 cmTuesday 4 km, 789 m, 98 cmWednesday 6 km, 967 m, 56 cmThursday 5 km, 5 m, 5 cm

Part 1:How long did Molly run on each of the days in terms of meters (e.g., 6,425 meters and 38 centimeters)?

Part 2:Write a sentence explaining how you found out the distance that she ran.



than 2 errors.



Proficient in Performance Part 1: Monday: 5,430 m and 0 cm; Tuesday:

4,789 m and 98 cm; Wednesday: 6,967 m and 56 cm; Thursday: 5,005 m and 5 cm.

Part 2: The sentence is logical and accurate.



Formative Instructional and Assessment TasksMapping A Run

On her iPhone Molly was able to track how far she ran each day this week. Here are her distances.

Day DistanceMonday 5 km, 430 m, 0 cmTuesday 4 km, 789 m, 98 cmWednesday 6 km, 967 m, 56 cmThursday 5 km, 5 m, 5 cm

Part 1: How long did Molly run on each of the days in terms of meters (e.g., 6,425 meters and 38 centimeters)?

Part 2: Write a sentence explaining how you found out the distance that she ran.


Formative Instructional and Assessment TasksFilling the Jugs4.MD.1-Task 8




Materials Paper and pencil, activity sheet (attached)Filling the Jug

For a class project there was a large 10 Liter jug that had to be filled with water. Unfortunately, the class only had a container marked in milliliters.Part 1:Complete the table below.

Amount in the jug Amount in Milliliters1 Liter1 Liter and 250 mL1 Liter and 750 mL2 Liters2 Liters and 400 mL2 Liters and 756 mL3 Liters

Part 2:Write a sentence to explain how you found the answer to one of the rows of the table.



than 2 errors.



Proficient in Performance Part 1: 1 L = 1,000 mL; 1 L, 250 mL; 1,250

mL; 1L, 750 mL= 1,750 mL; 2 L = 2,000 mL; 2L, 400 mL = 2,400 mL; 2L, 756 mL; 2,756 mL; 3L = 3,000 mL

Part 2: The sentence is logical and accurate.



Formative Instructional and Assessment TasksFilling the Jug

For a class project there was a large 10 Liter jug that had to be filled with water. Unfortunately, the class only had a container marked in milliliters.

Part 1: Complete the table below.

Amount in the jug Amount in Milliliters

1 Liter

1 Liter and 250 mL

1 Liter and 750 mL

2 Liters

2 Liters and 400 mL

2 Liters and 756 mL

3 Liters



Formative Instructional and Assessment TasksMaking Punch4.MD.1-Task 9




Materials Paper and pencil, activity sheet (attached)Making Punch

For a party Mrs. Laney is making punch. She filled a few different large punch bowls.Part 1:Complete the table below.

Punch Bowl Amount in Milliliters2 Liters and 5 milliliters2 Liters and 50 milliliters2 Liters and 500 milliliters3 Liters and 8 milliliters3 Liters and 80 milliliters3 Liters and 800 milliliters




than 2 errors.



Proficient in Performance Part 1: 2 L, 5 mL = 2,005 mL; 2L, 50 mL =

2,050 mL; 2L, 500 mL = 2,500 mL; 3 L, 8 mL = 3,008 mL; 3L, 80 mL = 3,080 mL; 3 L, 800 mL = 3,800 mL

Part 2: The explanation contains an accurate explanation.



Formative Instructional and Assessment TasksMaking Punch

For a party Mrs. Laney is making punch. She filled a few different large punch bowls.

Part 1: Complete the table below.

Punch Bowl Amount in Milliliters

2 Liters and 5 milliliters






Part 2: Write a sentence to explain how you found the answer to one of the rows of the table.


Formative Instructional and Assessment TasksWeighing the Books


to a smaller unit.Standard(s) 4.MD.2 Use the four operations to solve word problems involving distances, intervals of time,

liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

Materials Paper and pencilWeighing the Books

Mrs. Floyd and her classmates want to know how heavy a few of the books in their classroom are.Part 1:They want to know the masses of the objects in ounces; however the scale only gives the mass in pounds. Using the table below, find out how many ounces each book is.

Math book 2 1/2 poundsScience book 3 1/3 poundsDictionary 5 1/8 pounds

Part 2:Two copies of one book and two copies of another book weigh a total of 6 pounds. Each book weighs a whole number of ounces. How many ounces could each book weigh? Explain how you solved this problem.



than 2 errors.



Proficient in Performance Part 1: Math: 40 ounces, Science: 53 1/3

ounces, Dictionary: 82 ounces. Part 2: The books should have a combined

weight of 48 ounces, since 2 copies of both books will be 6 pounds or 96 ounces.

AND there is a clear and accurate explanation about how they found the distances in inches.



Formative Instructional and Assessment TasksWeighing the Books

Mrs. Floyd and her classmates want to know how heavy a few of the books in their classroom are.

Part 1: They want to know the masses of the objects in ounces, however the scale only gives the mass in pounds. Using the table below, find out how many ounces each book is.

Math book 2 1/2 pounds _______oz

Science book 3 1/3 pounds _______oz

Dictionary 5 1/8 pounds _______oz

Part 2: Two copies of one book and two copies of another book weigh a total of 6 pounds. Each book weighs a whole number of ounces. How many ounces could each book weigh? Explain how you solved this problem.


Formative Instructional and Assessment TasksGetting Ready for School


larger unit to a smaller unit.Standard(s) 4.MD.2 Use the four operations to solve word problems involving distances, intervals of

time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

Materials Paper and pencilGetting Ready for School

The bus comes to Steve’s house at 8:15 a.m. Prior to getting on the bus, he needs to:Eat breakfast: 15 minutesShower: 8 minutesGet dressed: 7 minutesRead a book: 12 minutes

Part 1:What is the latest that Steve can get up and still be on time for the bus?

Part 2:It takes Steve’s sister, Rachel, twice as long to get dressed and 5 minutes longer to eat breakfast. What is the latest Rachel can get up and still be on time for the bus? Write a sentence to explain how you found your answer.



than 2 errors.


OR their explanation in Part 3 is not accurate.

Proficient in Performance Part 1: Steve needs to be up by 7:33 a.m.

Part 2: Rachel needs to be up by 7:21 a.m. AND the explanation is clear and accurate.



Formative Instructional and Assessment TasksGetting Ready for School

The bus comes to Steve’s house at 8:15 a.m. Prior to getting on the bus, he needs to:Eat breakfast: 15 minutesShower: 8 minutesGet dressed: 7 minutesRead a book: 12 minutes

Part 1: What is the latest that Steve can get up and still be on time for the bus?

Part 2: It takes Steve’s sister, Rachel, twice as long to get dressed and 5 minutes longer to eat breakfast. What is the latest Rachel can get up and still be on time for the bus? Write a sentence to explain how you found your answer.


Formative Instructional and Assessment TasksAdding Up and Comparing Our Jumps




Materials Paper and pencil

Adding Up and Comparing Our Jumps

At school three students are have a jumping competition to see who can jump the farthest.

Part 1:Nancy jumped 3 feet and 11 inches. Miguel jumped 5 inches longer than Nancy.Sarah jumped 9 inches longer than Miguel.

How long did each person jump in feet and inches (e.g., 4 feet and 3 inches)?How long did each person jump in only inches?

Part 2:Write a sentence describing how you found the distances that each person jumped in inches.

Part 3:What was the combined length that all three students jumped in inches? What was their distance in feet and inches?

Part 4:Three other students jumped a combined distance of 15 feet. How much further did they jump compared to the combined distance of Nancy, Miguel, and Sarah?



than 2 errors.



Proficient in Performance Part 1: Nancy: 3 ft, 11 in or 47 in; Miguel: 4

ft, 4 in or 52 in; Sarah: 5 ft, 1 in or 61 in. Part 2: The sentence contains a logical and

accurate description. Part 3: 160 inches or 13 ft 4 in. Part 4: The other students jumped 1 ft and 8

inches further.


Formative Instructional and Assessment TasksAdding Up and Comparing Our Jumps


Part 1: Nancy jumped 3 feet and 11 inches. Miguel jumped 5 inches longer than Nancy. Sarah jumped 9 inches longer than Miguel.

How long did each person jump in feet and inches (e.g., 4 feet and 3 inches)?

How long did each person jump in only inches?


Part 3: What was the combined length that all three students jumped in inches?

What was their distance in feet and inches?

Part 4: Three other students jumped a combined distance of 15 feet. How much further did they jump compared to the combined distance of Nancy, Miguel, and Sarah?


Formative Instructional and Assessment TasksAdding Up and Comparing Our Jumps II




Materials Paper and pencil

Adding Up and Comparing Our Jumps II


Part 1:Timothy jumped 3 feet and 10 inches. Yani jumped 4 inches longer than Timothy.Mitch jumped 11 inches longer than Yani.

How long did each person jump in feet and inches (e.g., 4 feet and 3 inches)?How long did each person jump in only inches?

Part 2:Write a sentence describing how you found the distances that each person jumped in inches.

Part 3:What was the combined length that all three students jumped in inches? What was their distance in feet and inches?

Part 4:Three other students jumped a combined distance of 14 feet. How much further did they jump compared to the combined distance of Timothy, Yani, and Mitch?


Formative Instructional and Assessment TasksRubric

Level I Level II Level IIILimited Performance Students make

more than 2 errors.



Proficient in Performance Part 1: Timothy- 3 feet 10 inches or 46 inches;

Yani- 4 ft and 2 inches or 50 inches; Mitch- 5 ft 1 inch or 61 inches

Part 2: The sentence accurately describes an appropriate process to find out each distance in inches.

Part 3: The combined distance was 157 inches or 13 feet 1 inch.

Part 4: The three other students jumped 11 inches farther than Timothy, Yani, and Mitch.



Formative Instructional and Assessment TasksAdding Up and Comparing Our Jumps II


Part 1: Timothy jumped 3 feet and 10 inches. Yani jumped 4 inches longer than Timothy. Mitch jumped 11 inches longer than Yani.

How long did each person jump in feet and inches (e.g., 4 feet and 3 inches)?

How long did each person jump in only inches?


Part 3: What was the combined length that all three students jumped in inches? What was their distance in feet and inches?

Part 4: Three other students jumped a combined distance of 14 feet. How much further did they jump compared to the combined distance of Timothy, Yani, and Mitch?


Formative Instructional and Assessment TasksArea & Perimeter Exploration


larger unit to a smaller unit.Standard(s) 4.MD.3 Apply the area and perimeter formulas for rectangles in real world and

mathematical problems.Materials Paper and pencil, graph paper or square tilesTask Examining the relationship between area and perimeter and using area and perimeter

formulas for quick calculation.

Activity 1:Create all the possible arrays with an area of 36 square units.Draw them on grid paper and label their dimensions.How can you be sure that you found all the possible arrays with an area of 36 square units?Find the perimeter for each figure.What do you notice about the shapes and their perimeters?What is the relationship between the perimeter and the shape of an array?

Activity 2:Create all the possible arrays with a perimeter of 36 units.Draw your arrays on grid paper and label their dimensions.Use a chart to keep track of the area and dimensions for each rectangle.How can you be sure that you found all the possible arrays with a perimeter of 36 units? What do you notice about the shapes and their perimeters?What is the relationship between the area and the shape of an array?

Activity 3:What generalizations can be made about the relationship between the area and perimeter of a figure?How could this this information be used to solve a problem in real life? When might it be useful to have this information?

Possible Solution:Activity 1: All have area of 36 square units. Perimeter dimensions 74 units 1 x 36 40 units 2 x 18 30 units 3 x 12 26 units 4 x 9 24 units 6 x 6Possible conclusions: The closer a shape gets to being a square, the smaller its perimeter.


Formative Instructional and Assessment TasksActivity 2: All have a perimeter of 36 units.Area dimensions 17 1 x 17 32 2 x 16 45 3 x 15 56 4 x 14 65 5 x 13 72 6 x 12 77 7 x 11 80 8 x 10 81 9 x 9Possible response: The closer a shape gets to being a square, the larger its area.

Squares have the largest possible area and the smallest possible perimeter.


Limited Performance The student is unable to find

all the possible figures with an area of 36 and/or calculate the perimeter for each figure. The student is unable to find all the possible arrays with a perimeter of 36 and/or their areas. The student does not have an efficient strategy to check to make sure that s/he has found all the possible arrays that fit the requirements. They are unable apply the formula for area or perimeter to perform the required calculations.

Not Yet Proficient The student is able to find all

the possible arrays, areas, and perimeters for Activity 1 and Activity 2. They are unable to make generalizations about the relationship between area and perimeters of squares and rectangles. They are unable to generate an example of how this relationship might be useful in solving a real world problem.

Proficient in Performance The student is able to find all

the possible arrays, areas, and perimeters for Activity 1 and Activity 2. They are able to make generalizations about the relationship between area and perimeters of squares and rectangles, and to generate at least one example of how this relationship might be useful in solving a real world problem.



Formative Instructional and Assessment TasksArea & Perimeter Exploration

Activity 1: Create all the possible arrays with an area of 36 square units. Draw them on grid paper and label their dimensions. How can you be sure that you found all the possible arrays with an area of 36

square units? Find the perimeter for each figure. What do you notice about the shapes and their perimeters? What is the relationship between the perimeter and the shape of an array?

Activity 2: Create all the possible arrays with a perimeter of 36 units. Draw your arrays on grid paper and label their dimensions. Use a chart to keep track of the area and dimensions for each rectangle. How can you be sure that you found all the possible arrays with a perimeter of

36 units? What do you notice about the shapes and their perimeters? What is the relationship between the area and the shape of an array?

Activity 3: What generalizations can be made about the relationship between the area and

perimeter of a figure? How could this this information be used to solve a problem in real life? When

might it be useful to have this information?


Formative Instructional and Assessment TasksPutting Down Carpet

4.MD.3 - Task 2Domain Measurement and DataCluster Solve problems involving measurement and conversion of measurements from a


mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.

Materials Plastic square tiles, Paper, Pencil, Graph paper (optional)

Putting Down CarpetPart 1:You want to carpet 3 rooms of a house. Using the dimensions below, determine how much carpet is needed.

Room 1: Perimeter is 38 yards and the width of the room is 12 yards.Room 2: Perimeter is 50 yards and the width is 13 yards.Room 3: Perimeter is 46 yards and the width is 10 yards.

For each room, determine how much carpet is needed.

Part 2:Write a sentence and explain how you solved this task.



than 2 errors.



Proficient in Performance Part 1: Room 1: Width is 12, Length is 7.

Area is 84 square yards. Room 2: Width is 13 yards, Length is 12 yards. Area is 156 square yards. Room 3: Width is 10, Length is 13. Area is 130 square yards.

Part 2: The explanation is clear and accurate.



Formative Instructional and Assessment TasksPutting Down Carpet

Part 1:You want to carpet 3 rooms of a house. Using the dimensions below, determine how much carpet is needed.

Room 1: Perimeter is 38 yards and the width of the room is 12 yards.Room 2: Perimeter is 50 yards and the width is 13 yards. Room 3: Perimeter is 46 yards and the width is 10 yards.

For each room, determine how much carpet is needed.



Formative Instructional and Assessment TasksFencing Yards




Materials Plastic square tiles, Paper, Pencil, Graph paper (optional)Fencing Yards

Part 1:For a summer job, your older brother is working for a fencing company. Determine how much fencing is needed for each of these rectangular yards.

Yard 1: Area is 500 square meters. Length is 25 meters.Yard 2: Area is 567 square meters. Length is 9 meters.Yard 3: Area is 736 square meters. Length is 4 meters.




than 2 errors.



Proficient in Performance Part 1: Yard 1: Width is 20 meters. Fencing:

90 meters. Yard 2: Width is 63 meters. Fencing: 144 meters. Yard 3: Width is 184 meters. Fencing is 376 meters.

Part 2: The explanation is clear and accurate.



Formative Instructional and Assessment TasksFencing Yards

Part 1:For a summer job, your older brother is working for a fencing company. Determine how much fencing is needed for each of these rectangular yards.

Yard 1: Area is 500 square meters. Length is 25 meters.Yard 2: Area is 567 square meters. Length is 9 meters.Yard 3: Area is 736 square meters. Length is 4 meters.



Formative Instructional and Assessment TasksMaking a Dog Pen




Materials Plastic square tiles, Paper, Pencil, Graph paper (optional)Making a Dog Pen

Part 1:You want to make a rectangular dog pen using 20 yards of fencing. The side lengths must be in whole yards. Create as many different rectangular pens as you can.Part 2:Which dog pen gives your dog the most space to run around and play in? Write a sentence explaining how you know.Part 3:You want to build the rectangular dog pen with 20 yards of fencing against your house which is 20 yards wide. Which dimensions will give you the most space for your dog?



than 2 errors.



Proficient in Performance Part 1: The dimensions must add up to 10. 9x1,

8x2, 7x3, 6x4, 5x5. Part 2: The 5x5 pen gives the most space, 25

square yards. AND the explanation is clear and accurate.

Part 3: The 10x5 rectangle gives the most space. The 10 yard side runs parallel to the house while the 5 yard sides connect the house to the other side.



Formative Instructional and Assessment TasksMaking a Dog Pen

Part 1:You want to make a rectangular dog pen using 20 yards of fencing. The side lengths must be in whole yards. Create as many different rectangular pens as you can.

Part 2: Which dog pen gives your dog the most space to run around and play in? Write a sentence explaining how you know.

Part 3: You want to build the rectangular dog pen with 20 yards of fencing against your house which is 20 yards wide. Which dimensions will give you the most space for your dog?


Formative Instructional and Assessment Tasks Reading Survey

4.MD.4 - Task 1Domain Measurement and DataCluster Represent and interpret data.Standard(s) 3.MD.4 Generate measurement data by measuring lengths using rulers marked with halves

and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units— whole numbers, halves, or quarters.

Materials Paper, pencils, white boards and dry-erase markers (optional)Task Directions for students:

As a class, have students survey 10 classmates and ask them “How long do you think fourth graders should read each night at home?” They can choose ¼, ½, ¾ or 1 hour. Students should record results on a piece of paper.

Create a line plot to represent the data. Have students write a sentence about an observation that they notice from the line plot. If you were using this line plot to make a decision about how long students should read

each night, which time would you choose? Why?


Limited Performance Incorrect answer and work are

given.

Not Yet Proficient Finds the correct answer, but

there may be inaccuracies or incomplete justification of solution OR

Uses partially correct work but does not have a correct solution.

Proficient in Performance Accurately surveys and makes

a line plot, and analyses the results.

Uses an appropriate model to represent and justify the solution.



Formative Instructional and Assessment TasksHow High Did it Bounce?

4.MD.4-Task 2Domain Measurement and DataCluster Represent and interpret data.Standard(s) 4.MD.4 Make a line plot to display a data set of measurements in fractions of a unit (1/2,

1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.

Materials Paper, pencil, Activity sheetHow High Did it Bounce?

A class measures how high a bouncy ball will bounce compared to the height of the wall.Based on the data, make a line plot to display the data.

3/8 5/8 7/8 6/8 5/8 6/86/8 5/8 4/8 4/8 2/8 6/85/8 7/8 5/8 6/8 4/8 5/8

A) How many bouncy balls went halfway up the wall or higher?B) How may bouncy balls went 3/4 of the wall or higher?C) What is the combined height of all of the heights of the bouncy balls?



than 2 errors.


Proficient in Performance A) 16 balls, B) 7 balls, C) 11 and 3/8 of the

wall or 91 feet high.



Formative Instructional and Assessment TasksHow High Did it Bounce?

A class measures how high a bouncy ball will bounce compared to the height of the wall. Based on the data, make a line plot to display the data.

3/8 5/8 7/8 6/8 5/8 6/86/8 5/8 4/8 4/8 2/8 6/85/8 7/8 5/8 6/8 4/8 5/8

0 1/8 2/8

3/8 4/8

5/8

6/8 7/8 1

A)How many bouncy balls went halfway up the wall or higher?

B)How may bouncy balls went 3/4 of the wall or higher?

C) If the wall is 8 feet high, what is the combined height of all of the heights of the bouncy balls?


Formative Instructional and Assessment TasksMeasuring Strings

4.MD.4-Task 3Domain Measurement and DataCluster Represent and interpret data.Standard(s) 4.MD.4 Make a line plot to display a data set of measurements in fractions of a unit (1/2,

1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.

Materials Paper, pencil, Activity sheetMeasuring Strings

A basket of strings is measured by the class and graphed. Based on the line plot:1) How many strings are ½ of a foot or longer?2) How many strings are shorter than 3/8 of a foot?3) If students put the string together that is 1/8 or 2/8 of a foot long, how long would

that string be?4) If students put all of the pieces of string together, how long would that string be?



than 2 errors.


Proficient in Performance 1) 7. 2) 6, 3) 9/8 or 1 and 1/8, 4) 8 and 6/8

or 8 and 3/4



Formative Instructional and Assessment TasksMeasuring Strings

A basket of strings is measured by the class and graphed.

Lengths of string (feet)x x x xx x x x x x Xx x x x x x X

0 1/8 2/8 3/8 4/8 5/8 6/8 7/8 1

Based on the line plot:

1) How many strings are more than ½ of a foot or longer?

2) How many strings are shorter than 3/8 of a foot?

3) If students put the string together that is 1/8 or 2/8 of a foot long, how long would that string be?

4) If students put all of the pieces of string together, how long would that string be?


Formative Instructional and Assessment TasksIntersecting Roads

4.MD.5 – Task 1Domain Measurement and DataCluster Geometric measurement: understand concepts of angle and measure angles.Standard(s) 4.MD.5 Recognize angles as geometric shapes that are formed wherever two rays share a

common endpoint, and understand concepts of angle measurement: a. An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles.b. An angle that turns through n one-degree angles is said to have an angle measure of n degrees.4.MD.6 Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.

Materials Task handout, Protractor (optional)Task Intersecting Roads

Circle-town is shaped like a circle. All of the roads start in the center of the town and extend from the center like rays.Part 1:On the map draw the following roads and label the measure of each angle.

a) Smith Street extends completely horizontal to the right of the center of town.b) Smith Street and Main Street form a 45 degree angle.c) Thompson Street forms a 30 degree angle with Main Street.d) Young Avenue forms a 90 degree angle with Thompson Street.e) Turnberry forms a 120 degree angle with Young Avenue.

Part 2:Write an explanation about how you know your answers are correct in Part 1.

RubricLevel I a) 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.

Proficient in Performance The answers are correct. Part 1: Roads are drawn correctly and angles are

correctly labeled. Part 2: 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 TasksIntersecting Roads

Circle-town is shaped like a circle. All of the roads start in the center of the town and extend from the center like rays. Part 1:On the map draw the following roads and label the measure of each angle.

a) Smith Street extends completely horizontal to the right of the center of town.b) Smith Street and Main Street form a 45 degree angle.c) Thompson Street forms a 30 degree angle with Main Street.d) Young Avenue forms a 90 degree angle with Thompson Street.e) Turnberry forms a 120 degree angle with Young Avenue.

Part 2:Write an explanation about how you know your answers are correct in Part 1.

Extension: Create your own town and give direction as noted above.


Formative Instructional and Assessment TasksGoing Different Directions

4.MD.6 – Task 1Domain Measurement and DataCluster Geometric measurement: understand concepts of angle and measure angles.Standard(s) 4.MD.6 Measure angles in whole-number degrees using a protractor. Sketch angles of

specified measure.4.MD.5 Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: a. An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles.b. An angle that turns through n one-degree angles is said to have an angle measure of n degrees.

Materials Task handout, Protractor (optional)Task Going Different Directions

Pairs of students worked together to explore the idea of creating an angle.Part 1: Each student represents a point and each walk represents a ray. Draw the angle each situation below creates.

a) Students stood back to back and walked away from each other;b) One student faced forward while the other student turned 30 degrees and both

students walked forward;c) One student faced forward while the other student turned 90 degrees and both

students walked forward;d) One student faced forward while the other student turned 120 degrees and both

students walked forward.Part 2: Explain how you solved the tasks above.

RubricLevel I b) Level II Level III





Proficient in Performance The answers are correct. Part 1: Angles are drawn correctly. A is a 180

degree or straight angle. Part 2: The explanation is clear and accurate.



Formative Instructional and Assessment TasksGoing Different Directions

Pairs of students worked together to explore the idea of creating an angle. Each student represents a point and each walk represents a ray. Draw the angle each situation below creates.

Part 1:Draw each angle when:

c) Students stood back to back and walked away from each other.

d) One student faced forward while the other student turned 30 degrees and both students walked forward.

e) One student faced forward while the other student turned 90 degrees and both students walked forward.

f) One student faced forward while the other student turned 120 degrees and both students walked forward.

Part 2: Explain how you solved the tasks above.


Formative Instructional and Assessment TasksMaking Shapes4.MD.6 – Task 2

Domain Measurement and DataCluster Geometric measurement: understand concepts of angle and measure angles.Standard(s) 4.MD.6 Measure angles in whole-number degrees using a protractor. Sketch angles of

specified measure.4.MD.5 Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: a. An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles.b. An angle that turns through n one-degree angles is said to have an angle measure of n degrees.

Materials Task handout, Geoboard, ProtractorTask Making Shapes

Part 1:On the geoboard make the following shapes. Below, draw the shape and write the measurement of each angle.

a) A rectangleb) A trapezoidc) A parallelogram that is not a rectangled) A right trianglee) An isosceles trianglef) An obtuse triangle

Part 2: Write an explanation describing how you measured each of the angles in the isosceles triangle.

RubricLevel I g) Level II Level III





Proficient in Performance The answers are correct. Part 1: The shapes are drawn correctly and angle

measures are correctly labeled. Part 2: The explanation is clear and accurate.



Formative Instructional and Assessment TasksMaking Shapes

Part 1: On the geoboard make the following shapes. Below, draw the shape and write the measurement of each angle.

a) A rectangle

b) A trapezoid

c) A parallelogram that is not a rectangle

d) A right triangle

e) An isosceles triangle

f) An obtuse triangle

Part 2:Write an explanation describing how you measured each of the angles in the isosceles triangle.


Formative Instructional and Assessment TasksAdding Up Angles

4.MD.7-Task 1Domain Measurement and DataCluster Geometric measurement: understand concepts of angle and measure angles.Standard(s) 4.MD.7 Recognize angle measure as additive. When an angle is decomposed into non-

overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.

Materials Paper, pencil, ProtractorAdding Up Angles

A 90 degree angle is divided into two smaller angles.

Part 1:What type of angles are both of the smaller angles? How do you know?

Part 2:Give 3 possible combinations for the measurements of both angles. For each, draw the angles and write the angle measure.



than 2 errors.


OR the drawings are not close to the angle measure.

Proficient in Performance Part 1: Both angles have to be acute angles

since the sum of both is 90 degrees. Part 2: The sum of both angles has to be 90

degrees for all 3 answers AND the drawings are close to the angle measure.



Formative Instructional and Assessment TasksAdding Up Angles

A 90 degree angle is divided into two smaller angles.

Part 1:What type of angles are both of the smaller angles? How do you know?

Part 2: Give 3 possible combinations for the measurements of both angles. For each, draw the angles and write the angle measure.


Formative Instructional and Assessment TasksHow Can We Split Angles?

4.MD.7-Task 2Domain Measurement and DataCluster Geometric measurement: understand concepts of angle and measure angles.Standard(s) 4.MD.7 Recognize angle measure as additive. When an angle is decomposed into non-

overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.

Materials Paper, pencil, ProtractorHow Can We Split Angles?

Part 1:Use a protractor to split a 135 degree angle the following ways:

A) A right angle, a 35 degree angle and another acute angle. What is the measure of the other angle?

B) A right angle and another angle. What is the measure of the other angle?C) A 120 degree angle and another angle. What is the measure of the other angle?D) 3 angles that are the same size.E) A 15 degree angle and 2 angles that are the same size. What is the measure of the

other angles?Part 2:Describe how you solved one of the tasks above.



than 2 errors.


Proficient in Performance Part 1: A) The other angle is 10 degrees. B)

The other angle is 45 degrees. C) The other angle is 15 degrees. D) Each angle is 45 degrees. E) The other angles are each 60 degrees.

Part 2: Description is clear and accurate.



Formative Instructional and Assessment TasksHow Can We Split Angles?

Part 1: Use a protractor to split a 135 degree angle the following ways:

A)A right angle, a 35 degree angle and another acute angle. What is the measure of the other angle?

B)A right angle and another angle. What is the measure of the other angle?

C)A 120 degree angle and another angle. What is the measure of the other angle?

D)3 angles that are the same size. What is the measure of each of the angles?

E) A 15 degree angle and 2 angles that are the same size. What is the measure of the other angles?

Part 2:Describe how you solved one of the tasks above.


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