1. Grade 4 Extended Constructed Response Questions Marking Period 4

2. A dime is 𝟏 𝟏𝟎 of a dollar and a penny is 𝟏 𝟏𝟎𝟎 of a dollar.
10.ECR (to be used with Unit 10 in EDM)
#1 Teacher Model
A dime is 𝟏 𝟏𝟎 of a dollar and a penny is 𝟏 𝟏𝟎𝟎 of a dollar.
Micah has 3 dimes and 40 pennies. Dominic has 6 dimes and 3 pennies.
Micah thinks Dominic has more money than him because 3 dimes is only of a dollar and 6 dimes is of a dollar. Because is larger than , Dominic must have more money.
Do you agree or disagree with Micah? Use a model to show what fraction of a dollar Micah and Dominic have to justify your thinking. Be sure to express your thinking with fractions.
4.NF.5 -Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add fractions with respective denominators 10 and 100.

3. 10.ECR (to be used with Unit 10 in EDM)
#2 Student Practice
Students in Mrs. Smith’s class were solving the following problem:
= 9 100
Janet, Brian, Alyssa, and Jorge all came up with different answers. They were discussing their explanations to each other and realized they all have different solutions.
Here are the solutions they each have:
Janet: 𝟗 𝟏𝟎𝟎 Brian: 𝟗 𝟏𝟎 Alyssa: 𝟐𝟕 𝟏𝟎𝟎 Jorge: 𝟕𝟐 𝟏𝟎𝟎
Explain how each of the 4 students came up with their answers and why they are either correct or incorrect. Which student is correct? Justify your answer using a model.
4.NF.5 -Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add fractions with respective denominators 10 and 100.

4. 11.ECR (to be used with Unit 11 in EDM)
#3 Teacher Model
The park in Alyssa’s neighborhood had new equipment and play areas added. The picture to the left shows part of the new park.
The new playground space has a length of 8 yards and an area of 48 square yards. Attached to the playground is a square sandbox. The width of the sandbox is half the width of the playground.
Alyssa was wondering about the area of the sandbox. Show Alyssa the steps she could follow to find the area of the sandbox. What is the area of the sandbox?
4.MD.3 - Apply the area and perimeter formulas for rectangles in real world and mathematical problems.

5. 11.ECR (to be used with Unit 11 in EDM)
#4 Student Practice
Your teacher will split the class up into groups. Each group will be assigned to either group 1 or group 2 and will present their findings back to the class.
GROUP 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?
GROUP 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?
After presenting your findings, answer the following questions:
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?
4.MD.3 - Apply the area and perimeter formulas for rectangles in real world and mathematical problems.

6. 12.ECR (to be used with Unit 12 in EDM)
#5 Teacher Model
Zach is spending the holiday’s at his grandparents’ house in Greenville. He has to take the train to get there.
Part 1
A train left Zach's town and traveled for 3 hours and 50 minutes to Lancaster. Then it traveled 4 hours and 40 minutes and arrived in Greenville at 12:55 P.M. What time did the train leave Zach's town? Explain how you arrived at your answer.
Part 2
Zach purchased snacks while he was on the train. He paid $6 for five candy bars. What was the unit price for 1 candy bar? Show how you arrived at your result using numbers, diagrams or pictures.
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.

7. An algorithm (equation) A picture or model
12.ECR (to be used with Unit 12 in EDM)
#6 Student Practice
The length of Carter’s driveway is 12m, 38cm. His neighbor’s driveway is 4m, 99cm longer. How long is the neighbor’s driveway? Use each of the following methods to model this situation:
A number line diagram
An algorithm (equation)
A picture or model
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.