options: Describe and compare measurable attributes.

Geometric measurement: understand concepts of angle and measure angles.

Convert like measurement units within a given measurement system.

Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.

Classify objects and count the number of objects in each category.

Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.

Relate addition and subtraction to length.

Represent and interpret data.

Tell and write time.

Work with time and money.

Geometric measurement: understand concepts of area and relate area to multiplication and to addition.

Measure and estimate lengths in standard units.

Measure lengths indirectly and by iterating length units.

Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.

Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.
problem_activity: Narrative
In this activity, students are given expressions that represent strategies for finding the area of rectangles. The strategies are based on the distributive property and the associative property of multiplication. Students interpret the expressions by marking or shading area diagrams and connect each expression to the product of two factors (MP2). For instance, they see that to find the value of
\(2 \times (2 \times 6)\)
is to find the value of
\(4 \times 6\)
or
\(6 \times 4\)
.
MLR8 Discussion Supports:
Synthesis: Create a visual display of the diagrams. As students share their strategies, annotate the display to illustrate connections. For example, trace the area showing 5 columns of 3, and write
\(5 \times 3\)
.
Advances: Speaking, Representing
Engagement: Provide Access by Recruiting Interest.
Leverage choice around perceived challenge. Invite students to select at least 2 of the 3 problems to complete.
Supports accessibility for: Organization, Attention, Social-emotional skills
Required Materials
Materials to Gather
Colored pencils, crayons, or markers
Launch
Groups of 2
“Take a minute to read the directions of the activity. Then, talk to your partner about what you are asked to do.”
1 minute: quiet think time
1 minute: partner discussion
Answer any clarifying questions from students.
Give students access to colored pencils, crayons, or markers.
Activity
“Mark or shade each diagram to represent how each student found the area.”
3–5 minutes: independent work time
“Share with your partner how you used the rectangles to show each expression.”
3–5 minutes: partner discussion
Student Facing
Here are some rectangles and expressions that show how three students saw the area of the rectangles.
Noah
[IMG]
\((5\times 3)+(2 \times 3)\)
Priya
[IMG]
\(2 \times (2 \times 6)\)
Tyler
[IMG]
\((5 \times 8) + (3 \times 8)\)
For each rectangle:
Name the two factors that can be multiplied to find its area.
Mark or shade each rectangle to show how each student saw the area. Be prepared to explain your reasoning.
Student Response
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Activity Synthesis
“What are the two factors you can multiply to find the area of Noah’s rectangle?” (7 and 3)
“How are those numbers related to the expression that he wrote:
\((5\times 3)+(2 \times 3)\)
?”  (
\(7 \times 3\)
is 21. Finding
\(5\times3\)
, which is 15, then adding
\(2\times3\)
, which is 6, also gives 21.)
“Where do you see the two factors in his expression?” (The 7 is 5 and 2 combined. The 3 is in the
\(5 \times 3\)
and
\(2 \times 3\)
.)
Repeat the line of questioning with Priya’s rectangle and expression.


correct_option_index: 10