options: Use equivalent fractions as a strategy to add and subtract fractions.

Develop Understanding of fractions as numbers.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.

Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

Extend understanding of fraction equivalence and ordering.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.

Understand decimal notation for fractions, and compare decimal fractions.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.

Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
problem_activity: Narrative
In this activity, students find the perimeter of several shapes and write expressions that show their reasoning. Each side of the shape is labeled with its length, prompting students to notice repetition in some of the numbers. The perimeter of all shapes can be found by addition, but students may notice that it is efficient to reason multiplicatively rather than additively (MP8). For example, they may write
\(4 \times 6\frac{1}{3}\)
instead of
\(6\frac{1}{3} + 6\frac{1}{3} + 6\frac{1}{3} + 6\frac{1}{3}\)
.
MLR8 Discussion Supports.
Synthesis: Some students may benefit from the opportunity to rehearse what they will say with a partner before they share with the whole class.
Advances: Speaking
Launch
Groups of 2–4
Activity
3–4 minutes: independent work time
2 minutes: group discussion
Student Facing
Find the perimeter of each shape. Write an expression that shows how you find the perimeter.
[IMG]
Compare your expressions with your partners’ expressions. Make 1–2 observations.
Student Response
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Activity Synthesis
Invite students to share the expressions they wrote for the perimeter of each shape. Record the expressions.
For each shape, ask: “What is the same about these expressions? What is different?” (They each use the side lengths in the shape. They each show the total length around the shape. Some use addition, some use multiplication, some use both multiplication and addition.)
Highlight that when two or more sides have the same length, the perimeter can be found by adding, multiplying, or a combination of both.


correct_option_index: 5