Relate area to the operations of multiplication and addition.

a.  Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.

b.  Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.

[divider] [/divider] Students are able to… 

  • Determine the area of a rectangle by using square tiles or drawings to make an array (rows and columns).
  • Explain how multiplication can be used to determine area.
  • Use multiplication to solve word problems involving area.

[divider] [/divider] Students are able to…because teachers:

  • Provide opportunities for the students to create arrays with color tiles and drawings.
  • Make connections between length measurements and multiplication to determine the area of a rectangle.
  • Pose tasks that involve finding the area in real world situations.

[divider] [/divider] Questions to ask students:

  • How can your model help you determine the area?
    • Sample answer that indicates understanding: I can use the array made with color tiles or drawn on graph paper to find the area of the shape. I can either count the total number of squares in the model, or I could multiply the number of rows by the number of squares in each row to find the area. 
  • How can you use multiplication to find the area of a rectangle?
    • Sample answer that indicates understanding: Just like with an array, I would multiply the number of rows by the number of squares in each row. 4 rows of 3 squares has an area of 12 square units or  4 x 3 = 12.

[divider] [/divider] FSA Notes

Cognitive Complexity Level: 3 – Strategic Thinking and Complex Reasoning

Achievement Level Descriptors:

2- [intentionally left blank]

3- finds the area of a rectangle by tiling and shows that the area of a rectangle found when tiling is the same as would be found by multiplying the side lengths; multiplies the side lengths of a rectangle composed of two rectangles and uses the distributive property to find the overall area

4- finds areas of rectangles by multiplying the side lengths in the context of solving realworld problems; decomposes a rectilinear figure into multiple rectangular parts and finds the area of the new rectangles

5- creates area models to represent the distributive property for area of a rectangle

Assessment Limits:

Figures are limited to rectangles and shapes that can be decomposed into rectangles.

Dimensions of figures are limited to whole numbers.

All values in items may not exceed whole number multiplication facts of 10 × 10.

[divider] [/divider] Additional Resources:

Additional in depth content knowledge

Blog Post: Top 5 Things to Know  About Using Arrays to Model Multiplication and Division

LearnZillion Videos:

Relate Area to Arrays https://bit.ly/2LAte8w

Find the Area of a Rectangle:  Using Arrays https://bit.ly/2Ojf2iy

[divider] [/divider] Sample Formative Assessment Task: 

[divider] [/divider] Resources/Tasks to Help your Child at Home: 

Look for examples of square units covering the area of items in the real-world, for example: square tiles on a floor or ceiling.  Ask your child how they could find the number of squares without counting them all.  How do you know how many squares there are?  How could multiplication help you find the number of squares?

LearnZillion Video: Relate Area to Arrays https://bit.ly/2LAte8w

LearnZillion Video: Find the Area of a Rectangle:  Using Arrays https://bit.ly/2Ojf2iy

SheppardSoftware:  Area Shape Shoot Game https://bit.ly/1dvlTjG