The Areas of Squares and Their Side Lengths

The Areas of Squares
and Their Side Lengths

Lesson 1

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2019 Open Up Resources |

Let’s investigate
the squares and
their side lengths!

Today’s Goals

❏

I can find the area of a tilted square on a grid by using methods like
“decompose and rearrange” and “surround and subtract.”

❏

I can find the area of a triangle.

❏

I can explain what a square root is.

❏

I understand the meaning of expressions like √25 and √3.

❏

If I know the area of a square, I can express its side length using square
root notation.

Decomposing
to Find Area

Comprehend/ Apply:Activity 1.2
●

MLR7: Compare and Connect

Find the area of each shaded square (in square units).

You will work on both on the next two slides.

Draw

Find the area of the shaded square.

Use your knowledge from 6th and 7th grade to solve.

Draw

Find the area of the shaded square.

Use your knowledge from 6th and 7th grade to solve.

Estimating Side
Lengths from Areas

Comprehend/ Apply Activity 1.3
●

Anticipate, Monitor, Select, Sequence, Connect

●

Think Pair Share

●

MLR5: Co-Craft Questions and Problems

You will find the side length and area of each square on the next three slides.

Draw

What is the slide length of Square A?

What is the area of Square A?

Draw

What is the side length for Square C?

What is the area of Square C?

Draw

What is the side length of Square B?

What is the area of Square B?

How did you
determine the total
area of the shapes?

Organize: Activity 1.4 Synthesis

If you have a square
and know the side length,
how can you find the area?

Multiply the side length by
itself; square the side length.

Organize: Lesson 1 Synthesis

How can you find the
area of a square if you don’t
know the side lengths?

Enclose it in a square whose side
lengths you can find, find the areas of
the triangles, and subtract them from the
area of the big square.

The Sides and Area of Tilted Squares

Comprehend/ Apply: Activity 2.3
● Think Pair Share
● MLR8: Discussion Supports

Which of these squares must have a side length that is
greater than 5 but less than 6? Explain how you know.

square root

The square root of a positive
number n is the positive
number whose square is n.

It is also the side length of a
square whose area is n.

We write the square root of n
as √n.

What does it mean when we
write √100 = 10 in terms of
squares and side lengths?

A square with area 100 has
side lengths of 10.

Organize: Lesson 2 Synthesis

If √17 is a side length of a square,
what does that mean about the
area?

The area is 17 square units.

Today’s Goals

❏

I can find the area of a tilted square on a grid by using methods like
“decompose and rearrange” and “surround and subtract.”

❏

I can find the area of a triangle.

❏

I can explain what a square root is.

❏

I understand the meaning of expressions like √25 and √3.

❏

If I know the area of a square, I can express its side length using square
root notation.

It’s a
Square

Apply/ Summarize
Cool Down 1.5

Draw

Find the area of side lengths of Square ACEG.

What Is the Side Length?

Apply/ Summarize: Activity 2.4
Cool Down 2.4

Draw

Write the exact value of each side length.

Estimate if the exact value is not a whole number.