Reasoning About Square Roots

Let’s explore square
roots!

Today’s Goals

❏ I can find a decimal

approximation for square roots.

❏ I can plot square roots on the

number line.

❏ When I have a square root, I can

reason about which two whole
numbers it is between.

Squaring Lines

Comprehend/ Apply: Activity 4.2
● MLR8: Discussion Supports
● Anticipate, Monitor, Select, Sequence, Connect

If a number is not
rational, write it with
square root notation.

√17

Square Root of 3

Comprehend/ Apply: Activity 4.3
● Think Pair Share
● MLR1: Stronger and Clearer Each Time

What is the same
and what is different
about this diagram
and diagrams we’ve
seen in earlier
activities?

Begin working on
your own. (2-3 min)

Share your thinking
with your team.

Explain why 2.5 is
not a very good
approximation for
√3.

What is a good
approximation?

How can you approximate
the value of √130?
11² = 121
12² = 144

Organize: Lesson 4 Synthesis

So we know √130 is somewhere between
11 and 12.
Can we get more accurate than that? How?

We could try squaring numbers from
11 to 12, like 11.1, 11.2, etc., to find
the one closest to 130.

Let's Practice

Square Root
Values

Apply/ Comprehend: Activity 5.2
●MLR3: Clarify, Critique, Correct

●Think Pair Share

What two whole numbers does each
square root lie between? Be prepared to
explain your reasoning.
Begin working on your own. (2 min)
Compare your thinking with your team.

What strategy did
you use to figure
out the two whole

numbers?

Organize: Activity 5.2 Synthesis

Solutions on a
Number Line

Apply/ Comprehend: Activity 5.3

●

MLR1: Stronger and Clearer Each Time

●

Think Pair Share

Begin working on the task on your own. (2 min)
Compare your thinking with your team. Be prepared to
discuss your thinking with the whole class!

The numbers x, y, and z are positive, and x2 = 3, y2 = 16, and z2 = 30.

1. Plot x, y, and z on the number line.

2. Plot -√2 on the number line.

How can we find the whole numbers
that a square root lies between?

Look at the square of whole numbers
whose squares are greater than and
less than the number inside the
square root symbol, like 121 and 144
for √130.

Organize: Activity 5.3
Synthesis

How can we get a better
approximation?
Test value between
those two whole
numbers.

More Practice

Today’s Goals

❏ I can find a decimal

approximation for square roots.

❏ I can plot square roots on the

number line.

❏ When I have a square root, I can

reason about which two whole
numbers it is between.

Betweens

Apply/ Summarize:

Cool Down 5.4