Placing an Irrational Number

Trapping √2 between two numbers you know.

10 problems · about 19 minutes · 8.NS.A.2

What this lesson teaches

The child approximates an irrational number and locates it on a number line.

Trap an irrational number between the two perfect squares either side of it.
Narrow the interval by testing decimals until it is close enough.
An irrational decimal never ends and never repeats, so every value written is an approximation.

From earlier lessons. Loosen up before the new work.

3 problems

Review — Cube Roots: Cube root of 216?
Answer 6
Why 6.
Review — Square Roots and Irrational Numbers: What is √100?
Answer 10
Why 10.
Review — Calculating in Scientific Notation: (4 × 10⁵) × (2 × 10³). What is the exponent?
Answer 8
Why 8.

Straightforward practice. Get the method working first.

3 problems

√40 lies between which two whole numbers? Give the smaller.
Answer 6
Why Between 6 and 7.
√8 lies between which two whole numbers? Give the smaller.
Answer 2
Why 4 and 9.
√30 lies between which two whole numbers? Give the smaller.
Answer 5
Why 25 and 36.

The same ideas with more to keep track of.

2 problems

√49 exactly. What is it?
Answer 7
Why A perfect square.
Does the decimal for √2 ever repeat? 1 for yes, 0 for no.
Answer 0
Why That is what irrational means.

Mixed problems. Work out what kind of question it is before you start.

2 problems

The Trap: √5 lies between which two whole numbers? Give the smaller one.
Answer 2
Why Between 2 and 3.
The Bigger One: √20 lies between which two whole numbers? Give the smaller one.
Answer 4
Why Between 4 and 5.