Grade 8 Mathematics Unit 2 | Teacher Guide and Answers

Grade 8 Mathematics Unit 2 | Teacher Guide and Answers

Teach one lesson and eight questions each day. This original unit extends the number-structure focus in the Academy’s Week 2 plan. State standards alignment remains to be verified. Use one point per Day 5 question, accepting equivalent correct work; 6/8 is a suggested reteaching guide, not a validated proficiency score.

Emphasize that √n is the principal nonnegative root, whereas x² = n has two real solutions for positive n. Zero cannot be the base of a negative integer exponent. Check approximations by squaring or bracketing.

Day 1: Rational and irrational numbers

1. Both.
2. 1/4.
3. 2/3.
4. Irrational.
5. Irrational.
6. No, it is an approximation.
7. Yes.
8. Any integer n can be written as n/1.

Day 2: Squares and square roots

1. 8.
2. 8 and -8.
3. 0.
4. 5 and 6.
5. 8 and 9.
6. Yes, √81 = 9.
7. 7 cm.
8. √25 means the principal root 5; x² = 25 has solutions 5 and -5.

Day 3: Estimating and ordering

1. 3 and 4.
2. Yes.
3. Yes.
4. 1.96.
5. 2.25.
6. 1.4, √2, 1.5.
7. ≈.
8. √2 is irrational; 1.414 is a terminating rational decimal.

Day 4: Integer exponents and powers

1. 32.
2. 9.
3. 1.
4. 1/8.
5. 9.
6. -9.
7. No.
8. It is the reciprocal of positive 2³, namely 1/8.

Day 5: Independent assessment

1. Irrational.
2. 1/8.
3. -6 and 6.
4. 7 and 8.
5. Yes; 2.2² = 4.84 < 5.
6. 128.
7. 1/100 or 0.01.
8. √20 cm, between 4 cm and 5 cm.

Reteaching and extension

Use a number line, a table of perfect squares, and inverse checks to reteach. For extension, bracket √7 between 2.64 and 2.65, because 2.64² = 6.9696 and 2.65² = 7.0225; to round to the nearest hundredth, compare 7 with 2.645² = 6.996025, so √7 ≈ 2.65.