Lesson 5.1: Writing Equal Equations

Practice problems

1. Figure out which of the equals signs has problems in each of these complex equations.

a.

If you complete all of the calculations, you get: 8 = 8 = 15 = 15

So only the middle equals sign is unbalanced.

b.

If you complete all calculations, you get: 27 = 81 = 9 = 11 = 11

So the first 3 equals signs are unbalanced.

2. Fix each of the equations from #1 by making them into shorter one-step equations

a.

Notice that since the first step in this one is to multiply 6x4, that step is pulled out to be the first equation.

b.

c.

3. Fix each of the equations from #1 by making them into a complex equation where all numbers are included at each step.

a.

b.

The parentheses are optional in this equation because the standard order of operations would produce the same order and answer

c.

The parentheses in this equation are necessary because without the parentheses the standard order of operations would call for multiplying 4x4 before adding 3.

4. What is the primary goal of using true-false equations?

For students to practice identifying balanced equations (ones where the value on both sides of the equals sign is the same)

5. Put these true-false equations in order from easier to harder.

e. 3 + 4 = 8 (easiest because the equation is in standard order)

c. 3 = 3 (almost standard order)

b. 4 = 2 + 2 (not standard order, but with only one operation)

a. 8 - 2 = 3 + 3 (two operations, but without anything particularly tricky)

d. 2 + 5 = 7 - 1 (trickiest because 2+5=7)

6. Which of these missing number equations is trickiest?

b. 4 + 3 = __ + 2

is trickiest because the missing number directly follows the = sign, so it's tempting to answer 7 rather than 5.

7. Write a variety of missing number equations (at least 6), each with a different format

I would be looking for:

• at least one each of the equation formats a + b = c, a = b + c, a + b = c + d (where any of the + could be replaced with any operation: +, -, ×, ÷ .
• at least one equation of the tricky format used in # 6
• missing numbers in different positions in each equation.

One example of a full credit answer would be:

12 - _ = 8

10 = __ - 6

8 = 3 + __

__ + 2 = 6 + 5

14 - 2 = __ + 3

4 × 3 = 10 + __