Lesson 12 Equations with Unknowns

- Let’s represent equations with a ? for the unknown.

Warm-up True or False: Making Tens

Decide if each statement is true or false. Be prepared to explain your reasoning.

$40 = 10 + 27 + 3$
$47 = 20 + 7 + 3 + 10$
$60 = 3 + 47 + 10$

Activity 1 Number Line Riddles

Number line with endpoints of 50 and 65. Frog hopping on number line from 51 to 56, 56 to 60, and 60 to 63.

Solve riddles to find the mystery number.

For each riddle:

Write an equation that represents the riddle and write a ? for the unknown.
Write the mystery number. Represent the equation on the number line.

I started at 15 and jumped 17 to the right. Where did I end?
Equation:
Mystery number:
I started at a number and jumped 20 to the left. I ended at 33. Where did I start?
Equation:
Mystery number:
I started on 42 and ended at 80. How far did I jump?
Equation:
Mystery number:
I started at 76 and jumped 27 to the left. Where did I end?
Equation:
Mystery number:
I started at a number and jumped 19 to the right. I ended at 67. Where did I start?
Equation:
Mystery number:
I started at 92 and ended at 33. How far did I jump?
Equation:
Mystery number:

Activity 2 Make the Equations True

Find the number that makes each equation true.

Show your thinking on the number line.

$? - 48 = 19$
$86 - ? = 39$
$? + 57 = 72$
$73 + ? = 91$

Practice Problem

Problem 1

I started at a number on the number line and jumped back 37. I landed at 26. Where did I start?

Write an equation with a ? for the unknown.
Find the number that makes the equation true.
Represent your thinking on the number line.