Working Backwards: Solve Math Mysteries!

Math Grades 1st Grade 5:03 Video
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Lesson Description

Learn how to solve math problems by working backwards! Just like a detective, you can use the end result to figure out the beginning.

Video Resource

How to Work Backwards to Solve Problems

Miacademy Learning Channel

Duration: 5:03
Watch on YouTube

Key Concepts

  • Working backwards
  • Inverse operations (addition and subtraction)
  • Problem-solving strategies

Learning Objectives

  • Students will be able to solve simple word problems by working backwards.
  • Students will be able to identify situations where the 'working backwards' strategy is useful.
  • Students will be able to use addition and subtraction as inverse operations to solve problems.

Educator Instructions

  • Introduction (5 mins)
    Begin by asking students if they've ever tried to solve a puzzle by starting at the end. Introduce the idea of 'working backwards' as a problem-solving strategy. Show the video 'How to Work Backwards to Solve Problems' from Miacademy Learning Channel.
  • Discussion (5 mins)
    After the video, discuss the problem Paul faced in the video. Ask students why working backwards was helpful in that situation. Emphasize that we started with the final amount and did the opposite of what Paul did (subtracted when he added, and added when he subtracted) to find the starting amount.
  • Guided Practice (10 mins)
    Present a similar word problem to the class. For example: 'Lily had some stickers. Her friend gave her 3 more. Then she gave 2 stickers to her brother. Now she has 8 stickers. How many stickers did Lily start with?' Guide the students through the steps of working backwards. Ask guiding questions like: 'What did Lily have at the end?', 'What did she do right before that?', 'What is the opposite of giving away stickers?'
  • Independent Practice (10 mins)
    Provide students with a worksheet containing similar word problems. Encourage them to draw pictures or use manipulatives (like counters or blocks) to help them visualize the problem and work backwards. Example problem: 'Tom baked some cookies. He ate 1 cookie. Then, he gave 4 cookies to his neighbor. Now he has 5 cookies. How many cookies did Tom bake in the beginning?'
  • Wrap-up (5 mins)
    Review the key concept of working backwards. Ask students to share other situations where this strategy might be useful (e.g., figuring out what time to leave for school to arrive on time).

Interactive Exercises

  • Number Line Detective
    Draw a number line on the board. Present a problem like: 'I started at a number, jumped forward 3 spaces, then jumped back 1 space. Now I'm at 6. Where did I start?' Have students use the number line to visually work backwards and solve the problem.

Discussion Questions

  • Can you think of a time when you had to figure something out by starting at the end?
  • Why is it important to do the opposite (add instead of subtract, subtract instead of add) when working backwards?
  • When do you think working backwards will be most helpful for solving math problems?

Skills Developed

  • Problem-solving
  • Critical thinking
  • Addition and subtraction fluency
  • Logical reasoning

Multiple Choice Questions

Question 1:

Lily has some toys. She gives 2 toys away. Now she has 5 toys. How many toys did she start with?

Correct Answer: 7 toys

Question 2:

What do we do when we work backwards?

Correct Answer: Do the opposite

Question 3:

Tom has some blocks. He gets 3 more blocks. Then he gives 1 block to his friend. Now he has 6 blocks. How many blocks did Tom have to begin with?

Correct Answer: 4 blocks

Question 4:

If someone takes away, what do you do when you work backwards?

Correct Answer: Add

Question 5:

Mia had some stickers. She gave 4 stickers to her sister. Now she has 2 stickers. How many did she start with?

Correct Answer: 6 stickers

Question 6:

What is the opposite of adding?

Correct Answer: Subtraction

Question 7:

Ben had some cars. He gave 3 cars to his friend. Then he got 2 more cars. Now he has 7 cars. How many cars did Ben start with?

Correct Answer: 8 cars

Question 8:

When you are working backward, you start where?

Correct Answer: At the end

Question 9:

Sara had some candies. She ate 2 candies. Then her mom gave her 5 candies. Now she has 10 candies. How many candies did Sara start with?

Correct Answer: 8 candies

Question 10:

If you add when you work forward, you ________ when you work backwards?

Correct Answer: Subtract

Fill in the Blank Questions

Question 1:

Working _________ means starting at the end.

Correct Answer: backwards

Question 2:

If I take away when I'm moving forward, I _______ when I work backwards.

Correct Answer: add

Question 3:

When working backwards, you do the _______ of what happened in the problem.

Correct Answer: opposite

Question 4:

The opposite of plus is _______.

Correct Answer: minus

Question 5:

If I add 5, and then I subtract 2, when working backwards I would first _______ 2.

Correct Answer: add

Question 6:

Knowing where you _______ can help you solve the problem.

Correct Answer: end

Question 7:

If you add going forward, you _______ going backwards.

Correct Answer: subtract

Question 8:

Working backwards is a helpful ________ for solving math problems.

Correct Answer: strategy

Question 9:

Before you start, read the problem carefully to understand what it is ________.

Correct Answer: asking

Question 10:

Paul started with $7 in his piggy bank, then he worked _______ to add money.

Correct Answer: forward

Educational Standards

CCSS.Math.Content.1.OA.A.1:Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. CCSS.Math.Content.1.OA.D.8:Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = _ - 3, 6 + 6 = _. CCSS.Math.Content.1.OA.B.4:Understand subtraction as an unknown-addend problem. For example, subtract 10 - 8 by finding the number that makes 10 when added to 8.

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