Minds On

Exploring math strategies

If possible, work with a partner to solve Zinny’s problem. You can represent your thinking using a method of your choice. You can also use any mental math strategies that you know.

Zinny's problem

Zinny has created a table to show the number of shells they collected in 3 days.

Day Shells collected
1 124
2 ?
3 254

By the end of the third day, Zinny collected a total of 534 shells. How many shells did Zinny collect on the second day? Be sure to show your thinking. Feel free to also explore any mental math strategies that you know.


Student Success

Think-Pair-Share

If possible, share the strategies you used. Try to answer the following questions:

  • What strategies do you see?
  • Did any group use the same strategies as you did?
  • Did any group use a strategy you did not think to use?
  • Would you solve this problem differently if you had to solve it again?
  • If so, why?

Work on the next question. Use at least two different strategies to solve:

Suresh has 315 trading cards. Their brother gives Suresh 278 more. Suresh decides to give away 140 cards to their friends.

How many cards does Suresh have left?

You can represent your thinking using a method of your choice. You can also use any mental math strategies that you know.

Note to teachers: See your teacher guide for collaboration tools, ideas and suggestions.

Action

Count on

Strategies to do mental math calculations depend on the number facts. Let’s explore some different types of mental math strategies.

When there is one larger number and a second small number like 1, 2, 3, 4 or 5, counting on is one strategy to use.

The count on strategy can be used for addition (count on forward) or subtraction (count on backward).

There are many ways to count on.

Choose a few different count on strategies to use to solve the following questions:

187 + 2

196 − 4

110 + 5

Doubling

When you know the sum of a number added to itself, or doubled, you can use that to solve +1 or −1.

Let’s explore a number line together to better understand this doubling example! Use the number line to explore the doubles fact, doubles +1, and doubles −1 from the previous example. Then, you can try using it to explore doubling yourself.

Number lines

Number lines can be used in many ways. We can use number lines to compare, order and estimate numbers, to skip count and to add and subtract.

Student Success

Think-Pair-Share

Not all number lines start at zero. Using open number lines show different ways to complete the problems. How many different ways can you show your solutions using the open number line? Solve the question below. You can use a method of your choice to record your solution.

Starla started with 5 scrapbook stickers. They collected more stickers in 3 equal groups. They ended up with about 25 to 30 stickers.

How many stickers could have been in each group Starla collected? Explain how you know.

Use a number line to act it out.

A number line from 0 to 30.

Solve the following problems using a number line.

Then, choose one addition sentence and one subtraction sentence to complete the following:

  • using math language, explain how to use a number line to model solving problems
  • using math language, explain how using a number line helps to calculate math mentally

Note to teachers: See your teacher guide for collaboration tools, ideas and suggestions.

Press the ‘Activity’ button to access Addition and Subtraction on a Number Line. Activity (Open PDF in a new window)

Not all number lines have ticks. A number line with no tick marks is called an open number line.

There are many ways to show a solution using an open number line.



Student Success

Think-Pair-Share

Solve this!

Solve the following problems using a number line. Show as many ways to model the addition and subtraction sentences as possible using open number lines.

Note to teachers: See your teacher guide for collaboration tools, ideas and suggestions.

Estimation using rounding

Before you solve an addition or subtraction problem, you can estimate an answer. This way, when you do try to solve using pencil and paper or a calculator, you will know if your answer makes sense.

One way to estimate is to round the numbers in the addition or subtraction sentence and then solve.

It is important to follow rounding rules when estimating.

Rules for Rounding

Underline the number

Look next door

5 or greater? Add 1 more

4 or less? Let it rest

All the numbers after the underline change to zeros

Rounding to the nearest ten

24→ 20

57→ 60

Rounding to the nearest hundred

254 → 300

617 → 600


Student Success

Think-Pair-Share

Solve this!

Complete the activity. Share your thinking in your notebook.

Identify the better estimate for each sum: 351 plus 125 equals 370 or 400. 48 plus 16 equals 70 or 75. Identify the better estimate for each difference: 704 minus 85 equals 639 or 690. 119 minus 43 equals 90 or 80. Use math language to explain your choices.

Note to teachers: See your teacher guide for collaboration tools, ideas and suggestions.

Decomposing

When we break larger numbers up into smaller numbers, we call that decomposing numbers. We use decomposition to simplify and solve problems.

Explore decomposition with two- and three-digit math sentences.

Consolidation

Show what you know

Answer the questions in parts A, B, and C to show what you know and reflect on what you have learned.

Part A

Complete the following question.

Question:

Saroud used 516 snap cubes to build 2 towers. One tower has 12 more pieces than the other tower. How many pieces are in each tower? Use the strategies you have learned in this lesson to help you solve the problem. Explain your solution.

What is the problem to solve?

What is the plan you have made to solve it?

Reflect on your answer. How do you know it is correct?

Explain the mental math strategies that helped you solve the problem.

Part B

In your notebook, use these sentence starters to explain your thinking about this question using math language.

Part C

Record your thoughts in a journal reflection. Answer the following questions:

How did recording my solution help me better understand my strategies?

What did I learn from seeing a solution in another way?

What strategies helped me most when solving this math problem?

Reflection

How do you feel about what you have learned in this activity?  Which of the next four sentences best matches how you are feeling about your learning? Press the button that is beside this sentence.

I feel...

Now, record your ideas about your feelings using a voice recorder, speech-to-text, or writing tool.

Press ‘Discover More’ to extend your skills.