Minds On
Working with patterns
Solve this problem. There are 5 addition and subtraction statement patterns. Each pattern begins with a number based on the pattern rule at the top. Can you find the mistakes?
| 68 + 10 | 945–50 | 46 + 100 | 29 + 200 | 911–100 |
|---|---|---|---|---|
| 78 | 895 | 146 | 229 | 811 |
| 88 | 835 | 246 | 429 | 711 |
| 100 | 795 | 364 | 529 | 611 |
| 118 | 745 | 446 | 829 | 501 |
| 128 | 695 | 546 | 1,029 | 411 |
In each pattern, there is one wrong number. Use as many strategies as you can to find the errors in each pattern.
- What strategies did you use to solve?
- Share your answers and strategies in your notebook.
Did you use any other strategies? What strategies did you use and why?
In this lesson, we will be learning how to represent and solve addition and subtraction problems using different strategies, tools and algorithms.
Addition or subtraction?
An important part of problem solving is knowing when to use addition and when to use subtraction to solve the question. When we read word problems, there are key words to help us decide which operations to use to solve.
Addition
in all, add, altogether, total, plus, join, both, sum, more, combined
Subtraction
difference, remain, fewer, how many more, take away, are left, less, minus
Types of addition and subtraction situations
Situations involving adding and subtracting may include:
Change Situation:
a quantity is added to or removed from an existing amount
Example:
Mary blew up 67 balloons for the celebration. 14 of the balloons burst before the guests arrived. How many balloons were left?
Combine Situation:
combining two or more quantities
Example:
Benjamin and Fareed used 545 building blocks to build 2 robots. Fareed used 345 pieces. How many pieces did Benjamin use?
Compare Situation:
two or more quantities are being compared
Example:
Giuliana counted 55 cars on the way to school. Tiersha counted 37 cars. How many more cars did Giuliana count compared to Tiersha?
Practice
Create one of each type of addition or subtraction situation represented in a word problem. Share your word problems with a family member or friend and see if they can solve your word problems.
Share your work in your notebook.
Action
Solving problems using addition and subtraction
Here are two strategies that could be used to check each number pattern.
Skip counting solution
One way to check the numbers in the pattern is to skip count the number being added or subtracted.
For example, 46 + 100: I know that the hundreds column of the answer will increase by 1 each time, so I can skip count 46 + 100 = 146, then 246, 346, 446, and so on. I see that where 346 should be the answer is 364. I know that when we count by 100’s the only digit to change is the hundreds digit, so this number is the pattern is incorrect. The number should be 346.
Models solution
Another way to solve is to use models, like base ten blocks. I can use base ten blocks to add or remove 10’s and 100’s from patterns.
Adding and subtracting: opposite operations
Addition and subtraction are opposite operations. We call addition and subtraction inverse operations. When we add, we put together parts to make a whole. When we subtract, we take the whole and break it into parts.
Part/whole models
We can use part/whole models to represent and solve addition and subtraction problems.
Student Success
Think-Pair-Share
Practice
Solve the problem below. Include a variety of representations to show your thinking.
Share your answers in your notebook.
Note to teachers: See your teacher guide for collaboration tools, ideas and suggestions.
Acting it out
We can use objects, drawings and diagrams to help us understand and solve addition and subtraction problems. When we act it out, we are modelling the situation. An example of acting out a situation is to use a part-whole model. Let’s explore some other ways to act it out.
Student Success
Think-Pair-Share
Objects
Counters, base ten blocks and snap cubes are just some examples of objects we can use to act out a math problem.
Examples of objects to act out or model a situation: 1. Jar of coloured beads. 2. Coloured Base 10 Blocks. 3. Coloured snap cubes. 4. Counters. 5. Any concrete object like shells.
Explore your learning environment. What are some objects you can use to help you solve addition and subtraction problems? Share your ideas in your notebook.
Note to teachers: See your teacher guide for collaboration tools, ideas and suggestions.
Drawings and diagrams
We use pictures like drawings and diagrams to represent and solve math problems. Some examples include number lines, bar models and place value charts.
Student Success
Think-Pair-Share
Practice
Solve the following word problems:
Problem # 1:
Jordan has 38 rocks from the garden. On Monday, Jordan put 13 rocks back and got 18 new ones. Jordan did that every day. How many rocks did Jordan have on Wednesday? How many rocks did Jordan have on Saturday?
Problem # 2:
| Day | Merry-Go-Round | Rollercoaster |
|---|---|---|
| Friday | 319 | 267 |
| Saturday | 294 | 541 |
Using the table above, create an addition word problem and a subtraction word problem. Use objects, drawings and/or diagrams to model the problem and the solution.
Share your work in your notebook.
Note to teachers: See your teacher guide for collaboration tools, ideas and suggestions.
Algorithms
We can solve addition and subtraction situations using an algorithm. An algorithm is a set of steps we follow to solve the problem.
Student Success
Think-Pair-Share
Use algorithms to represent and solve the following word problem.
Janella wrote 137 letters to pen pals around the world in 6 months. Janella wrote 59 to pen pals in India and 86 to pen pals in Thailand.
Based on the letters Janella wrote to pen pals in India and Thailand, is the sum correct?
If the sum is not correct, how many letters would Janella have to add or subtract to make the total number of letters equal 137?
Show your work using an addition algorithm to support your thinking.
Note to teachers: See your teacher guide for collaboration tools, ideas and suggestions.
Consolidation
How can you help?
Part A:
Represent and solve the following question using various models, tools and strategies including:
- bar model
- concrete objects
- drawings and diagrams
- algorithms
In each situation, answer the following reflection questions:
Why did you choose the model, tool or strategy for the question?
In what ways did using the model, tool or strategy help to represent and solve the question?
Question
Jasmine needs to collect 75 paper cups and Suni needs to collect 62 straws for a science experiment.
a) Jasmine has collected 118 paper cups. Does Jasmine have enough or more than enough? By how much?
- How did you solve this problem? Is there another way to solve it? How?
b) Suni has collected 45 straws. How many more does Suni need to collect?
- How did you solve this problem? Is there another way to solve it? How?
Part B:
Create a brochure describing the different ways to represent and solve addition and subtraction problems. Include the following strategies in your brochure:
- bar model (part-whole model)
- concrete objects
- drawings and diagrams
- algorithms
- any other mental math strategies that you use
A brochure:
- is a page of paper folded into three sections that can be handed out or displayed
- has a title on the front cover
- has images and pictures on the front and back of the page
- has words, phrases and sentences to inform the reader about the topic
A child examines a brochure. The brochure has three panels.
Panel 1 says Learn to add and subtract!
Panel 2 has a part/whole model with instructions on how to use the model for subtraction. It
also has a number line diagram which shows how to represent an addition problem.
Panel 3 has addition and subtraction facts that are represented with linking cubes. It says You
can use any kind of objects to help you add and subtract!
Press the Activity button to access the Blank Brochure Template.
Activity (Open PDF in a new window)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.