Minds On
True or false?
Explore the statements below and decide if they are true or false.
If the statement is false, identify why.
Record your ideas using a method of your choice.
- one pound of bricks is equal to one pound of feathers
- 10 cents is equal to one dime
- 5 is equal to 8
- 10 is less than 5
- One meter is less than 1 kilometer
Action
Task 1: Understanding inequality
An inequality is the relationship between two expressions or values that are not equal.
The relationship between two expressions can instead be described as greater than, less than, greater than or equal to, less than or equal to, or not equal.
There are symbols that represent each of these relationships:
Description
Less than is represented by a triangle bracket that opens to the right. Greater than is represented by a triangle bracket that opens to the left. Less than or equal to is represented by a triangle bracket that opens to the right with a horizontal line underneath. Greater than or equal to is represented by a triangle bracket that opens to the left with a horizontal line underneath. Not equal to is represented by an equal sign with an angled line crossing through it.
Develop a strategy that you can use to help you remember which symbol represents which inequality.
What strategies did you come up with?
Task 2: Identifying and labeling inequalities
For each question there are either 2 numbers or 2 expressions that represent an inequality. Choose a symbol to place between those 2 expressions to describe the relationship. You can record your thoughts using a method of your choice. The first has been done for you.
- 6 < 8
Select the correct answer.
Is there more than one possible answer? Explain.
Try it on your own
Write the following inequalities in word form.
For example,
5 ≠ 3 x 2, 5 is not equal to 3 x 2
Record your answers using a method of your choice.
For each equation, select the correct answer.
Task 3: Plotting inequalities on a number line
Sometimes, inequalities can include variables and has information about the value of that variable. For example, in the inequality n < 7, you know that n can only be 6, 5, 4, 3, 2, 1, or 0. These numbers are called the solution set because they are the possible solutions for n.
Student Success
Think-Pair-Share
Check the teacher guide to access a website that allows the use of a digital number line.
Note to teachers: See your teacher guide for collaboration tools, ideas and suggestions.
Step 1. Create your number line.
1, 2, 3, 4, 5, 6, 7, 8, 9, 10......
Step 2. Indicate the number 7 by circling it on the number line. This means that the variable cannot be 7. If the symbol is greater/less than or equal to (≤ or ≥), indicate that by using a closed circle because that number is also a possibility.
Step 3. Include an arrow representing the direction of the inequality. If it is less than, the arrow goes towards the smaller numbers. If it is greater than, the arrow goes towards the bigger numbers. The answer to the question would be the arrow pointing towards the smaller numbers (6, 5, 4, 3, 2, 1).
Now try it yourself!
If you would like, you can complete the next activity using TVO Mathify. You can also use your notebook or a method of your choice.
Determine the numerical inequality for the following relationships and include a digital or print number line, and list 3 possible numbers in the solution set.
- k is less than or equal to 6
- h is greater than 15 + 7
- i is greater than or equal to 5 x 5
- 6 x 2 < r
- 64 ÷ 4 ≤ p
- 50 – 37 > t
Press the ‘Activity’ button to access this resource for your note-taking document.
Activity(Open PDF in a new window)Press the question to access a possible solution to check your work.
k is less than or equal to 6
k ≤ 6; (3,4,5)
A number line from 1 to 10. There is a filled in circle at 6 and an arrow that stretches out to the left pointing towards 1.
h is greater than 15 + 7
h > 22; (24, 28, 101)
A number line from 15 to 33. There is an unfilled in circle at 22 and an arrow that stretches out to the right pointing towards 33.
i is greater than or equal to 5 × 5
i ≥ 25; (25, 55, 2,019)
A number line from 20 to 33. There is a filled in circle at 25 and an arrow that stretches out to the right pointing towards 33.
6 x 2 < r
12 < r so r > 12; (12.1, 34, 598)
A number line from 12 to 24. There is an unfilled in circle at 12 and an arrow that stretches out to the right pointing towards 24.
64 ÷ 4 ≤ p
16 ≤ p so p ≥ 16; (16, 16.1, 64)
A number line from 12 to 24. There is a filled in circle at 16 and an arrow that stretches out to the right pointing towards 24.
50 – 37 < t
13 > t so t is < 13; (12.99, 1, −1)
A number line from 6 to 19. There is an unfilled in circle at 13 and an arrow that stretches out to the left towards 6.
Connect with a TVO Mathify tutor
Think of TVO Mathify as your own personalized math coach, here to support your learning at home. Press ‘TVO Mathify’ to connect with an Ontario Certified Teacher math tutor of your choice. You will need a TVO Mathify login to access this resource.
(Opens in new window)Task 4: Inequalities in real-life scenarios
A caterer is buying muffins. She plans to spend $55. The muffins are each $4. Determine an inequality for this situation, with the number of muffins the Caterer will buy represented by m.
Step 1. Use words in the problem to determine what the symbol will be. If she has $55 to spend, then her spending’s must be less than or equal to 55.
55 ≥
Step 2. Determine the expression that represents the price of the muffins she will buy.
4m
Step 3. Represent these terms as an inequality.
55 ≥ 4m
Try the next two examples on your own using a method of your choice to solve. Record your ideas digitally, orally, or in print.
- A school is buying paint for the art room. The school has $75 to spend. Each jar of paint is $6. Determine an inequality for this situation, with the number of jars of paint the school will buy represented by p.
- A contestant at a contest is handing out cookies to 4 judges. The contestant has 18 cookies and they want to have at least 6 left. Use c to represent the amount of cookies each judge will get. Determine an inequality for this scenario. Is there more than one possibility?
Press ‘Answers’ to access a possible solution to check your work.
Problem 1
- $6p ≤ $75
- The school could buy 12 jars of paint which would cost $72. $72 < $75. If they bought 13 jars it would be $78 which is too much!
Problem 2
- 18 - 4c ≤ 6
- c could be anything less than 3. If they gave each judge 3 cookies, then they would have 6 left. If they gave each judge 2, they would have 10 left.
Consolidation
Task 1: Inequalities based on number line
Student Success
Think-Pair-Share
Use the descriptions or the number line to determine the inequality. Record your answer using a method of your choice. If possible, be prepared to discuss with a partner.
- A number line includes values from 1 to 10. There is a solid dot on the number 3 and an arrow extending from 3 and pointing to larger values.
- A number line includes values from 80 to 100, counting by 1s. There is a circle at number 89. There is an arrow starting at 89 and pointing towards values less than 89.
- A number line has values from 80 to 100, counting by 1s. There is a circle around number 98. There is an arrow which starts at 98 and points to numbers greater than 98.
Note to teachers: See your teacher guide for collaboration tools, ideas and suggestions.
Task 2: Real-life scenarios
Create your own real-life scenario where an inequality is required. Include the numerical or written inequality in words form, a number line representation or a table of values, and 5 possibilities in the solution set. You can record your response using a method of your choice.
Task 3: Think about your learning
Answer the following questions:
- Why is it important to identify inequalities?
- What are some strategies we can use in order to solve inequalities?
- What area of solving inequalities you will continue to deepen your understanding for?
Reflection
As you read through these descriptions, which sentence best describes how you are feeling about your understanding of this learning activity? Press the button that is beside this sentence.
I feel...
Now, record your ideas using a voice recorder, speech-to-text, or writing tool.