Grade 5 Lesson 1:

Solving Inequalities

(Approximate Length: 2- 60 Minute Lessons)

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Content

N.B. Inequalities are part of the new math curriculum, however you do not need to do the Grade 4 lesson prior.

This lesson includes the background knowledge needed.

Expectations:

Algebra

C2.3: Solve inequalities that involve one operation and whole numbers up to 50, and verify and graph the solutions

Big Idea:

In this lesson, to the best of their ability, students will learn to think critically and creatively and use positive motivation and perseverance. They will apply strategies such as: using an iterative approach by trying out different methods, including guessing and checking to promote problem solving. They will be making connections, evaluating choices, reflecting on and assessing strategies.

Learning Goals

We want students to understand...

What an inequality is.
How to solve an inequality
How to verify it is correct.
How to show the expression on a number line.

Success Criteria

I understand that any single algebraic expression describes many situations.
I understand what an inequality is.
I can test variables to prove the inequality true or false.
I understand how to graph the expression on a number line.

teacher background

Variables-symbols used to represent unknown and/or varying values are used in expressions. An expression is something like m + 5, which indicates that 5 is added to a number (m), no matter what the number m is. Students must learn how to recognize that “n -10” means “take 10 from the value of n” as compared to “10- n” which means “how much less n is than 10”.
They must recognize that any single algebraic expression describes many situations. For example, m + 5 > 10 describes a multitude of situations and how to express it on a number line.
Graphs are effective models for describing relationships between various variables and quantities.
Source: Adapted from: Small, M. (2013) Making Math Meaningful to Canadian Students, K-8. Nelson Education (pp.620-621)

Prior Knowledge

Representing Variables

Find out if your students understand how to represent variables. You can pre teach using algebra tiles app.
Knowledge Hook Mission

Pedagogy

Minds On

Source: https://www.mathsisfun.com/algebra/inequality.html

1)Review the symbols <, >, =

2)Have the students complete this minds on task:

https://docs.google.com/document/d/1vglUaInRFihjoZ-fGQb7osq-KEhafHSjTuVrsYrq6_k/edit?usp=sharing

Open Questions:

1.Fill in the blanks to make a three-digit number and a one digit number. Explain how you chose your number.

Sample Response: I chose 400 / 5. I chose 5 first and multiplied it by 80 to get 400.

2. What if you change the equal sign in the question above to a greater than or less than sign (inequality sign). Give two examples: a set of numbers that could satisfy the answer, and a set of numbers that couldn't satisfy it.

Student handout for this task: https://docs.google.com/document/d/1zFwPyO67FKVjVqD3xBTtssUGCpzFM2D3MwjgQXS9Q1c/edit?usp=sharing

Additional Activity: Introduction to Inequalities: Number Talks: Minilessons for Extending Addition and Subtraction: “Money Model: Equivalence, Variation” Pg. 63 (need Canadian Coins and some foreign coins)

Action!

Source: https://www.mathsisfun.com/algebra/inequality.html

Teacher directed: a) Discuss what inequalities are: Inequality tells us about the relative size of two values. Mathematics is not always about "equals", sometimes we only know that something is greater or less than.
b) Look back at their inequality statements for the minds on activity. Are they correct? Did they use the less than symbol? What did they come up with for greater than inequality statements?
c) Discuss “greater than and equal to” or “lesson than and equal to” and how the symbols are written .
Give the example: You must be 13 years or older to watch some movies. Written as an inequality: 13
Solving Inequalities: (Go to practice at the end of the page.)

Open Questions: Action:

You have learned a lot of facts about operations. For example, you can add numbers in any order: a + b = b + a. Choose three facts about operations and represent each fact using variables.

Sample Response: You can multiply numbers in any order: a x b = b x a. Another fact about multiplication is that you can halve one factor and double another and not change the product:

A x b= (a x 2) x (2 x b). When you subtract one number from another number, you can add the same amount to both numbers without changing the difference: a-b = (a + c) - (b + c).

Source: Small, M. (2016) Open Questions: For the Three-Part Lesson Grades 4-8 Measurement, Patterning and Algebra. Pg.82

Consolidation Of Learning

Source: Math is Fun Website

Follow the explanations on the above website under these subheadings:

1)”Adding Or Subtracting a Value":

Use these examples and use a number line to show inequality.

2) “What do I do if the “x” is on the right

3) Multiplying or Dividing by a Value (positive)

Inequalities using addition and subtraction: https://www.youtube.com/watch?v=UTs4uZhu5t8

Click on this link for support and visuals on: How to Graph Inequalities

Additional Support: Inequalities using addition and subtraction video

Open Question: Consolidate

The solution to four different equations is 5. One is an addition equation, one is a subtraction equation, one is a multiplication equation and one is a division equation. What could the equations be?

Have students record their thinking on this sheet:

https://docs.google.com/document/d/1mIYO1nkcNuFk8xYkUyKwUWC8J4RWCGVlQ4ohUbTZPLk/edit?usp=sharing

Source: Small, M. (2016) Open Questions: For the Three-Part Lesson Grades 4-8 Measurement, Patterning and Algebra. Pg.83

Independent Task / Assessment Opportunities

Independent Practice:

Comparing Values(Review)

Adding or Subtracting A Value, One-Step Multiplying and Dividing, (Make a Practice Page)

Graphing Inequalities (Go to practice at the end of the page)

Practicing: Algebraic equations basics, one-step equation intuition, one step addition and subtraction equations, one-step multiplication and division equations

Khan Academy

Graphing Inequalities Using

Desmos

Click here for support or find out why Desmos is a great math tool/resource.

Technology

Algebra Tiles App

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