Lesson 1:
Solving Inequalities involving two operations
(Approximate Length: 2- 60 Minute Lessons)
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Content
Content
N.B. This lesson does not follow the three part math format, it requires direct instruction.
Expectations:
Expectations:
Algebra
C2.3: Solve inequalities that involve two operations and whole numbers up to 100, and whole numbers up to 100 and verify and graph the solutions
Big Idea:
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
Learning Goals
We want students to understand...
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
Success Criteria
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
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)
Math Background: Knowledgehook: Simple Linear Equations
Prior Knowledge
Prior Knowledge
Solving Equations with One Variable (using algebra tiles)
(N.B. You may need to look at the Grade 5 lesson and pre teach, as inequalities are new to the 2020 math curriculum.)
Find out if your students understand solving an equation for one variable. Also, you can pre teach how to represent variables using the algebra tiles app.
Pedagogy
Pedagogy
Minds On
Minds On
Source: Math is Fun Website
1)Review the symbols <, >, =
2) Provide students with this mind's on task: https://docs.google.com/document/d/1vglUaInRFihjoZ-fGQb7osq-KEhafHSjTuVrsYrq6_k/edit?usp=sharing
One Step Inequalities Khan Academy
Open Questions:
Open Questions:
The solution to an equation involving at least one big number is 32. What could the equation be?
Action!
Action!
Direct instruction: Source: Khan Academy
Solving two operation Inequality questions: Demonstrate.
Two step Inequality problem(for more see Khan academy website):
Timmins generally gets 20 cm more snow than New Liskeard by January. In 2020, they both got about 1/4 less of the snow they usually get but made up for it in rainfall precipitation, both averaging about 20 cm of rain in a year. What can you say about the amount of snow Timmins had in comparison to New Liskeard? What would you say about the total accumulation of precipitation when comparing both communities? How do you know?
Student task: https://docs.google.com/document/d/1a9A8TT3YyRy1no0-duuIMQ4f9gd5HipsoCAB9JzIt_g/edit?usp=sharing
Open Question: Suppose 3 x A + 4 x B=96. Determine four possible pairs of values for A and B. Choose two of your pairs. How does the difference in the A values compare to the difference in the B values?
Sample Response
A=4 and B= 21, A=8, and B=18, a=0 and B=24, A=32 and B=0
When I compared 4 and 21 with 0 and 24, I saw that when A went down by 4, B went up by 3. OR
When I compared 4 and 21 with 8 and 18, I saw that A went up by 4, B went down by 3.
Source: Small, M. (2016) Open Questions: For the Three-Part Lesson Grades 4-8 Measurement, Patterning and Algebra. Pg.114
Consolidation Of Learning
Consolidation Of Learning
Open Question: Consolidate
A and B are whole numbers and 3 x A = 2 x B. What do you know about A? What do you know about B? What might the equation represent?
Sample response:
I know that A must be an even number since 3 x A is even only if A is even and 3 x A must be even because it equals 2 times something. I know that A is less than B but more than half of B unless they are both 0. The equation could be the price of tickets if two of one kind of ticket costs the same as three of another kind of ticket.
Source: Small, M. (2016) Open Questions: For the Three-Part Lesson Grades 4-8 Measurement, Patterning and Algebra. Pg.115
Independent Task / Assessment Opportunities
Independent Task / Assessment Opportunities
Independent Practice:
One-Step and Two-step Inequality Equations (Make a Practice Page)
Graphing Inequalities using Desmos
Click here for support or to find out why Desmos is a great math tool/resource.
Technology
Technology
Algebra Tiles App
Algebra Tiles App
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