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Algebra : Expressions, Equations, and Inequalities

Connections With Other Strands

Algebra is used in all areas of mathematics. Developing students’ algebraic reasoning in a variety of contexts also develops their problem-solving strategies, social-emotional skills and work habits.

The following examples illustrate how understanding algebra is applied in other strands of the course.

When examining each question, reflect on the knowledge and skills from the overall and specific expectations in the Algebra strand that students will use, as well as the connections to the key concepts.

Number: Exponents

Specific Expectations: B2.2, C1.4
Mathematical Processes: Connecting, Representing, Reflecting

​Students use the relationships between exponents to expand and simplify algebraic expressions and solve equations.

  1. Rewrite this algebraic expression in a simpler form. \(-x^2\left(-2x^2+13\right)+3x\left(-4x^3+12x-5\right)\)
  2. Determine at least two algebraic expressions equivalent to the expression \(12x^3-25x+6\) in the form of a polynomial composed of at least five monomials and using the four basic operations (+, -, ×, ÷).

​Data: Making Predictions

Specific Expectations: B1.2, C1.5, D1.3
Mathematical Processes: Problem Solving, Reasoning and Proving, Reflecting

Students are asked to collect data on the length of two body parts from a group of people, for example, foot, leg, arm, hand, head, waist. Students create a scatter plot and determine the equation of the linear regression model of their data. Students can use the equation from this regression model to make predictions such as:

  1. How long could the foot of a 200 cm tall person be?
  2. What values are possible? What is not possible? What are the limits?

Geometry and Measurement: Units of Measurement

Specific Expectations: B3.5, C1.5, E1.3, ​E1.4
Mathematical Processes: Problem Solving, Reasoning and Proving, Connecting

Claudia has a wooden box with a square base and a total area of 2184 cm². She’d like to construct a similar box with all dimensions doubled. However, she needs to convert the measurements to inches and feet to buy the necessary wood.

  1. Determine the total area of the new box in square inches.
  2. Knowing that she can buy boards measuring 1 foot by 1 foot, 1 foot by 2 feet or 2 feet by 2 feet, what would you suggest she buys? Justify your choice.

Financial Literacy: Budget

Specific Expectations: B3.5, C4.2, F1.4
Mathematical Processes: Problem Solving, Reasoning and Proving, Connecting, Communicating

The school’s woodworking class wants to make two types of wooden toys for local children.

The first toy is a train with three cars, and each toy costs $50 in materials.

The second toy is a wooden puzzle and costs $36 in materials.

The school budget is $1800.

  1. How many of each toy could be made? Justify your choice, using graphs and symbolic representations.
  2. Demand was so strong that next year, the school would like to produce 1.5 times as many toys. Suggest at least three changes to the budget to make this possible.

Multi-Strand Task

Specific Expectations: B3.5, C1.5, C3.2, C3.3, D1.3
Mathematical Processes: Problem Solving, Reflecting, Connecting, Communicating

Ask students to determine how many cards per second they can throw into a container (bin) placed 4 feet in front of them.

  1. Mrs. Trudel, is an expert card thrower with an average rate of 2.12 cards per second. To make the competition fairer, she gives a 50-card lead to her challengers. Using the average throw rate of one of your team members, determine how long the competition would have to last for Mrs. Trudel to catch up to your team member.
  2. Use the students’ data (number of cards in the tray, duration of the experiment), and ask them to ​​create a scatter plot.
    1. Is there a correlation between the two variables?
    2. What would be a ​good regression model to represent these data?

Reflection

  • How can high-impact instructional practices help students apply their understanding of algebra using context-appropriate strategies?
  • What characterizes high-impact instructional practices that assist students in making connections between algebra and all other mathematical strands?
  • How does the use of contexts from other strands promote the development of algebraic thinking in students and enable them to establish meaningful connections?