Minds On
Area of a rectangle
The area of a rectangle is found by multiplying the base length by the height. We use the formula:
The variable b represents the base length and the variable h represents the height. The formula for the area of a rectangle is an equation.
Using this equation, solve for the height of the rectangle if you know that the area is 35 cm2 and the base length of the rectangle is 7 cm.
What strategy did you use to figure it out? Record your ideas digitally, orally or in print.
Action
Exploring equations
Task 1
Four different numbers added together have a sum of 80.
What four numbers could they be?
What are some possible numbers?
Hint: You could have any numbers that total 80. You could use guess and check to see if the numbers work.
Press ‘Answer’ to reveal the answer to the problem.
How could we write: Four different numbers added together have a sum of 80 using variables?
Press ‘Answer’ to reveal the answer to the problem.
Task 2
Three students (Neebin, Clara and Gabby) shared 18 pencil crayons amongst themselves.
Can you rewrite this as an expression with variables?
Press ‘Hint’ to reveal a hint about the problem.
Neebin took double the amount of pencil crayons than Clara. Gabby took triple the amount of pencil crayons than Clara. How many pencil crayons did Clara take?
Can you use the information provided to figure out how many pencil crayons each student took?
Press ‘Answer’ to reveal the answer to this problem.
Neebin = a, Clara = b, Gabby = c
So,
So b is Clara, Clara took 3 pencils.
a is Neebin, Neebin took 6 pencils.
c is Gabby, Gabby took 9 pencils.
Calculating distance
Three cars are driving to the city. Car 1 is 2 km ahead of Car 2, and Car 2 is 4 km ahead of Car 3.
- If Car 1 is at 30 km, how far are Car 2 and Car 3?
- If Car 3 is at 25 km, how far are Car 1 and Car 2?
- The total distance of the three cars is 112 km, how far is Car 2?
Create equations to represent each distance relationship.
How can you use models to solve each distance?
How can you check your answer?
Record your ideas digitally, orally or in print.
Press ‘Answer’ to reveal the answer to this problem.
Let Car 1 = a, Car 2 = b, and Car 3 = c.
1. If car 1 is 30 km, then:
And
So, Car 2 is 28km and Car 3 is 24km.
2. If Car 3 is at 25km, then:
So, Car 1 is at 31km and Car 2 is at 29km.
3. If the total distance of the three cars is 112km, then:
If
Then,
Consolidation
Algebra problem solving
Translate the sentences into equations and solve.
- Seven less than triple a number is twenty-six.
- If a number is tripled, the result is ninety.
- 4.2 plus a number reduced by two gives you eighteen.
- Three times a number is six and three tenths.
- Increase the product of one and two tenths and a number by 24.8 to obtain 56.
- A number divided by six is twenty and one-half.
- If a number is tripled and then reduced by nine, the result is sixty-six.
Press ‘Answer’ to reveal the answer to this problem.
Brainstorm your own problem and then record your ideas using a method of your choice:
- Create a problem that can be solved using an equation with multiple terms.
- Record the equation, then solve the problem.
- How could you have solved the problem without creating an equation? Explain.
Be prepared to share your work.
Reflection
As you read the following descriptions, select the one that best describes your current understanding of the learning in this activity. Press the corresponding button once you have made your choice.
I feel...
Now, expand on your ideas by recording your thoughts using a voice recorder, speech-to-text, or writing tool.
When you review your notes on this learning activity later, reflect on whether you would select a different description based on your further review of the material in this learning activity.