Represent and solve problems with two unknowns efficiently
I can represent problems with two unknowns and solve using an efficient strategy.
Represent and solve problems with two unknowns efficiently
I can represent problems with two unknowns and solve using an efficient strategy.
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Lesson details
Key learning points
- The model can represent a scaling structure with one part being __ times the size of the other.
- The model can represent an additive structure.
Keywords
Coefficient - A coefficient is number used to multiply an unknown value.
Efficient - To solve something efficiently means to solve a problem quickly whilst also maintaining accuracy.
Common misconception
Pupils think that the removal of the multiplication symbol can result in the number becoming a two-digit number rather than two, single digits being multiplied together.
Using the language of 'lots of' may support pupils to see that an algebraic equation with coefficients represents multiplication. For example: 40 can be read as 'four lots of 0'.
Equipment
Licence
Lesson video
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Prior knowledge starter quiz
6 Questions
Q1.When the sum and the multiplicative relationship between two unknown numbers is known, how many possible solutions are there?
Q2.What is the value of a in this equation? a × 6 = 42
Q3.a represents a larger numbers and b represent a smaller number.
The sum of a and b is 340, and the difference between them is 40
What number does b represent?
Q4.Grace is 32 years younger than her father. The sum of their ages is 64 years. How old is Grace’s father? years old.
Q5.The sum of two numbers is 240
One number is five times the size of the other number. What are the two numbers?
Q6.The sum of two numbers is 500
One number is one-third times the size of the other number. What is the value of the largest number?
Assessment exit quiz
6 Questions
Q1.5 × a + 7 × b can also be written as:
Q2.Tick the problems that, when written as a pair of equations, would share the same coefficient.
Q3.What is the value of the gap marked ? in the bar model? Give your answer in pence. p
Q4.What is the value of b in the bar model? Give your answer in pence. p
Q5.What is the value of k? Give your answer in pence. p