Expressions, formulas and substitution
Terms, variables, coefficients and constants; replace a letter with a number (negative numbers too) and use formulas from real life. Read one step, play with it, then tap “I understand this”.
The parts of an expression
An algebraic expression like 4x + 3y − 7 uses letters for numbers. 4x means 4 × x: we leave out the times sign.
Take the expression apart
Tap a button to light up those parts.
Replace the letter with a number
Substitution means: put a number in place of the letter and work it out. If x = 2, then 3x + 5 = 3 × 2 + 5 = 11.
The substitution machine
Choose an expression and change x. Try negative numbers too.
If x = −3, then x² = (−3) × (−3) = 9, not −9. Always put negative numbers in brackets.
Without brackets, 3x with x = −2 looks like 3 − 2, which is 1. With brackets you read it right: 3 × (−2) = −6. The brackets keep the minus sign with the number.
Formulas in real life
A formula is a rule with letters that you can use over and over. A taxi owner does not have to think out every trip: he just uses the formula.
Use the formula
Choose a formula and change the values.
The letter is a place for any number. One formula like P = 2(l + b) works for every rectangle in the world. You just put the numbers in.
Like terms
Like terms have exactly the same letter with the same exponent: 3x, x and 12x are like terms. 3x and 3y are not, and neither are x and x². Only like terms can be added together: 3x + 5x = 8x.
Find the partners
Tap all the like terms, then tap “Check”.
Think of fruit: 3 apples + 5 apples = 8 apples. But 3 apples + 2 bananas stays 3 apples + 2 bananas.
x and y can be different numbers. 3 apples and 2 bananas are not 5 apples or 5 bananas. Only when the letters (and exponents) are the same do you add the numbers in front of them.
Play: substitute and calculate
Substitution game
Choose the right answer.
Correct: 0Check yourself
- Terms are separated by + and −. Coefficient = the number in front of the letter.
- Substitute: put the number in place of the letter. Negative numbers in brackets.
- Like terms: the same letter and exponent. 3x + 5x = 8x.
Write these points in your maths book. Read them again the night before the test.
Quick questions
Tap an answer. If you get one wrong, read why and go back to that step. You get new questions every time.
You ticked all 5 steps! Now you are ready for the quiz.- Practice sheet for this classQuestions + memo · 1 A4 pagePractice sheet
- Numbers, Patterns and Algebra8 pages · PDFPaperMemo
- Patterns and algebra8 pages · PDFPaperMemo
Ready for more? The Grade 7 formulas quiz gives you new questions every time.
- One step a day is enough. Ten calm minutes work better than an hour the night before the test.
- Make a formula for something at home together, like pocket money: “R20 a week plus R5 for every chore.” Then ask: “How much do you get if you do 3 chores?”
- Ask your child to tell you the rule in their own words. If they can explain it, they understand it.
- The ticks (“I understand this”) are saved on this device only. We never ask for names or emails.
Follows CAPS for Grade 7 Maths. Always check your teacher’s notes and textbook too.