Problem solving with expressions and equations | Maths

Starter quiz

Which of the below accurately completes the sentence? An algebraic term __________
- must contain an $x$
- must contain a constant.
- contains at least one variable or unknown. ✓
- must have an equals sign after it.
Simplify $a+2b+c+b+2c+d$ by collecting like terms.
- $a+3b+3c+d$ ✓
- $a+2b^2+2c^2+d$
- $a+2bc+2bc+d$
- $a+4bc+d$
Pick a number, any number. Double it. Add 10. Halve your answer. Subtract your original number. What did you notice?
- There is no pattern.
- The answer is always the number you started with.
- The answer is always 5. ✓
- The answer is always 5 but it only works for whole numbers.
"Pick a number, any number. Double it. Add 10. Halve your answer. Subtract your original number". Which of the below expressions models this?
- $n \times 2 +10 \div 2-n$
- $(n \times 2 +10) \div 2-n$ ✓
What number comes next in this sequence? $n, n+1, n+2, n+3...$
- $4$
- $4n$
- $n+4$ ✓
- $4n+6$
Add any two consecutive whole numbers. Which of the below are true?
- The result is always odd. ✓
- The result is always "One more than double the smaller of your two numbers". ✓
- The result is always "One less than double the bigger of your two numbers". ✓
- The result is always even.
- The result can be odd or even.

$n + (n+1) + (n+2)$ is an algebraic __________ for the sum of three consecutive numbers.
- term
- expression ✓
- equation
- formula
Some ink has spilled onto this addition pyramid. What would the expression in the top box of the pyramid be?
- $a + b + c$
- $2(a + b + c)$
- $a + 2b + 2c$
- $a + 2b + c$ ✓
If we were working on a proof about six consecutive whole numbers, which expressions would we use?
- $n, n, n, n, n, n,$
- $n, n+6$
- $n, 2n, 3n, 4n, 5n, 6n$
- $n, n+1, n+2, n+3, n+4, n+5, n+6$
- $n, n+1, n+2, n+3, n+4, n+5$ ✓
We can express the number trick, "Pick a number. Multiply it by 6. Add 15. Divide by 3. Subtract 5" algebraically as (6n+15)\div3-5$$. What does it prove?
- We end up with the number we started with.
- We always end up with double the number we started with. ✓
- We always end up with 2.
Sam writes $n+(n+1)+(n+2) \equiv 3n+3 \equiv 3\times n+1$ and says, "I have proven that the sum of three consecutive numbers is one more than a multiple of 3". Where is their error?
- $n+(n+1)+(n+2)$ are not consecutive numbers.
- Adding $n+(n+1)+(n+2)$ incorrectly.
- Incorrectly factorising $3n+3$ ✓
Which of the below algebraic expressions supports the proof that the sum of two consecutive whole numbers is always odd?
- $n + 2n \equiv 3n$
- $(n) + (2) \equiv n+2$
- $n + (n+1) \equiv 2n+1$ ✓

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Standardised notation is important when using algebra.
Algebra allows us to generalise real life problems.
Algebra allows us to express relationships so that everyone can understand them.

A variable and an unknown are the same thing.

A variable's value is not fixed. It can take any value within a given range. This means algebraic statements using variables can form proofs

Expression - Expressions contain one or more terms, where each term is separated by an operator.
Variable - A variable is a quantity that can take on a range of values.