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.