Primary 6 Algebra Study Guide
Primary 6 algebra in six short steps: a letter for a number, like terms, substitution, tables, equations and figures. Each step has a picture to work through and one question to try.
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What is algebra in Primary 6?
A letter stands for a number nobody has counted yet.
In ratio, your child drew a block and called it 1 unit. In algebra, the same block gets a letter, such as n. The letter is the number inside the box, not the box itself, so it can be added to, multiplied and shared out like any other number.
In this chapter, your child learns to:
- write an expression such as n + 3, 3n or n ÷ 3 from a story;
- collect like terms to write an expression in its simplest form;
- substitute a value for the letter and work out the expression;
- build one expression from a table of daily amounts;
- solve a simple equation to find the number the letter stands for;
- use the sides of a rectangle or square to find the letter.
Step 1
Algebraic expressions from words
Give the unknown number a letter, then write what the story does to it. If every box holds n buns, 1 box and 3 more buns is n + 3. Three boxes is n + n + n, written 3n with the times sign left out. Sharing 1 box into 3 bags gives n ÷ 3, which is usually written as the fraction n over 3. When the answer is an expression, the unit goes outside a bracket: (n + 3) buns.
Tap a story
A bakery packs kaya buns into boxes. Every box holds n buns. There are 4 boxes, and 2 more buns beside them. How many buns are there altogether?
Step 2
Simplifying algebraic expressions
Put the same kinds together: letters with letters, numbers with numbers. A term is a letter with its number in front, or a plain number, and it takes the sign written just before it. Collect the letter terms, then the plain numbers. When there is just one n, write n, not 1n. When no other terms can be combined together, the expression is in its simplest form.
Tap Next
Simplify 15 + 7n + 9 − 3n − 4 + 2.
Step 3
Algebra substitution
When the question gives the letter a value, every copy of the letter changes at once. Putting a number in place of a letter is called substitution: we now substitute n to be 6. Write the whole expression again with the number in place of every n, then work it out. The plain numbers come across untouched.
Tap Substitute
Find the value of 5n − 4 when n = 7.
Step 4
Algebra word problems with a table
One line in a table can stand for many days, so count the days first. Write the whole week as one line, in the order the table gives it. Then collect the terms with n, then the plain numbers. Substitute only at the end, when the question gives n a value.
Tap Next
A library lends 3n books each day from Monday to Thursday, and n + 12 books on Friday. How many books does it lend in the 5 days when n = 8?
Step 5
Solving simple equations
Put back what the story removed, then share the whole equally. When two things are the same amount, write them with an equals sign: that is an equation. Undo the story in reverse order. A short question can be done with arithmetic alone; an equation keeps a longer story tidy.
Tap Next
A baker fills 6 boxes with c cookies in each box. She has 4 cookies left over. She has 58 cookies altogether. How many cookies are in each box?
Step 6
Algebra perimeter and area questions
Fill in every side first, then add them. In a rectangle, opposite sides are equal; in a square, all four sides are equal. Perimeter means all four sides added, so write each side, collect the terms, and solve. Once the letter is known, each side has a length, and the area follows.
Tap Next
A rectangle is (2k + 1) cm long and 5 cm wide. Its perimeter is 40 cm. Find the value of k.
Primary 6 algebra questions, worked step by stepHave a go on paper first. Then open a hint, or reveal the working one line at a time.
Simplify 9k + 14 − 4k − 6 + k.
- Keep each sign with its term: 9k − 4k + k + 14 − 6.
- Letter terms: 9k − 4k + k = 6k.
- Plain numbers: 14 − 6 = 8. No other terms can be combined together.
Find the value of 8k − k ÷ 3 + 4 when k = 6.
- Substitute k to be 6: 8 × 6 − 6 ÷ 3 + 4.
- Multiply and divide first: 48 − 2 + 4.
- Then from left to right: 48 − 2 + 4 = 50.
A stall bakes 3m muffins each day from Monday to Thursday. On Friday it bakes 5m − 8 muffins, and on Saturday 4m + 30 muffins. (a) Write the total for the six days in terms of m, in its simplest form. (b) Find the total when m = 12.
- One line, in table order: 4 × 3m + 5m − 8 + 4m + 30.
- Collect: 12m + 5m + 4m − 8 + 30 = 21m + 22.
- Substitute m to be 12: 21 × 12 + 22 = 252 + 22 = 274.
Hui Min buys 4 boxes of markers with b markers in each box. She gives 9 markers to her brother and then buys 5 loose markers. She now has 48 markers. How many markers are in each box?
- As it happened: 4b − 9 + 5 = 48.
- Collect the plain numbers: 4b − 4 = 48.
- Undo the minus 4: 4b = 48 + 4 = 52.
- Share into 4 boxes: b = 52 ÷ 4 = 13.
A rectangle is (3d + 2) cm long and (d + 4) cm wide. Its perimeter is 52 cm. (a) Find the value of d. (b) Find the area of the rectangle.
- All four sides: 3d + 2 + 3d + 2 + d + 4 + d + 4 = 52.
- Collect: 8d + 12 = 52, so 8d = 52 − 12 = 40.
- d = 40 ÷ 8 = 5.
- Length 3 × 5 + 2 = 17 cm, breadth 5 + 4 = 9 cm, area 17 × 9 = 153 cm².
Step 7
Check yourself
Five short questions across the chapter. Nothing is saved; each answer points to the subtopic to look at next.
1. A tray holds t eggs. There are 5 trays and 4 more eggs. How many eggs are there?
2. Simplify 8n + 10 − 2n − 3.
3. Find the value of 6n − 5 when n = 4.
4. A stall sells 2n cups of juice each day from Monday to Friday, and 3n + 6 cups on Saturday. Write the total in terms of n.
5. A square has sides of (k + 3) cm. Its perimeter is 36 cm. Find the value of k.
Algebra arrives in Primary 6 as a new name for something your child already knows. The ratio unit becomes a letter, and the same block drawings carry on: blue for the number nobody has counted, purple for the numbers given. If your child gets stuck, ask what the letter stands for, in words, before any working is written.
Ask your child to write the working as one line that keeps going, the way the steps above do: the whole sum first, then the like terms, then the value. When a letter has been found, put it back into the story and see whether the numbers fit. That check needs no answer key.
More study guides
P6 Algebra lessons and practice
6 lesson videos and 53 questions across six subtopics, from Basic to Challenge, each with a worked solution.
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