Singapore Math Drills Team · 3 November 2026
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Every wizard school needs a spellbook. This one is an old hardback wrapped in brown paper, with glowing runes drawn on the cover. The curtains are drawn, the enchanted lights are fairy lights over the bed, and the wand is a stick from the garden. The Mastermind, in a paper cone hat and a starry blanket for a robe, announces the ancient secret: "Five questions. Every day." The Partner, with a bath towel over his shoulders and a juice box in hand, is not convinced. "...Five?"
That is The Ancient Spellbook, the sixth episode of our comedy series, The Mastermind. Watch it first (it is under a minute), then read on. The spell at the heart of it is Primary 6 algebra.
After a practice montage in which a tap of the wand sends one simple equation after another floating down onto the desk, the spellbook's clasp pops and the book falls open on the final spell: 2a + 5 = 17. It is worked out on screen: 2a = 17 − 5 = 12, so a = 12 ÷ 2 = 6. Then it is checked: 2 × 6 + 5 = 17. The Partner is flat: "That's not a spell. That's algebra." The answer comes in a whisper: "Shh. Ancient algebra."
The good news is that this spell can be taught, and it needs no magic at all.
Algebra arrives in Primary 6. The big idea is small: a letter just stands for a number. In 2a + 5 = 17, the letter a is a number we have not found yet. It is a mystery number, not a mystery word.
Two bits of notation are worth saying aloud, because they trip up many children:
2a means 2 × a. It is two groups of the mystery number, not "twenty-something". If a were 6, then 2a would be 12.2a + 5 = 17 says that two a's and 5 more make exactly 17.At this level the equations are simple ones with a whole-number coefficient, such as a + 4 = 9, 3a = 21 or 2a + 5 = 17. The spell list in the episode links Algebra with Ratio and Percentage, the other two Primary 6 topics on the mission chart.
The method is to undo the steps in reverse order. Think about how 2a + 5 was built: start with a, double it, then add 5. To get back to a, undo those steps in the opposite order: take away the 5 first, then halve.
Step 1: Say what it means. Two groups of the mystery number, plus 5 more, make 17.
Step 2: Draw the bar model. Draw one long bar for the total, 17. Split it into three parts: two equal bars, each labelled a, and a short bar labelled 5.
| a | a | 5 |
|---|---|---|
| Total: 17 |
Step 3: Undo the adding. The last thing done was "plus 5", so take the 5 bar away first. That leaves the two a bars: 2a = 17 − 5 = 12.
Step 4: Undo the doubling. Two equal bars make 12, so each bar is half of 12: a = 12 ÷ 2 = 6.
Step 5: Check by putting the answer back in. Replace a with 6 in the original: 2 × 6 + 5 = 12 + 5 = 17. It matches, so a = 6 is right.
Step 5 is the one that makes a child confident. They no longer need to wait for a teacher to say "correct". The equation tells them. If the check does not give 17, something went wrong, and they can go back and look.
The practice montage in the episode shows four quick equations. Each one is solved by one undo step, and each is checked the same way:
| Spell | Undo | Answer | Check |
|---|---|---|---|
a + 4 = 9 | take away 4: 9 − 4 | a = 5 | 5 + 4 = 9 |
3a = 21 | share into 3: 21 ÷ 3 | a = 7 | 3 × 7 = 21 |
a − 7 = 5 | put the 7 back: 5 + 7 |
Notice the pattern: undoing uses the opposite operation. Adding is undone by taking away, taking away by adding back, multiplying by sharing equally, and sharing by multiplying. The third spell is the one to watch: a − 7 = 5 is undone by adding 7, which gives 12.
If the letters feel slippery, think of paper cups. Hide the same number of counters under two cups, then put 5 loose counters beside them. Tell your child there are 17 counters altogether. Take away the 5 loose counters and 12 are left under the cups. Two cups hold 12, so each cup holds 6. Lift a cup to check. Objects first, then a drawing, then the number sentence: this is the concrete, pictorial, abstract order of Singapore math teaching, and the bar model is the drawing in the middle.
2a + 5, the 5 was added last, so it comes off first.a − 7 = 5 answered as a = 5 − 7. Ask, "Was something taken away from a? How do we put it back?"2a as 2 + a. If a is 6, then 2a is 12, not 8. Substituting a number for the letter makes the meaning clear.2 × 6 + 5 takes ten seconds and catches most slips.You do not need worksheets for this. Paper, a pencil and a few counters or coins are enough.
2a + 3 = 11. Hand it to your child to solve. Swap roles afterwards. Building an equation is a good way to see why undoing it works.3a + 2 = 14, and ask for a bar model before any numbers: three equal a bars and a bar of 2, with a total of 14. Then 3a = 14 − 2 = 12, a = 12 ÷ 3 = 4, and the check is 3 × 4 + 2 = 14.Keep each session short and stop while your child still wants to play. When your child is stuck, ask "What was done last?" before showing a step, and praise the method rather than the speed.
If your child is also working on word problems, our bar models parent guide shows the same drawing used for other topics, and our guide to Primary 6 sample questions explained walks through the shape of a P6 paper. Looking further ahead, moving from P6 to Sec 1 covers the bigger picture.
In the episode, the ancient ritual is five questions a day, and the day counter goes Day 1, Day 7, Day 30. It only ever goes up. Algebra becomes comfortable the same way: a few equations, met often and checked with a picture and a quick substitution your child trusts.
That is the idea we built Singapore Math Drills around:
The Mastermind guards his spellbook to the very end. Then, quietly: "Shh. Ancient algebra."
Try a free interactive Primary 6 worksheet and see how calm practice feels, with no signup or credit card required.
a = 1212 − 7 = 5 |
4a = 32 | share into 4: 32 ÷ 4 | a = 8 | 4 × 8 = 32 |