Primary 2 Maths | Times Tables 2-9 Guide | Groups Of, Commutativity, Deriving Unknown Facts

2026-11-09

Tutor lesson-prep guides · Primary Maths

A child recites seven eights are fifty-six and then says fifty-four, because what was memorised was the sound of the words, not seven groups of eight. Put the array back on paper and the wrong sentence cancels itself.

Objectives — Students can: (1) restate any times-table fact as groups of something and draw it as an array or on a number line; (2) explain with an array why 8 times 7 and 7 times 8 give the same answer; (3) derive a forgotten fact from a known one, for example 7 times 8 from 7 times 7.

01 Prerequisites (3-minute check)

If any of these fails, fix it before the lesson starts.

Skill	Quick check	Pass mark
Counting in 2s, 5s, 10s	Count up in fives to 50	Counts accurately
Addition with carrying	What is 7 plus 7 plus 7	Correct within 24
Rows and columns	How many in 3 rows of 4	Counts them out

02 Lesson flow (60 minutes)

Time	Stage	Tutor does	Student does
0-6 min	Diagnose	Ask for the seven times table and note where it stalls	Recite once
6-16 min	Groups of	Draw each fact as 7 rows of 8 dots	Draw one and explain
16-28 min	Order	8 times 7 and 7 times 8 are one array turned 90 degrees	Give three examples
28-42 min	Derive	From 7 times 7 equals 49 add one more 7 to reach 56	Derive two facts
42-52 min	Quick recall	Only the 6, 7, 8 and 9 families	Answer orally
52-60 min	Exit check	Three questions collected and marked	Work independently

03 Teaching script (read it out)

Scene 1: Every fact must turn back into groups of something

Seven eights are fifty-six is not a string of sounds; it is 7 rows of 8 dots. 7 times 8 means 7 rows with 8 in each row, so 56 dots in total.
Why draw it? A child who has memorised a wrong sentence sees the gap the moment the array appears. Counting the array gives 56, and the number itself rejects the wrong sentence without the tutor repeating anything. The fixed order is: draw the array, count it, then write the number sentence. Never the other way round.

Students do: draw 4 rows of 6 dots, count 24, and write 4 times 6 equals 24.

Scene 2: Order does not matter, so half the facts are free

Turn an array 90 degrees and rows become columns while the count stays the same. So 7 times 8 and 8 times 7 both give 56.
The practical value: the 2 to 9 tables hold 81 facts, and commutativity removes roughly half the memorising. Learn 7 times 8 and 8 times 7 comes free. Be explicit that this only works for multiplication. Addition also swaps, subtraction and division do not.

Students say: using the array, explain why 6 times 7 equals 7 times 6 equals 42.

Scene 3: A forgotten fact can be rebuilt from its neighbour

A missing 7 times 8 does not mean starting the table again. From 7 times 7 equals 49, add one more 7 to get 56; or from 8 times 8 equals 64, subtract one 8 to get 56. Both routes agree, which is the point: the answer survives two independent checks.
That is also the sanity check. The answer must sit between 7 times 7 and 8 times 8, so 56 fits between 49 and 64. An answer of 54 does not, because 54 is only 5 above 49.

Students do: without reciting, derive 9 times 8 equals 72 and name the fact used as the base.

04 Question types and worked steps

Type	Example	Steps	Answer
Direct recall	What is 7 times 8	Rebuild it as 7 groups of 8 and count	54 means the words were memorised wrongly
Commutativity	Relationship of 8 times 7 and 7 times 8	One array turned 90 degrees	Same answer, not one more
Deriving	Forgotten 9 times 8	Use 8 times 8 minus one 8	Name the base fact
Word problem	6 sweets per bag, 4 bags	Write the number sentence, compute, state units	Answer sentence needs units

Sanity check (teach this): Sanity check: 7 times 8 is 56, not 54; swapping the factors never changes the product, 6 times 7 is 42; a product exceeds each factor greater than 1; 49 plus 7 and 64 minus 8 both reach 56; the largest fact in the tables is 9 times 9 equals 81.

05 Independent practice (3 questions)

Question	Answer	What to watch
Arrays	Draw the arrays for three facts	Rows and columns match the factors
Swapping	Write four facts with the factors swapped	Products unchanged
Deriving	From 7 times 7 derive 7 times 8 and 7 times 9	Base fact named
Word problems	Four bags of 6	Units written

06 Common mistakes and what to say

Mistake	Student writes	Say this
Memorising neighbouring numbers	Seven eights are fifty-four	Was that 7 groups of 8 or 8 groups of 7? Draw it and count.
Treating the swap as plus one	Thinking 8 times 7 is one more than 7 times 8	Turn the array round. Does the number of dots change? Count together.
Deriving with the wrong step	Getting 54 from 49	How many 7s is 7 times 8 more than 7 times 7? What is 54 minus 49?
Adding in a word problem	Writing 4 plus 6 for 4 bags of 6	Four bags with 6 in each is four groups of six. Which operation is that?

07 Homework (paper, section and question numbers)

Primary maths chapter index — All chapters by level
Teaching guide index — Same structure, other subjects
Redo this chapter — Questions 1 to 4 again, drawing the array before writing each sentence

08 Exit check (last 5 minutes)

Question	Answer	Decision
7 times 8	56	54 means a memorised error, back to act one
Are 8 times 7 and 7 times 8 the same	Yes, both 56	One more means act two again
Forgotten 9 times 8	8 times 8 minus 8 gives 72	Starting the table again means act three

09 Tutor FAQ

Must they be word perfect?

Fluent, but fluent means being able to say groups of, not reciting fast. A fast reciter still picks the wrong operation in word problems.

Can half be skipped?

Commutativity saves about half, but the 6, 7, 8 and 9 families must each be secure, because they dominate fractions and division.

When does division start?

Only after the tables are secure. Teaching division too early produces guessing, and guessing cannot be diagnosed.

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A TutorZone lesson-prep guide. Written by the TutorZone team; questions and lesson flow are original and are not taken from any school or publisher material.