Multiplication and Division Facts: a week of ready-to-teach maths

Five days of lessons for Year 4 Algebra. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet, plus cut-out fact triangles and tricky-fact cards, a mini-check and every answer.

Start here: five minutes to Monday

1. Skim the week at a glance on the next page.
2. Print the five days. Each day is two A4 sheets: a plan and a worksheet.
3. Cut out the two card sheets once; the cards are reused across the week.
4. Open the free interactive unit on your board. Every plan tells you which picture to show and which buttons to press.
5. Teach straight from the plan. Timings, talk prompts, misconceptions and answers are all on the one page.

No maths background needed

This pack is written for the busy generalist teacher. Each plan explains the idea in plain words, lists the misconceptions children bring, and gives the answers. Recall matters, but the week does not rely on chanting. Each fact is an array, comes with a partner and two division facts, sits in a table with a pattern, and can be rebuilt from a fact already known. A child who forgets 7 × 8 can still reach 56 quickly, and that is what makes the facts stick.

One day, one lesson

The five lessons fill a week of maths, one lesson of about 50 minutes a day. Run them in order: each day stands on the one before. Every plan marks a split point if your timetable runs two shorter sessions.

A few minutes every day

Fluency grows from short, frequent practice. Each plan suggests a two-minute warm-up with the fact triangles. Keep it going after the week: a quick round a day does more than a long test once a term.

The week at a glance

One lesson a day for a week. Each day stands on the day before, so run them in order.

How the week builds

Days 1 and 2 halve the work: every fact comes with a partner from turning the array, and with two division facts from its family. Day 3 finds the patterns that make each table easier to hold. Day 4 rebuilds the tricky facts from known ones, and Day 5 stretches the same facts to bigger numbers in the head. It builds on Finding Unknowns (AC9M4A01) and on multiplying by 10 (AC9M4N05).

Materials for the week (one trip)

• From the classroom: scissors, pencils, coloured pencils (Day 3), this pack printed.
• Optional: counters or square tiles for building arrays on Day 1.
• Cut out once, use all week: the fact triangles and the tricky-fact cards in this pack.

Words for the word wall

array, row, column, factor, product, multiply, divide, fact family, times table, pattern, double, halve, strategy

Dear families

This week in maths, Year 4 works on the multiplication facts to 10 × 10 and the division facts that go with them, and on using them for bigger numbers without a calculator.

Try this at home

• Play two minutes a day: cover one corner of a fact triangle and say the missing number.
• Spot arrays: egg cartons, muffin trays, windows. How many rows? How many in each row?
• If a fact is forgotten, rebuild it: 9 × 7 is 10 × 7, take away one 7.
• Try a bigger one: 6 × 12 is 6 × 10 and 6 × 2. What is 7 × 30?

My facts this week

Fill one row a day. Write a fact you found tricky, and the known fact that helped.

Printed from the free seegongsik Multiplication and Division Facts teaching pack · seegongsik.com/au/y4/algebra/AC9M4A02/pack

Facts as arrays

A multiplication fact is an array: 7 rows of 8 is 7 × 8, and the array holds 56 dots. Turn the array on its side and it becomes 8 rows of 7, so 8 × 7 is 56 too. Every fact children learn gives them its partner free, which halves the facts to learn.

We are learning to

• read an array as rows times columns,
• write both multiplication facts for an array,
• use a fact we know to give its turnaround.

Success criteria

• I can write two multiplication facts for an array.
• I can say a fact’s turnaround and explain why it has the same answer.

You need

Counters or square tiles, a handful per pair. The fact triangles (cut-out sheet 1) for the warm-up. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with Part B.

Watch for these ideas

• Counting every dot one by one. Count one row, then count in rows: 8, 16, 24.
• Expecting 4 × 6 and 6 × 4 to have different answers. The array is the same dots.
• Swapping rows and columns partway. Rows go across; say which you counted first.

Answers

• Part A: 4 rows of 6, 4 × 6 = 24, turned 6 × 4 = 24; 3 rows of 7, 3 × 7 = 21, turned 7 × 3 = 21; 5 rows of 8, 5 × 8 = 40, turned 8 × 5 = 40.
• Part B: 6 rows of 3 (or 3 rows of 6): 6 × 3 = 18 and 3 × 6 = 18. Part C: 9 × 2 = 18; 8 × 3 = 24; 7 × 5 = 35; 6 × 10 = 60.

Facts as arrays

A. Write both facts for each array

B. Draw an array for 6 × 3. Write both facts.

C. Free facts: write the turnaround of each fact

Fact families

Every multiplication fact belongs to a family of four: 6 × 7 = 42, 7 × 6 = 42, 42 ÷ 6 = 7 and 42 ÷ 7 = 6. Division asks the multiplication question backwards: 42 ÷ 6 means how many sixes make 42, or 6 times what is 42. A child who knows the multiplication fact already knows two division facts.

We are learning to

• write the four facts in a fact family,
• find a division fact by thinking of its multiplication fact,
• find a missing number in a multiplication or division fact.

Success criteria

• I can write all four facts in a family.
• I can solve a division by asking which multiplication fact it comes from.

You need

The fact triangles (cut-out sheet 1), one set per pair. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with the missing numbers.

Watch for these ideas

• Dividing a factor by the product, as in 7 ÷ 8 = 56. The product is always the number being divided.
• Thinking order does not matter in division as it does in multiplication: 42 ÷ 6 is not 6 ÷ 42.
• Dividing when the box is the product: □ ÷ 6 = 7 needs 6 × 7 = 42.

Answers

• Part A: 6 × 7 = 42, 7 × 6 = 42, 42 ÷ 6 = 7, 42 ÷ 7 = 6; 8 × 9 = 72, 9 × 8 = 72, 72 ÷ 8 = 9, 72 ÷ 9 = 8; 4 × 8 = 32, 8 × 4 = 32, 32 ÷ 4 = 8, 32 ÷ 8 = 4; 5 × 6 = 30, 6 × 5 = 30, 30 ÷ 5 = 6, 30 ÷ 6 = 5.
• Part B: 54 ÷ □ = 9, box 6; □ × 7 = 49, box 7; 36 ÷ 4 = □, box 9; 8 × □ = 64, box 8; □ ÷ 6 = 7, box 42; 81 ÷ □ = 9, box 9. Part C: no. 42 ÷ 6 = 7 shares 42 into sixes; 6 ÷ 42 shares 6 into 42 parts, which is less than 1. Multiplication can be turned around; division cannot.

Fact families

A. Write the four facts in each family house

B. Find the missing number

C. Mia says 42 ÷ 6 is the same as 6 ÷ 42. Is she right? Explain.

Patterns in the tables

Each times table has patterns that make it easier to hold. The 9s go 9, 18, 27, 36: the tens go up by one, the ones go down by one, and the digits add to 9. The 4s are double the 2s and the 8s are double the 4s. Every 5s fact ends in 5 or 0. Children fill rows of the grid, describe the patterns, and find every place 24 appears.

We are learning to

• build a times table row by adding the same step,
• describe a pattern in a table’s products,
• use links between tables, such as the 8s being double the 4s.

Success criteria

• I can describe a pattern in the 9s, the 4s and 8s, or the 5s.
• I can use one table to find facts in another.

You need

Coloured pencils. The fact triangles for the warm-up. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with the 4s row.

Watch for these ideas

• Losing the step when skip counting: 9, 18, 28. Check with the pattern: the ones go down by one.
• Doubling by adding 2: the 8s are double the 4s, so 4 × 6 = 24 gives 8 × 6 = 48.
• Not seeing that row 4 and column 4 hold the same numbers. They are turnarounds.

Answers

• Part A: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90; the tens go up by one and the ones go down by one, and the digits add to 9. Part B: 4s 4, 8, 12, 16, 20, 24, 28, 32, 36, 40; 8s 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, each double the 4s.
• Part C: 24 is at 3 × 8, 4 × 6, 6 × 4, 8 × 3; the 5s row ends in 5, 0, 5, 0. A pattern of their own: the 2s are all even, or the 10s end in 0.

Patterns in the tables

C. Colour every 24 in one colour and the whole 5s row in another

Write the facts that make 24:

What do you notice about the 5s row?

A pattern of my own, in another row:

Use a fact you know

Most children know their 2s, 5s and 10s and stumble on facts such as 7 × 8. Each tricky fact can be rebuilt from a known one: double a fact (8 × 6 is double 4 × 6), ten lots take one lot (9 × 8 is 80 − 8), five lots and some more (7 × 8 is 40 + 16), or half of ten lots (5 × 7 is half of 70). With practice, a rebuilt fact becomes a remembered one.

We are learning to

• choose a known fact that helps with a tricky one,
• double, take one lot from ten lots, add lots to five lots, or halve ten lots,
• explain the strategy we used.

Success criteria

• I can work out a tricky fact from a fact I know.
• I can explain which fact I used and how.

You need

The tricky-fact cards and strategy headers (cut-out sheet 2), one set per pair. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with the card sort.

Watch for these ideas

• Taking away 1 instead of one lot: 9 × 8 is 80 − 8, not 80 − 1.
• Adding 2 instead of two lots: 7 × 8 is 5 × 8 and two more eights, 40 + 16.
• Halving the wrong number: 5 × 7 is half of 70, not half of 7.

Answers

• Part A: 6 × 7 = 42 (5 × 7 + 1 × 7 = 35 + 7); 9 × 8 = 72 (10 × 8 − 8 = 80 − 8); 8 × 6 = 48 (double 4 × 6 = double 24); 7 × 7 = 49 (5 × 7 + 2 × 7 = 35 + 14); 9 × 6 = 54 (10 × 6 − 6 = 60 − 6); 4 × 9 = 36 (double 2 × 9 = double 18); 6 × 8 = 48 (double 3 × 8 = double 24); 7 × 8 = 56 (5 × 8 + 2 × 8 = 40 + 16). Other known facts are fine with a reason.
• Card sort: Double a fact I know: 4 × 7 = 28, 8 × 8 = 64, 4 × 9 = 36, 8 × 6 = 48; Ten lots, take one lot: 9 × 6 = 54, 9 × 7 = 63, 9 × 8 = 72, 9 × 4 = 36; Five lots and some more: 6 × 6 = 36, 7 × 7 = 49, 6 × 4 = 24, 7 × 8 = 56; Half of ten lots: 5 × 7 = 35, 5 × 8 = 40, 5 × 9 = 45, 5 × 6 = 30.

Use a fact you know

A. Rebuild each tricky fact from a fact you know

The first row is done for you.

B. Pick one card from each pile of your sort. Write how the strategy worked.

Bigger numbers, no calculator

Known facts reach much bigger numbers. Split a number by place value: 6 × 12 is 6 × 10 and 6 × 2, so 72. Use tens: 7 × 30 is 7 × 3 tens, 21 tens, 210. Divide by place value: 84 ÷ 4 is 80 ÷ 4 and 4 ÷ 4, so 21. Children work each one in their heads and write only the steps.

We are learning to

• multiply a two-digit number by splitting it into tens and ones,
• multiply by a multiple of ten with a known fact,
• divide by splitting the number by place value.

Success criteria

• I can stretch a known fact to a bigger calculation without a calculator.
• I can show the steps I used.

You need

The fact triangles for the warm-up. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part B; start Session B with the divisions.

Watch for these ideas

• Multiplying only the tens: 6 × 12 = 60 + 2. Both parts are multiplied by 6.
• Adding a zero to each number: 7 × 30 is 21 tens, which is 210.
• Forgetting to share the ones: 84 ÷ 4 is 20 + 1, not 20 + 4.

Answers

• Part A: 6 × 12 = 60 + 12 = 72; 7 × 13 = 70 + 21 = 91; 4 × 15 = 40 + 20 = 60; 3 × 24 = 60 + 12 = 72. Part B: 7 × 30 = 21 tens = 210; 8 × 40 = 32 tens = 320; 6 × 50 = 30 tens = 300; 9 × 20 = 18 tens = 180.
• Part C: 80 ÷ 4 (8 tens ÷ 4 = 2 tens) = 20; 80 ÷ 4 + 4 ÷ 4 = 20 + 1 = 21; 120 ÷ 6 (12 tens ÷ 6 = 2 tens) = 20; 60 ÷ 3 + 3 ÷ 3 = 20 + 1 = 21. Part D: 4 × 25 = 100; 4 × 15 = 60; 8 × 25 = 200.

Bigger numbers, no calculator

A. Split the bigger number into tens and ones

B. Use a tens fact

C. Divide by place value

D. Double, then double again

Times 4 is double and double again; times 8 is one more double.

Fact triangles

Cut out the twelve triangles, one set per pair. One partner covers a corner with a thumb; the other says the hidden number and the fact that finds it. Cover the top to multiply, a bottom corner to divide.

Teacher note: these are the facts children most often find tricky. Add triangles of your own on blank card as the class needs them.

Strategy headers and tricky-fact cards

Cut out the four headers and the sixteen fact cards (Day 4). Lay the headers in a row and put each fact under the strategy that fits it best, then solve it that way.

Headers

Fact cards

Teacher note: there are four cards for each strategy, and the key is on the Day 4 plan. A child who sorts a card differently and can say why the strategy works is right too.

What we know: Multiplication and Division Facts

No calculator. Show your steps for questions 5 to 8.

1. 7 × 6 = ____    8 × 9 = ____    6 × 6 = ____
2. Write the fact family for 5 × 8 = 40: ______________________________________
3. 63 ÷ 7 = ____    48 ÷ 6 = ____
4. 4 × □ = 36.   The box is ______
5. Use 10 × 7 to work out 9 × 7: ______________________
6. 6 × 12 = 6 × 10 + 6 × 2 = ______
7. 8 × 30 = ______
8. 84 ÷ 4 = ______   Show how you split it: ______________________

Answers and marking guide

Answers

1. 42, 72, 36.
2. 5 × 8 = 40, 8 × 5 = 40, 40 ÷ 5 = 8, 40 ÷ 8 = 5.
3. 9, 8.
4. 9 (4 × 9 = 36).
5. 10 × 7 = 70, take away one 7: 63.
6. 60 + 12 = 72.
7. 8 × 3 tens = 24 tens = 240.
8. 80 ÷ 4 + 4 ÷ 4 = 20 + 1 = 21.

A quick three-level guide

Eight questions, three ideas. A child at standard recalls most facts quickly, rebuilds the rest from known ones, and stretches facts to bigger numbers in the head.

Weekly class record

Jot a tick as you move around the room; the mini-check fills any gaps. A tick a day is plenty.

The five columns are the five days: arrays, families, patterns, known facts, and bigger numbers.