NumIO math adventure

Multiply by grouping

The market has equal baskets. Find how many things there are altogether.

Learning goal

Build several-digit multiplication with equal groups, arrays, and partial products.

Skills you will practise

Multiply several-digit numbers
Read arrays and partial products

Worked examples

96 × 5 = 480

There are 5 baskets with 96 apples in each one. We want the total, so we multiply 96 × 5. Split 96 into 90 and 6 to make it easier.
Multiply the tens part: 90 × 5 = 450. Then multiply the ones part: 6 × 5 = 30.
Add the two parts together: 450 + 30 = 480. So there are 480 apples in all.
Check by dividing back: 480 ÷ 5 = 96. This is the number in each basket.

124 × 3 = 372

There are 3 shelves with 124 books on each shelf. We want the total, so we multiply 124 × 3. Split 124 into 100, 20 and 4.
Multiply each part by 3: 100 × 3 = 300, 20 × 3 = 60, and 4 × 3 = 12.
Add all three parts: 300 + 60 + 12 = 372. So there are 372 books in all.
Check by dividing back: 372 ÷ 3 = 124. This is the number on each shelf.

25 × 12 = 300

There are 12 boxes with 25 stickers in each box. We multiply 25 × 12. Split 12 into 10 and 2, which makes 10 boxes and 2 more boxes.
Find the stickers in 10 boxes: 25 × 10 = 250. Then find the stickers in 2 boxes: 25 × 2 = 50.
Add the two parts together: 250 + 50 = 300. So there are 300 stickers in all.
Check another way: 4 boxes hold 25 × 4 = 100 stickers, and 12 boxes are 3 groups of 4 boxes, so 100 × 3 = 300.

Common mistake

When you split a number into place-value parts, you must multiply every part and add every product. Do not forget one part or drop a zero from the tens or hundreds product. When the multiplier has two digits, split it into tens and ones, and do not forget to add the tens product at its own place value.

Teach-back question

Why can we split a big number into tens and ones, multiply each part, and add the products? How can you check your answer with division?

How to play

Read the short story, explore the visual model, and complete five untimed questions. Use the hint when you need a new way to think.

Classroom idea

Ask the learner to explain the model or strategy before choosing an answer, then celebrate a clear explanation as well as a correct result.

Frequently asked questions

What grade is “Multiply by grouping” for?

“Multiply by grouping” is a Grade 3 Math lesson in NumIO. It practises: multiply several-digit numbers, read arrays and partial products.

How does the “Multiply by grouping” mission work?

Each mission has five untimed questions. If an answer is not right yet you can try again, and the hint button offers another way to think.

Is “Multiply by grouping” free, and do I need an account?

Yes, it is free and there is no account or sign-up. Progress is saved in this browser, so you can come back and continue the mission later.

Back to the adventure map

Elementary math curriculum

First discoveries

Counting Companions — Count objects carefully and match each object to one number.
Bigger, Smaller, In Order — Compare groups and numbers, then put them in a clear order.
Parts Make a Whole — Split numbers into parts and find the missing friend that makes ten.
Pattern Steps — Use equal jumps of two or five to continue a number pattern.
Number Board Trail — Move right, left, up, and down on a number board to find a number.
Add and Take Away — Join and separate small groups to solve addition and subtraction stories.

Level 1

Tens and Ones to 100 — Read two-digit numbers and see how tens and ones build each number.
Twenty-Step Addition — Add and subtract within twenty, including missing parts of an equation.
Compare and Complete — Compare numbers with words and signs, then complete a missing-number equation.
Shape and Place — Name familiar shapes and describe where objects are using position words.
Measure and Tell Time — Compare lengths, measure with a simple unit, and read an hour on a clock.
Patterns and Groups — Continue repeating patterns, sort objects by a feature, and read a small count.

Level 2

Hundreds, Tens, Ones — Build three-digit numbers with hundreds, tens, and ones.
Three-Digit Adding and Taking Away — Add and subtract three-digit numbers, including regrouping when needed.
Equal Groups and Times Tables — See multiplication as equal groups, arrays, and repeated addition.
Units and Time Journeys — Choose a useful unit, convert simple lengths, and find elapsed time.
Flat Shapes and Repeating Designs — Recognize plane figures by their properties and continue a repeating design.
Tables and Picture Graphs — Read a table or graph, compare categories, and find totals and trends.

Level 3

Multiply by grouping — Build several-digit multiplication with equal groups, arrays, and partial products.
Share and find remainders — Divide equal groups and explain both the quotient and the remainder.
Fractions and decimals — See fractions and decimals as parts of one whole and compare their sizes.
Measure the journey — Add and subtract lengths, capacities, masses, and durations with matching units.
Angles, triangles, and circles — Recognize angle sizes and describe triangles and circles with accurate measures.
Read data and relationships — Read tables and bar charts, then use a simple rule to find a related number.

Level 4

Large numbers and rounding — Read the place value of large numbers and round them to a requested place.
Big multiplication and division — Use place value, products, and equal groups to solve larger multiplication and division.
Add and subtract parts — Add and subtract fractions with the same denominator and decimals by place value.
Shape clues — Use angle clues to describe triangles and quadrilaterals and classify their properties.
Perimeter and unit paths — Find the perimeter of shapes and convert measurements between familiar units.
Lines and rules — Read change on line graphs and use a correspondence rule to predict a value.

Level 5

Factor and Multiple Village — Find factors, multiples, common factors, common multiples, GCF, and LCM.
Fraction Bridge — Simplify, make equivalent fractions, use common denominators, and add or subtract fractions.
Product Workshop — Multiply fractions and decimals and explain how the product changes.
Congruence and Symmetry Garden — Recognize congruent shapes, lines of symmetry, and rotational symmetry.
Perimeter and Area Camp — Find perimeters and areas of rectangles, squares, triangles, parallelograms, and trapezoids.
Mean and Chance Harbor — Find means and describe the chance of outcomes with data models.

Level 6

Fraction Division Rapids — Divide fractions by multiplying by the reciprocal.
Decimal Division Station — Divide decimals by scaling place values and checking the size of the quotient.
Ratio and Percent Observatory — Connect ratios, percents, and proportions to solve scale problems.
Circle Circuit — Find circumference and area using the explicit classroom value π = 3.14.
Solid Shape Workshop — Find volume and surface area of cubes and cuboids.
Data Chart Lookout — Read strip and pie charts to compare, total, and interpret data.