NumIO math adventure

Share and find remainders

The explorer shares supplies fairly. Count the full groups, then check what is left.

Learning goal

Divide equal groups and explain both the quotient and the remainder.

Skills you will practise

Division and quotient
Division with a remainder

Worked examples

90 ÷ 9 = 10

Put 90 supplies into groups of 9. We want to know how many groups we can make, so this is a division problem.
Think of a multiplication fact: 9 × 9 = 81 is not enough yet, but 9 × 10 = 90 matches the total exactly.
So there are 10 groups of 9, and nothing is left over. The quotient is 10 and the remainder is 0.
Check by multiplying back: 9 × 10 = 90. This is the number of supplies we started with.

58 ÷ 9 = 6 remainder 4

Put 58 shells into groups of 9. Make as many full groups as you can, then see what is left.
Find the closest multiplication fact that does not go over 58: 9 × 6 = 54. So we can make 6 full groups.
Subtract to find the remainder: 58 − 54 = 4. The remainder 4 is smaller than the divisor 9, so no more full group fits.
Check with the divisor, quotient and remainder: 9 × 6 + 4 = 58. This is the number we started with.

100 ÷ 7 = 14 remainder 2

Share 100 cards equally among 7 friends. Each friend gets the same number, and the cards that cannot be shared evenly are left over.
Find the closest multiplication fact that does not go over 100: 7 × 14 = 98. So each friend gets 14 cards.
Subtract to find what is left: 100 − 98 = 2. The remainder 2 is smaller than the divisor 7.
Check by putting the parts back together: 7 × 14 + 2 = 100. This is the total number of cards.

Common mistake

Do not leave a remainder that is as large as the divisor or larger. If it is, another full group still fits, so the quotient is too small. When you check, multiply the divisor by the quotient first and then add the remainder.

Teach-back question

Why must the remainder always be smaller than the divisor? How can you check a division with a remainder by multiplying and adding?

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 “Share and find remainders” for?

“Share and find remainders” is a Grade 3 Math lesson in NumIO. It practises: division and quotient, division with a remainder.

How does the “Share and find remainders” 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 “Share and find remainders” 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.