NumIO math adventure

Fractions and decimals

A trail marker is divided into equal parts. Name each part and compare two markers.

Learning goal

See fractions and decimals as parts of one whole and compare their sizes.

Skills you will practise

Fraction meaning and comparison
Decimal meaning and comparison

Worked examples

3/4

Cut a pizza into 4 equal pieces and color 3 of them. We write the colored part as a fraction.
The denominator 4 tells how many equal parts the whole has. The numerator 3 tells how many parts are colored. So the fraction is 3/4.
The part that is not colored is 1 piece out of 4, so it is 1/4.
Check by putting the parts together: 3/4 + 1/4 = 1. The colored and uncolored pieces make the whole pizza.

5/8 > 3/8

Two ribbons are each cut into 8 equal pieces. One ribbon has 5 pieces and the other has 3 pieces.
Both fractions have the denominator 8, so every piece is the same size. We only need to compare the numerators.
Compare the numerators: 5 > 3. So 5/8 is greater than 3/8.
Find how much greater: 5/8 − 3/8 = 2/8. The first ribbon has 2 more pieces.

2.3 > 2.1

Mark 2.3 and 2.1 on a number line. The number farther to the right is greater.
The ones digits are both 2, so look at the tenths digits. They are 3 and 1.
The number 2.3 is 23 tenths and 2.1 is 21 tenths. Compare them: 23 > 21, so 2.3 > 2.1.
Check the gap: 2.3 − 2.1 = 0.2. That is 2 tenths, the same as the difference between the tenths digits.

Common mistake

Do not think that a fraction with a bigger denominator is bigger. When the denominators are the same, the pieces are the same size, so the fraction with more pieces is greater. For decimals, compare the ones digit first, then the tenths digit, and never compare by how long the number looks.

Teach-back question

What does the denominator count and what does the numerator count? How can you use a number line to tell which of two decimals is greater?

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 “Fractions and decimals” for?

“Fractions and decimals” is a Grade 3 Math lesson in NumIO. It practises: fraction meaning and comparison, decimal meaning and comparison.

How does the “Fractions and decimals” 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 “Fractions and decimals” 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.