Fractions

67 Skills in Mathematics. 52 are ready to try — three verified questions each, no account needed.

Ready to try

Ages 5–6
Finding halves and quarters (age 5+)
Recognise, find, and name a quarter as one of four equal parts of an object, shape, or quantity
5 verified questions on this shelf
Ages 5–6
What Is a Half?
Recognise, find, and name a half as one of two equal parts of an object, shape, or quantity
10 verified questions on this shelf
Ages 6–7
Decomposing a shape into more equal shares
Understand that decomposing a shape into more equal shares creates smaller shares
19 verified questions on this shelf
Ages 6–7
Fractions of amounts
Recognise, find, name, and write fractions 1/3, 1/4, 2/4, and 3/4 of a length, shape, set of objects, or quantity
12 verified questions on this shelf
Ages 6–7
Understanding fractions
Write simple fractions (e.g. 1/2 of 6 = 3) and recognise the equivalence of 2/4 and 1/2
9 verified questions on this shelf
Ages 7–8
Comparing fractions
Compare and order unit fractions, and fractions with the same denominator
9 verified questions on this shelf
Ages 7–8
Equivalent fractions
Recognise and show, using diagrams, equivalent fractions with small denominators
12 verified questions on this shelf
Ages 7–8
Fractions on a number line
Recognise and use fractions as numbers: place unit fractions and non-unit fractions with small denominators on a number line
10 verified questions on this shelf
Ages 7–8
Simple Fraction Sums
Add and subtract fractions with the same denominator within one whole (e.g. 5/7 + 1/7 = 6/7)
10 verified questions on this shelf
Ages 7–8
Unit fractions
Recognise, find, and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators
10 verified questions on this shelf
Ages 8–9
Adding Fractions (Same Denominator)
Add and subtract fractions with the same denominator, including results greater than one whole (e.g. 5/8 + 6/8 = 11/8)
9 verified questions on this shelf
Ages 8–9
Comparing fractions (age 8+)
Compare two fractions with the same numerator or the same denominator by reasoning about size; record comparisons with >, =, or < symbols
7 verified questions on this shelf
Ages 8–9
Decimal place value
Round decimals with one decimal place to the nearest whole number
9 verified questions on this shelf
Ages 8–9
Decimal place value (age 8+)
Compare numbers with the same number of decimal places up to two decimal places
9 verified questions on this shelf
Ages 8–9
Dividing by 10 and 100
Find the effect of dividing a one- or two-digit number by 10 and 100, identifying the value of the digits as ones, tenths, and hundredths
9 verified questions on this shelf
Ages 8–9
Equivalent fractions (age 8+)
Generate simple equivalent fractions and explain why they are equivalent using visual fraction models
9 verified questions on this shelf
Ages 8–9
Equivalent fractions on a number line
Understand two fractions as equivalent if they are the same size or the same point on a number line; recognise and show families of common equivalent fractions using diagrams
9 verified questions on this shelf
Ages 8–9
Fraction-Decimal Equivalents
Recognise and write decimal equivalents of 1/4, 1/2, and 3/4
9 verified questions on this shelf
Ages 8–9
Fractions as parts of shapes
Partition shapes into parts with equal areas and express the area of each part as a unit fraction of the whole
28 verified questions on this shelf
Ages 8–9
Fractions of a whole
Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a/b as a parts of size 1/b
10 verified questions on this shelf
Ages 8–9
Fractions of a whole (age 8+)
Express whole numbers as fractions (e.g. 3 = 3/1) and recognise fractions equivalent to whole numbers (e.g. 4/4 = 1, 6/1 = 6)
8 verified questions on this shelf
Ages 8–9
Fractions of amounts (harder)
Solve problems involving increasingly harder fractions to calculate quantities, including non-unit fractions where the answer is a whole number
9 verified questions on this shelf
Ages 8–9
Fractions on a number line (age 8+)
Represent fractions on a number line: partition the interval 0 to 1 into b equal parts to locate 1/b, then mark off a lengths of 1/b from 0 to locate a/b
9 verified questions on this shelf
Ages 8–9
Tenths (age 8+)
Count up and down in hundredths; recognise that hundredths arise when dividing an object by 100 or dividing tenths by 10
9 verified questions on this shelf
Ages 9–10
Adding and subtracting mixed numbers
Add and subtract mixed numbers with like denominators, including by converting to improper fractions or using properties of operations
6 verified questions on this shelf
Ages 9–10
Adding fractions (different denominators)
Add and subtract fractions with denominators that are multiples of the same number by finding a common denominator
9 verified questions on this shelf
Ages 9–10
Comparing Decimals
Compare two decimals to hundredths (or up to three decimal places) by reasoning about size using place-value understanding; record with >, =, <
11 verified questions on this shelf
Ages 9–10
Converting tenths to hundredths
Express a fraction with denominator 10 as an equivalent fraction with denominator 100 and use this to add fractions with denominators 10 and 100 (e.g. 3/10 + 4/100 = 34/100)
9 verified questions on this shelf
Ages 9–10
Decimal place value (age 9+)
Round decimals with two decimal places to the nearest whole number and to one decimal place
9 verified questions on this shelf
Ages 9–10
Decimals to three places
Solve problems involving numbers with up to three decimal places
9 verified questions on this shelf
Ages 9–10
Equivalent fractions (age 9+)
Explain why a fraction a/b is equivalent to (n×a)/(n×b) using visual models; use this principle to recognise and generate equivalent fractions, including tenths and hundredths
9 verified questions on this shelf
Ages 9–10
Fractions of a whole (age 9+)
Solve word problems involving multiplication of a fraction by a whole number using visual models and equations
9 verified questions on this shelf
Ages 9–10
Mixed numbers and improper fractions
Recognise mixed numbers and improper fractions; convert from one form to the other (e.g. 2/5 + 4/5 = 6/5 = 1 1/5)
27 verified questions on this shelf
Ages 9–10
Percentage and decimal equivalents
Solve problems requiring knowledge of percentage and decimal equivalents of 1/2, 1/4, 1/5, 2/5, 4/5 and fractions with denominators that are multiples of 10 or 25
9 verified questions on this shelf
Ages 9–10
Tenths (age 9+)
Recognise and use thousandths; relate them to tenths, hundredths, and their decimal equivalents (e.g. 1/1000 = 0.001, 35/1000 = 0.035)
9 verified questions on this shelf
Ages 9–10
Understanding fractions (age 9+)
Understand a fraction a/b with a > 1 as a sum of fractions 1/b (e.g. 3/5 = 1/5 + 1/5 + 1/5)
9 verified questions on this shelf
Ages 10–11
Adding Fractions (Unlike Denominators)
Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions to produce a common denominator
10 verified questions on this shelf
Ages 10–11
Area with Fractions
Find the area of a rectangle with fractional side lengths by tiling with unit-fraction squares; show that the area equals the product of the side lengths
9 verified questions on this shelf
Ages 10–11
Comparing fractions (age 10+)
Compare and order fractions including fractions greater than 1, by converting to common denominators or using benchmarks
9 verified questions on this shelf
Ages 10–11
Decimals and fractions (age 10+)
Associate a fraction with division and calculate decimal fraction equivalents for simple fractions (e.g. 3/8 = 0.375); recall and use equivalences between simple fractions, decimals, and percentages in different contexts
9 verified questions on this shelf
Ages 10–11
Dividing by Fractions
Interpret and compute division of a whole number by a unit fraction (e.g. 4 ÷ 1/5 = 20); use visual models and the relationship between multiplication and division to explain why the quotient is larger than the dividend
10 verified questions on this shelf
Ages 10–11
Dividing fractions (unit fractions)
Interpret and compute division of a unit fraction by a non-zero whole number (e.g. 1/3 ÷ 4 = 1/12); use visual models and the relationship between multiplication and division to explain the result
9 verified questions on this shelf
Ages 10–11
Dividing unit fractions and whole numbers
Solve real-world problems involving division of unit fractions by whole numbers and whole numbers by unit fractions, using visual models and equations
10 verified questions on this shelf
Ages 10–11
Fraction Word Problems
Solve word problems involving addition and subtraction of fractions with unlike denominators, using visual models and benchmark fractions to estimate and assess reasonableness
9 verified questions on this shelf
Ages 10–11
Fractions of a whole (age 10+)
Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b); solve word problems involving division of whole numbers leading to fractional or mixed-number answers
9 verified questions on this shelf
Ages 10–11
Multiplying fractions (age 10+)
Multiply a fraction or whole number by a fraction, including proper fractions by proper fractions; interpret (a/b) × q as a parts of q partitioned into b equal parts; write answers in simplest form
9 verified questions on this shelf
Ages 10–11
Real-world fraction multiplication
Solve real-world problems involving multiplication of fractions and mixed numbers, using visual fraction models or equations
12 verified questions on this shelf
Ages 10–11
Simplifying Fractions
Use common factors to simplify fractions to their simplest form; use common multiples to express fractions with a common denominator
9 verified questions on this shelf
Ages 11–13
Decimals and fractions (age 11+)
Work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 and 3/8); convert fluently between the two forms
9 verified questions on this shelf
Ages 11–12
Dividing fractions
Divide a fraction by a fraction using the 'keep-change-flip' method and visual models; interpret and solve word problems involving division of fractions by fractions
13 verified questions on this shelf
Ages 11–13
Mixed & Improper Fractions
Use the four operations with formal written methods applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative
24 verified questions on this shelf
Ages 11–12
Multiplying fractions (age 11+)
Interpret fractions and percentages as operators — find a fraction or percentage of an amount by multiplying, understanding that 'of' means multiply (e.g., 3/4 of 200 = 3/4 × 200 = 150)
9 verified questions on this shelf

Being planted

These Skills are on the map, but their questions are still being written and checked.

Ages 6–9
Fraction Notation
Coming soon
Ages 6–7
Halves & Quarters of Shapes
Coming soon
Ages 7–8
Comparing fractions (age 7+)
Coming soon
Ages 7–8
Splitting shapes into equal parts (age 7+)
Coming soon
Ages 7–8
Tenths
Coming soon
Ages 8–11
Decimal & Percent Notation
Coming soon
Ages 8–9
Decimal equivalents of tenths and hundredths
Coming soon
Ages 8–9
Decimals and fractions
Coming soon
Ages 9–10
Addition and subtraction word problems
Coming soon
Ages 9–10
Comparing fractions (age 9+)
Coming soon
Ages 9–10
Decimals for Tenths & Hundredths
Coming soon
Ages 9–10
Fraction Addition Concepts
Coming soon
Ages 9–10
Multiplying fractions
Coming soon
Ages 9–10
Understanding Percentages
Coming soon
Ages 10–11
Multiplication as scaling
Coming soon

Skill names and descriptions include the Marble Skill Taxonomy © Generative Spark, Inc. (withmarble.com), licensed under ODbL 1.0 (database) and CC BY-SA 4.0 (content). Practice questions are GlowGrades's own, each checked by independent verifiers that must agree before a child ever sees it.