   # Number topics for Secondary

Below are the Secondary topics available for the category "Number" at Free Math Games.

These free math topics offer a complete set of basic Number topics for Secondary pupils (Grade 7 to Grade 9, ages 11 to 14). The Number category is divided into sub-categories such as "Decimals", "Fractions", "Multiples Factors Primes", etc. Each sub-category has multiple sub-sub-categories, and within them are the topics with between 6 and 10 question and answer pairs for the lessons, plus additional question answer pairs for the games and tests.

For each question/answer pair in a topic you get the question as picture, equation or text, the spoken question read by a robot, and an answer as both number or text and as audio. For most topics there are also 3 wrong answers prepared for each question.

### Number ➔ Decimals

#### Number ➔ Decimals ➔ Scaling decimals

0.81 x 100
Multiply decimals by 10 100 1000
Multiply by powers of 10 up to 1000 by moving the digits the correct number of columns to the left
4.31 ÷ 10
Divide decimals by 10 100 1000
Divide by powers of 10 up to 1000 by moving the digits the correct number of columns to the right

#### Number ➔ Decimals ➔ Decimals and fractions

0.25 = ¼
Decimals to fractions
Convert terminating decimals to their equivalent, simplified fractions

#### Number ➔ Decimals ➔ Operations

1.4 + 2.3
Add decimals by first aligning the decimal points of each number
2.5 - 0.2
Subtract decimals
Subtract decimals by first aligning the decimal points
1.4 x 1.1
Multiply decimals
Multiply decimals by initially removing the decimal point
1.8 ÷ 2
Divide decimals by integers
Divide decimal numbers by integers
6 ÷ 1.2
Divide integers by decimals
Divide integer values by decimal numbers
1.8 ÷ 0.5
Divide decimals by decimals
Divide decimals by decimals

#### Number ➔ Decimals ➔ Decimals and fractions

¼ = 0.25
Fractions to decimals
Convert fractions to their equivalent terminating decimals

### Number ➔ Fractions

#### Number ➔ Fractions ➔ Fraction basics

Identify unit fractions
Identify the fractions that are unit fractions, or will simplify to unit fractions
¼ of 9 cm
Calculate fractions of amounts
Calculate fractions of quantities, e.g. one third of 12 grams, etc.
Identify improper fractions
Identify the fraction or fractions that are improper fractions
Identify mixed fractions
Identify the fraction or fractions that are mixed fractions
Identify equivalent fractions
Identify the pairs of fractions that are equivalent

#### Number ➔ Fractions ➔ Add fractions

Add fractions with a common denominator
Add fractions by scaling up the fraction with the smaller denominator; simplify answers where possible

#### Number ➔ Fractions ➔ Subtract fractions

Subtract fractions: common denominator
Subtract fractions which share a common denominator
Subtract fractions: scale denominator
Subtract fractions by scaling up the fraction with the smaller denominator
Subtract fractions: LCD
Subtract fractions by finding the lowest common denominator (LCD) of the two fractions

#### Number ➔ Fractions ➔ Multiply fractions

Multiply simple fractions
Multiply fractions with cancelling
Multiply fractions by cross cancelling numbers first

#### Number ➔ Fractions ➔ Divide fractions

Divide fractions
Divide fractions by flipping one of the fractions (get the reciprocal of the fraction) and multiplying them

#### Number ➔ Fractions ➔ Multiply fractions

⅖ of 40 km
Fractions of amounts
Find fractions of amounts by first dividing by the fraction denominator then multiplying by the numerator

### Number ➔ Multiples Factors Primes

#### Number ➔ Multiples Factors Primes ➔ Primes

PRIME
2, 3, 5..
Prime numbers
Identify the prime number or numbers in each of the given lists

#### Number ➔ Multiples Factors Primes ➔ Factors

4=1,2,4
Identify factors
Identify the correct set of factors for numbers up to 50

#### Number ➔ Multiples Factors Primes ➔ Multiples

3, 4=12
Lowest common multiples
Identify the lowest common multiple (LCM) of 2 numbers

#### Number ➔ Multiples Factors Primes ➔ Factors

6&10=2
Highest common factor
Identify the Highest Common Factor (HCF) for the given sets of numbers

### Number ➔ Order & compare

#### Number ➔ Order & compare ➔ Ascending integers

7, 12,
41, 57
Order positive integers
Select the set of positive integers that are in ascending order
-17, -9,
-2 -1
Order negative integers
Arrange negative integers in ascending order from smallest to largest
-17, -2,
2, 17
Arrange integers ascending
Choose the set of positive and negative integers that are in correct ascending order

#### Number ➔ Order & compare ➔ Ascending numbers

Positive fractions: ascending order
Arrange these sets of positive fractions in ascending order
0.82, 0.9,
0.94
Positive decimals
Choose the set of positive decimals that are in ascending order

### Number ➔ Percentages

#### Number ➔ Percentages ➔ Fractions decimals percent

25% = ¼
Percentages to fractions
Identify the correct, simplified fraction for each of the given percentages
20% = 0.2
Percentages to decimals
Identify the correct decimal for each of the given percentages
¼ = 25%
Fractions to percentages
Identify the correct percentage for each of the given fractions
⅕ = 20%
= 0.2
Fractions and percentages
Compare by converting both fractions and percentages to decimals; select the larger decimal

#### Number ➔ Percentages ➔ Non calculator

30% of 20
Find percentages: multiples of 10
Find a percentage using multiples of 10

### Number ➔ Powers & Roots

#### Number ➔ Powers & Roots ➔ Squares and cubes

0, 1, 4, 9,
16, 25, 36
Identify square numbers
Identify the square numbers in each of the given groups of integers

#### Number ➔ Powers & Roots ➔ Indices

3 x 3 x 3
= 3³
Convert exponents to expanded form
Convert between base with exponent and expanded form e.g. 3³ <=> 3 x 3 x 3

### Number ➔ Rounding & estimating

#### Number ➔ Rounding & estimating ➔ Round to nearest

449
Round numbers: nearest 10
Round each of the given numbers to the nearest 10
4949
Round numbers: nearest 100
Round each given number to the nearest 100
49,499
Round numbers: nearest 1000
Round each of the given numbers to the nearest 1000
4.49
Round decimals: nearest integer
Round each of the given decimals to the nearest whole number (integer)

### Number ➔ Decimals

#### Number ➔ Decimals ➔ Operations

1.4 + 2.3
Add decimals by first aligning the decimal points of each number
2.5 - 0.2
Subtract decimals
Subtract decimals by first aligning the decimal points
1.4 x 1.1
Multiply decimals
Multiply decimals by initially removing the decimal point
1.8 ÷ 2
Divide decimals by integers
Divide decimal numbers by integers
6 ÷ 1.2
Divide integers by decimals
Divide integer values by decimal numbers
1.8 ÷ 0.5
Divide decimals by decimals
Divide decimals by decimals

#### Number ➔ Decimals ➔ Decimals and fractions

0.125 = ⅛
Decimals to fractions
Convert terminating decimals to their equivalent, simplified fraction or improper fraction

### Number ➔ Fractions

#### Number ➔ Fractions ➔ Fraction basics

Identify improper fractions
Identify the fraction or fractions that are improper fractions
Identify mixed fractions
Identify the fraction or fractions that are mixed fractions
Identify equivalent fractions
Identify the pairs of fractions that are equivalent

#### Number ➔ Fractions ➔ Add fractions

Add fractions with a common denominator
Add fractions by scaling up the fraction with the smaller denominator; simplify answers where possible

#### Number ➔ Fractions ➔ Subtract fractions

Subtract fractions: common denominator
Subtract fractions which share a common denominator
Subtract fractions: scale denominator
Subtract fractions by scaling up the fraction with the smaller denominator
Subtract fractions: LCD
Subtract fractions by finding the lowest common denominator (LCD) of the two fractions

#### Number ➔ Fractions ➔ Multiply fractions

Multiply simple fractions
Multiply fractions with cancelling
Multiply fractions by cross cancelling numbers first

#### Number ➔ Fractions ➔ Divide fractions

Divide fractions
Divide fractions by flipping one of the fractions (get the reciprocal of the fraction) and multiplying them

### Number ➔ Multiples Factors Primes

#### Number ➔ Multiples Factors Primes ➔ Multiples

25=5x5
Identify multiples of numbers to 12
Identify multiples of numbers up to 12

#### Number ➔ Multiples Factors Primes ➔ Primes

12=2²x3
Prime factors
Identify the prime factors of each given number using product notation

#### Number ➔ Multiples Factors Primes ➔ Factors

48 & 60
2² x 3
HCF using product notation
Identify the Highest Common Factor (HCF) using product notation

#### Number ➔ Multiples Factors Primes ➔ Multiples

16 & 24
2⁴ x 3
LCM using product notation
Identify the lowest common multiple (LCM) of 2 numbers using product notation

### Number ➔ Order & compare

#### Number ➔ Order & compare ➔ Ascending numbers

0.82, 0.9,
0.94
Decimals: ascending order
Choose the set of decimals, both positive and negative, that are in the correct ascending order
Fractions: arrange ascending
Arrange these sets of fractions in ascending order
All positive numbers: ascending
Choose the sets of all positive numbers that are in ascending order

#### Number ➔ Order & compare ➔ Descending numbers

97, 36,
0.1, 0.02
Positive numbers: descending order
Select the set of numbers that are in descending order
-0.1, -9,
-11, -90
Negative numbers: descending order
Select the set of negative numbers that are in descending order
9, 2,
-1, -9
Positive and negative: : descending
Arrange these lists of positive and negative numbers in descending order

#### Number ➔ Order & compare ➔ Using symbols

7+5=12
Expressions: equal or not equal
Identify whether the expressions are equal or not equal

### Number ➔ Percentages

#### Number ➔ Percentages ➔ Fractions decimals percent

25% = ¼
Percentages to fractions
Identify the correct, simplified fraction for each of the given percentages
20% = 0.2
Percentages to decimals
Identify the correct decimal for each of the given percentages
¼ = 25%
Fractions to percentages
Identify the correct percentage for each of the given fractions
⅕ = 20%
= 0.2
Fractions and percentages
Compare by converting both fractions and percentages to decimals; select the larger decimal

#### Number ➔ Percentages ➔ Using percentages

2mm of 2cm
Express quantities as percentages
Express one quantity as a percentage of another

#### Number ➔ Percentages ➔ Non calculator

30% of 20
Find percentages: multiples of 10
Find a percentage using multiples of 10
15% of 20
Find percentages: multiples of 5
Find percentages using multiples of 5

#### Number ➔ Percentages ➔ Calculator

5 + 20%
Find percentages: simple multiplier
Find the quantity using a simple decimal multiplier
84 + 13%
Find percentages: medium multiplier
Find the quantity using a medium decimal multiplier

### Number ➔ Powers & Roots

#### Number ➔ Powers & Roots ➔ Squares and cubes

1, 8, 27, 64,
125, 216, ..
Identify cube numbers
Identify the cube numbers in each group of integers
√25
Calculate square roots
Calculate the square root or nearest integer to the square root for the given numbers
³√27
Cube roots
Identify the cube root or nearest integer cube root of each of the given numbers

#### Number ➔ Powers & Roots ➔ Indices

3 x 3 x 3
= 3³
Convert exponents to expanded form
Convert between base with exponent and expanded form e.g. 3³ <=> 3 x 3 x 3

### Number ➔ Rounding & estimating

#### Number ➔ Rounding & estimating ➔ Round to nearest

4949
Round numbers: nearest 100
Round each given number to the nearest 100
49,499
Round numbers: nearest 1000
Round each of the given numbers to the nearest 1000
4.49
Round decimals: nearest integer
Round each of the given decimals to the nearest whole number (integer)

#### Number ➔ Rounding & estimating ➔ Round to decimal place

0.437
Round decimals to 1 dp
Round each of the given decimal values to 1 decimal place (1 dp)
2.674
Round decimals to 2 dp
Round each of the given decimal values to 2 decimal places (2 dp)
4.449
Round decimals to 3 dp
Round each of the given decimal values to 3 decimal places (3 dp)

#### Number ➔ Rounding & estimating ➔ Round to sig. fig.

0.01
Round numbers to 1 sig fig
Round large and small numbers to 1 significant figure (1 sig fig / 1 s.f.)
0.012
Round numbers to 2 sig figs
Round large and small numbers to 2 significant figures (2 sig figs / 2 s.f.)
0.0123
Round numbers to 3 sig figs
Round large and small numbers to 3 significant figures (3 sig figs)

#### Number ➔ Rounding & estimating ➔ Estimate

3.51 x 5.17
Estimale by rounding to 1 s.f.
Use rounding to 1 significant figure (1 sig fig / 1 s.f.) to estimate answers to the given calculations

### Number ➔ Fractions

2¼ + 1¾

#### Number ➔ Fractions ➔ Subtract fractions

3¼ - 2¾
Subtract fractions: mixed
Subtract mixed fractions by subtracting the whole numbers and the fraction parts separately

#### Number ➔ Fractions ➔ Multiply fractions

2¼ x 3¾
Multiply mixed fractions
Multiply mixed fractions by turning them to improper fractions and multiplying across; answers as improper fractions

#### Number ➔ Fractions ➔ Divide fractions

4¼ ÷ 2¾
Divide mixed fractions
Divide mixed fractions by turning them to top heavy fractions then flipping signs and the second fraction; answers as improper fractions

### Number ➔ Multiples Factors Primes

#### Number ➔ Multiples Factors Primes ➔ Multiples

25=5x5
Identify multiples of numbers to 12
Identify multiples of numbers up to 12

#### Number ➔ Multiples Factors Primes ➔ Primes

12=2²x3
Prime factors
Identify the prime factors of each given number using product notation

#### Number ➔ Multiples Factors Primes ➔ Factors

48 & 60
2² x 3
HCF using product notation
Identify the Highest Common Factor (HCF) using product notation

#### Number ➔ Multiples Factors Primes ➔ Multiples

16 & 24
2⁴ x 3
LCM using product notation
Identify the lowest common multiple (LCM) of 2 numbers using product notation

#### Number ➔ Multiples Factors Primes ➔ Standard form

9.91 x 10²
Standard form: largest number
Compare numbers in standard form and identify the largest
1 x 10⁻²
Standard form: smallest number
Compare numbers in standard form and identify the smallest
6 x 10² +
8 x 10¹
Add or subtract numbers in standard form
2 x 10⁰ x
6 x 10⁴
Standard form: multiply and divide
Multiply or divide numbers in standard form

### Number ➔ Percentages

#### Number ➔ Percentages ➔ Using percentages

5mm to 2cm
Percentage change
Compare two quantities to work out the percentage increase or decrease

#### Number ➔ Percentages ➔ Non calculator

15% of 20
Find percentages: multiples of 5
Find percentages using multiples of 5
30% of 20m
Find percentages: units and decimals
Find percentages using units and decimals

#### Number ➔ Percentages ➔ Calculator

5 + 20%
Find percentages: simple multiplier
Find the quantity using a simple decimal multiplier
84 + 13%
Find percentages: medium multiplier
Find the quantity using a medium decimal multiplier
67 - 5.7%
Find the quantity using an advanced decimal multiplier

### Number ➔ Powers & Roots

#### Number ➔ Powers & Roots ➔ Squares and cubes

√25
Calculate square roots
Calculate the square root or nearest integer to the square root for the given numbers
³√27
Cube roots
Identify the cube root or nearest integer cube root of each of the given numbers

#### Number ➔ Powers & Roots ➔ Indices

6y³ x 7y²
= 42y⁵
Multiply indices
Multiply indices with the same base by adding powers e.g. 5a³ x 6a² = 30a⁵
6b⁵ ÷ 2b²
= 3b³
Divide Indices
Divide indices with the same base by subtracting powers e.g. 6b⁵ ÷ 2b² = 3b³

### Number ➔ Rounding & estimating

#### Number ➔ Rounding & estimating ➔ Round to decimal place

0.437
Round decimals to 1 dp
Round each of the given decimal values to 1 decimal place (1 dp)
2.674
Round decimals to 2 dp
Round each of the given decimal values to 2 decimal places (2 dp)
4.449
Round decimals to 3 dp
Round each of the given decimal values to 3 decimal places (3 dp)

#### Number ➔ Rounding & estimating ➔ Round to sig. fig.

0.01
Round numbers to 1 sig fig
Round large and small numbers to 1 significant figure (1 sig fig / 1 s.f.)
0.012
Round numbers to 2 sig figs
Round large and small numbers to 2 significant figures (2 sig figs / 2 s.f.)
0.0123
Round numbers to 3 sig figs
Round large and small numbers to 3 significant figures (3 sig figs)

#### Number ➔ Rounding & estimating ➔ Estimate

3.51 x 5.17
Estimale by rounding to 1 s.f.
Use rounding to 1 significant figure (1 sig fig / 1 s.f.) to estimate answers to the given calculations

In addition to the Number topics shown above, the secondary section of Free Math Games has 4 other top level categories of topics to choose from. Each top level category offers a full breadth of topics to cover the secondary curriculum. Use these topics to reinforce key math concepts in a fun and engaging way that will keep your pupils enthused and energised with the math they are learning. The top level categories available are:  