# 100 Maths Homework Activities Year 6 Answers

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**Free Math Worksheets for Grade 6**

This is a comprehensive collection of free printable math worksheets for sixth grade, organized by topics such as multiplication, division, exponents, place value, algebraic thinking, decimals, measurement units, ratio, percent, prime factorization, GCF, LCM, fractions, integers, and geometry. They are randomly generated, printable from your browser, and include the answer key. The worksheets support any grade 6 math program, but have been specifically designed to match Math Mammoth grade 6 curriculum.

The worksheets are randomly generated each time you click on the links below. You can also get a new, different one just by refreshing the page in your browser (press F5).

You can print them directly from your browser window, but first check how it looks like in the "Print Preview". If the worksheet does not fit the page, adjust the margins, header, and footer in the Page Setup settings of your browser. Another option is to adjust the "scale" to 95% or 90% in the Print Preview. Some browsers and printers have "Print to fit" option, which will automatically scale the worksheet to fit the printable area.

All worksheets come with an answer key placed on the 2nd page of the file.

In sixth grade, students will start the study of beginning algebra (order of operations, expressions, and equations). They learn about ratios & percent and start using integers. Students also review long division, factoring, fraction arithmetic, and decimal arithmetic.In geometry, the focus is on the area of triangles and polygons and the volume of rectangular prisms. Other topics include rounding, exponents, GCF, LCM, and measuring units. Please note that these free worksheets do not cover all 6th grade topics; most notably, they do not include problem solving.

### Multiplication and Division and Some Review

**Long multiplication**

**Long division**

- 1-digit divisor, 5-digit dividend, no remainder
- 1-digit divisor, 5-digit dividend, with remainder
- 1-digit divisor, 6-digit dividend, no remainder
- 1-digit divisor, 6-digit dividend, with remainder
- 1-digit divisor, 7-digit dividend, no remainder
- 1-digit divisor, 7-digit dividend, with remainder
- 2-digit divisor, 5-digit dividend, no remainder
- 2-digit divisor, 5-digit dividend, with remainder
- 2-digit divisor, 6-digit dividend, no remainder
- 2-digit divisor, 6-digit dividend, with remainder
- 2-digit divisor, 7-digit dividend, no remainder
- 2-digit divisor, 7-digit dividend, with remainder
- 3-digit divisor, 6-digit dividend, no remainder
- 3-digit divisor, 6-digit dividend, with remainder
- 3-digit divisor, 7-digit dividend, no remainder
- 3-digit divisor, 7-digit dividend, with remainder
- Multiply decimals, writing the numbers under each other (0-2 decimal digits)
- Divide a whole number or a decimal by a whole number, need to add zeros to the dividend
- Convert a fraction to a decimal using long division, rounding the answers to three decimals

**Convert measuring units using long division & multiplication**

**Primary Grade Challenge Math** by Edward Zaccaro

A good book on problem solving with very varied word problems and strategies on how to solve problems. Includes chapters on: Sequences, Problem-solving, Money, Percents, Algebraic Thinking, Negative Numbers, Logic, Ratios, Probability, Measurements, Fractions, Division. Each chapter’s questions are broken down into four levels: easy, somewhat challenging, challenging, and very challenging.

### Exponents

### Place value/Rounding

### Algebra

**Order of operations**

- Three operations, uses ÷ for division, no exponents
- Four operations, uses ÷ for division, no exponents
- Two or three operations, uses the fraction line for division, no exponents
- Two or three operations, uses the fraction line for division, exponents included
- Two, three, or four operations, uses the fraction line, exponents included

**Expressions**

**Equations**

**Key to Algebra Workbooks**

Key to Algebra offers a unique, proven way to introduce algebra to your students. New concepts are explained in simple language, and examples are easy to follow. Word problems relate algebra to familiar situations, helping students to understand abstract concepts. Students develop understanding by solving equations and inequalities intuitively before formal solutions are introduced. Students begin their study of algebra in Books 1-4 using only integers. Books 5-7 introduce rational numbers and expressions. Books 8-10 extend coverage to the real number system.

=> Learn more

### Fractions vs. Decimals

- Decimals to fractions or mixed numbers (tenths/hundredths/thousandths)
- Decimals to fractions or mixed numbers (up to millionths)
- Mixed numbers to decimals (denominators 10, 100, and 1000)
- Proper and improper fractions to decimals (denominators 10, 100, or 1000)
- Proper fractions to decimals (denominators powers of ten till 1,000,000)
- Mixed numbers to decimals (denominators powers of ten, till 1,000,000)
- Fractions or mixed numbers to decimals (easy, varied denominators)
- Fraction to decimals - need long division
- Fractions to decimals - mixed practice

### Decimal Addition and Subtraction

**Key to Decimals Workbooks**

This is a workbook series by Key Curriculum Press that begins with basic concepts and operations on decimals. Then the books cover real-world uses of decimals in pricing, sports, metrics, calculators, and science.

The set includes books 1-4.

=> Learn more

### Decimal Multiplication

**Mental multiplication**

**Multiply in columns**

### Decimal Division

**Mental division**

- Easy decimal division (dividend has 1-2 decimal digits, a whole number divisor)
- Like above, but missing dividend or divisor
- Divide decimals by decimals (Think of how many times the divisor fits into the quotient.)
- Mixed multiplication and division problems 1 (1 decimal digit)
- Divide whole numbers and decimals by 10, 100, or 1000
- Same as above, missing dividend or divisor
- Multiply or divide decimals & whole numbers by 10, 100, and 1000
- Divide whole numbers and decimals by 10, 100, 1000, or 10,000
- Divide whole numbers and decimals by 10, 100, 1000, or 10,000 - missing dividend or divisor

**Long division**

### Measuring units

**Customary system**

*Convert measuring units using long division & multiplication (paper & pencil) or mental math*

- Convert between inches & feet
- Convert between inches, feet, and yards
- Convert between ounces & pounds
- Convert between tons & pounds
- Convert between cups, pints, and quarts
- Convert between cups, pints, quarts, and gallons
- Convert between ounces, cups, and quarts
- All customary units except miles - mixed practice
- All customary units except miles - mixed practice - a challenge

**Convert using a calculator, with decimals**

**Metric system**

- Convert between mm, cm and m - using decimals
- Convert between mm, cm, m, and km - using decimals
- Convert between ml & l and g & kg - using decimals
- All metric units mentioned above - mixed practice - using decimals
- Metric system: convert between the units of length (mm, cm, dm, m, dam, hm, km)
- Metric system: convert between the units of weight (mg, cg, dg, g, dag, hg, kg)
- Metric system: convert between the units of volume (ml, cl, dl, L, dal, hl, kl)
- Metric system: convert between the units of length, weight, and volume

### Ratio

### Percent

### Prime factorization, GCF, and LCM

### Fraction addition and subtraction

### Fraction multiplication

*In all fraction multiplication and division problems, it helps to simplify before you multiply.*

### Fraction division

### Convert fractions to mixed numbers and vv

### Simplify or equivalent fractions

### Fractions vs. Decimals

### Integers

**Coordinate grid**

**Addition & subtraction**

*Addition and subtraction of integers are beyond the Common Core Standards for grade 6 but some curricula or standards may include them in 6th grade.*

**Multiplication & Division**

*Multiplication and division of integers are beyond the Common Core Standards for grade 6 but the worksheets links are included here for completeness sake, as some curricula or standards may include them in 6th grade.*

### Geometry

*Area **- these worksheets are done in the coordinate grid.*

*Volume & surface area*

*Since these worksheets below contain images of variable sizes, please first check how the worksheet looks like in print preview before printing. If it doesn't fit, you can either print it scaled (such as at 90%), or make another one by refreshing the worksheet page (F5) until you get one that fits.*

## Optional topics

### Proportions

### Circle

If you wish to have more control on the options such as number of problems or font size or spacing of problems, or range of numbers, just click on these links to use the worksheet generators yourself:

These free primary maths resources for KS1 and KS2 (around 3,000 of them) are sorted by year group and learning objective. They are also seperated into resources for both teachers and students and include videos, games, apps and maths worksheets.

### Year 1 objectives

- count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number
- count, read and write numbers to 100 in numerals; count in multiples of 2s, 5s and 10s
- given a number, identify 1 more and 1 less
- identify and represent numbers using objects and pictorial representations including the number line, and use the language of: equal to, more than, less than (fewer), most, least
- read and write numbers from 1 to 20 in numerals and words
- read, write and interpret mathematical statements involving addition (+), subtraction (-) and equals (=) signs
- represent and use number bonds and related subtraction facts within 20
- add and subtract one-digit and two-digit numbers to 20, including 0
- solve one-step problems that involve addition and subtraction, using concrete objects and pictorial representations, and missing number problems such as 7 = ? ? 9
- solve one-step problems involving multiplication and division, by calculating the answer using concrete objects, pictorial representations and arrays with the support of the teacher
- recognise, find and name a half as 1 of 2 equal parts of an object, shape or quantity
- recognise, find and name a quarter as 1 of 4 equal parts of an object, shape or quantity
- Compare, describe and solve practical problems for: lengths and heights [for example, long/short, longer/shorter, tall/short, double/half]; mass or weight [for example, heavy/light, heavier than, lighter than]; capacity/volume [for example, full/empty, more than, less than, half, half full, quarter]; time [for example, quicker, slower, earlier, later];
- measure and begin to record the following: lengths and height; mass/weight; capacity and volume; time (hours, minutes, seconds)
- recognise and know the value of different denominations of coins and notes
- sequence events in chronological order using language (for example, before and after, next, first, today, yesterday, tomorrow, morning, afternoon and evening)
- recognise and use language relating to dates, including days of the week, weeks, months and years
- tell the time to the hour and half past the hour and draw the hands on a clock face to show these times
- Recognise and name common 2-D and 3-D shapes, including: 2-D shapes (for example, rectangles (including squares), circles and triangles); 3-D shapes (for example, cuboids (including cubes), pyramids and spheres);
- describe position direction and movement including whole half quarter and three quarter turns

### Year 2 objectives

- count in steps of 2, 3, and 5 from 0, and in 10s from any number, forward and backward
- recognise the place value of each digit in a two-digit number (10s, 1s)
- identify, represent and estimate numbers using different representations, including the number line
- compare and order numbers from 0 up to 100; use <, > and = signs
- read and write numbers to at least 100 in numerals and in words
- use place value and number facts to solve problems
- Solve problems with addition and subtraction: using concrete objects and pictorial representations (including those involving numbers, quantities and measures) and applying their increasing knowledge of mental and written methods
- recall and use addition and subtraction facts to 20 fluently, and derive and use related facts to 100
- add and subtract numbers using concrete objects, pictorial representations, and mentally, including: a two-digit number and 1s; a two-digit number and 10s; 2 two-digit numbers; adding 3 one-digit numbers
- show that addition of two numbers can be done in any order (commutative) and subtraction cannot
- recognise and use the inverse relationship between addition and subtraction and use this to check calculations and solve missing number problems
- recall and use multiplication and division facts for the 2, 5 and 10 times tables
- recognise odd and even numbers
- calculate mathematical statements for multiplication and division within the times tables and write them using the multiplication (×) division (÷) and equals (=) signs
- show that multiplication of two numbers can be done in any order (commutative) and division cannot
- solve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in contexts
- recognise, find, name and write fractions (third/quarter/two quarters/three quarters) of a length, set of objects or quantity
- write simple fractions of quantities (eg. Half of 6 is 30)
- recognise the equivalence of half and two quarters
- choose and use appropriate standard units to estimate and measure length/height in any direction (m/cm); mass (kg/g); temperature (°C); capacity (litres/ml) to the nearest appropriate unit, using rulers, scales, thermometers and measuring vessels
- compare and order lengths / mass / volume/capacity and record the results using > < and =
- recognise and use the symbols for pounds (£) and pence (p); combine amounts to make a particular value
- find different combinations of coins that equal the same amounts of money
- solve simple problems in a practical context involving addition and subtraction of money of the same unit including giving change
- compare and sequence intervals of time
- tell and write the time to five minutes including quarter past/to the hour and draw the hands on a clock face to show these times
- know the number of minutes in an hour and the number of hours in a day
- identify and describe the properties of 2-D shapes including the number of sides and line symmetry in a vertical line
- identify and describe the properties of 3-D shapes including the number of edges vertices and faces
- identify 2-D shapes on the surface of 3-D shapes [eg. a circle on a cylinder and a triangle on a pyramid]
- compare and sort common 2-D and 3-D shapes and everyday objects
- order and arrange combinations of mathematical objects in patterns and sequences
- use mathematical vocabulary to describe position direction and movement, including movement in a straight line, and distinguishing between rotation as a turn and in terms of right angles for quarter half and three-quarter turns (clockwise and anti-clockwise)
- interpret and construct simple pictograms, tally charts, block diagrams and tables
- ask and answer simple questions by counting the number of objects in each category and sorting the categories by quantity
- ask-and-answer questions about totalling and comparing categorical data

### Year 3 objectives

### Year 4 objectives

- count in multiples of 6 7 9 25 and 1000
- find 1000 more or less than a given number
- count backwards through 0 to include negative numbers
- recognise the place value of each digit in a four-digit number (ThHTU)
- order and compare numbers beyond 1000
- identify represent and estimate numbers using different representations
- round any number to the nearest 10 100 or 1000
- solve number and practical problems that involve all of the above and with increasingly large positive numbers
- read Roman numerals to 100 (I to C) and know that over time the numeral system changed to include the concept of 0 and place value
- add and subtract numbers with up to 4 digits using the formal written methods of columnar addition and subtraction where appropriate
- estimate and use inverse operations to check answers to a calculation
- solve addition and subtraction two-step problems in contexts deciding which operations and methods to use and why
- recall multiplication and division facts for multiplication tables up to 12 × 12
- use place value known and derived facts to multiply and divide mentally including: multiplying by 0 and 1; dividing by 1; multiplying together 3 numbers
- recognise and use factor pairs and commutativity in mental calculations
- multiply two-digit and three-digit numbers by a one-digit number using formal written layout
- solve problems involving multiplying and adding, including using the distributive law to multiply two-digit numbers by 1 digit, integer scaling problems and harder correspondence problems such as n objects are connected to m objects
- recognise and show (using diagrams) families of common equivalent fractions
- count up and down in hundredths; recognise that hundredths arise when dividing an object by 100 and dividing tenths by 10
- solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities, including non-unit fractions where the answer is a whole number
- add and subtract fractions with the same denominator
- recognise and write decimal equivalents of any number of tenths or hundreds
- recognise and write decimal equivalents to half, quarter and three quarters
- find the effect of dividing a one- or two-digit number by 10 and 100, identifying the value of the digits in the answer as ones, tenths and hundredths
- round decimals with 1 decimal place to the nearest whole number
- compare numbers with the same number of decimal places up to 2 decimal places
- solve simple measure and money problems involving fractions and decimals to 2 decimal places
- convert between different units of measure [for example, kilometre to metre; hour to minute]
- measure and calculate the perimeter of a rectilinear figure (including squares) in centimetres and metres
- find the area of rectilinear shapes by counting squares
- estimate, compare and calculate different measures, including money in pounds and pence
- read, write and convert time between analogue and digital 12- and 24-hour clocks
- solve problems involving converting from hours to minutes, minutes to seconds, years to months, weeks to days
- compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes
- identify acute and obtuse angles and compare and order angles up to 2 right angles by size
- identify lines of symmetry in 2-D shapes presented in different orientations
- complete a simple symmetric figure with respect to a specific line of symmetry
- describe positions on a 2-D grid as coordinates in the first quadrant
- describe movements between positions as translations of a given unit to the left/right and up/down
- plot specified points and draw sides to complete a given polygon
- interpret and present discrete and continuous data using appropriate graphical methods, including bar charts and time graphs
- solve comparison, sum and difference problems using information presented in bar charts, pictograms, tables and other graphs

### Year 5 objectives

- read, write, order and compare numbers to at least 1,000,000 and determine the value of each digit
- count forwards or backwards in steps of powers of 10 for any given number up to 1,000,000
- interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers, including through 0
- round any number up to 1,000,000 to the nearest 10, 100, 1,000, 10,000 and 100,000
- solve number problems and practical problems that involve all of the above
- read Roman numerals to 1,000 (M) and recognise years written in Roman numerals
- add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar addition and subtraction)
- add and subtract numbers mentally with increasingly large numbers
- use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy
- solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why
- identify multiples and factors, including finding all factor pairs of a number, and common factors of 2 numbers
- know and use the vocabulary of prime numbers, prime factors and composite (non-prime) numbers
- establish whether a number up to 100 is prime and recall prime numbers up to 19
- multiply numbers up to 4 digits by a one- or two-digit number using a formal written method, including long multiplication for two-digit numbers
- multiply and divide numbers mentally, drawing upon known facts
- divide numbers up to 4 digits by a one-digit number using the formal written method of short division and interpret remainders appropriately for the context
- multiply and divide whole numbers and those involving decimals by 10, 100 and 1,000
- recognise and use square numbers and cube numbers, and the notation for squared (²) and cubed (³)
- solve problems involving multiplication and division, including using their knowledge of factors and multiples, squares and cubes
- solve problems involving addition, subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals sign
- solve problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates
- compare and order fractions whose denominators are all multiples of the same number
- identify, name and write equivalent fractions of a given fraction, represented visually, including tenths and hundredths
- recognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements > 1 as a mixed number [eg. 2/5 + 4/5 = 6/5 = 1 1/5]
- add and subtract fractions with the same denominator, and denominators that are multiples of the same number
- multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams
- read and write decimal numbers as fractions [for example, 0.71 = 71/100]
- recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents
- round decimals with 2 decimal places to the nearest whole number and to 1 decimal place
- read, write, order and compare numbers with up to 3 decimal places
- solve problems involving number up to 3 decimal places
- recognise the per cent symbol (%) and understand that per cent relates to ‘number of parts per 100’, and write percentages as a fraction with denominator 100, and as a decimal fraction
- solve problems which require knowing percentage and decimal equivalents of 1/2, 1/4, 1/5, 2/5, 4/5 and those fractions with a denominator of a multiple of 10 or 25
- convert between different units of metric measure [for example, kilometre and metre; centimetre and metre; centimetre and millimetre; gram and kilogram; litre and millilitre]
- understand and use approximate equivalences between metric units and common imperial units such as inches, pounds and pints
- measure and calculate the perimeter of composite rectilinear shapes in centimetres and metres
- calculate and compare the area of rectangles (including squares), including using standard units, square centimetres (cm²) and square metres (m²), and estimate the area of irregular shapes
- estimate volume [for example, using 1 cm³ blocks to build cuboids (including cubes)] and capacity [for example, using water]
- solve problems involving converting between units of time
- use all four operations to solve problems involving measure [for example, length, mass, volume, money] using decimal notation, including scaling
- identify 3-D shapes, including cubes and other cuboids, from 2-D representations
- know angles are measured in degrees: estimate and compare acute, obtuse and reflex angles
- draw given angles, and measure them in degrees
- identify: angles at a point and 1 whole turn (total 360 degrees); angles at a point on a straight line and half a turn (total 180 degrees); and other multiples of 90 degrees
- use the properties of rectangles to deduce related facts and find missing lengths and angles
- distinguish between regular and irregular polygons based on reasoning about equal sides and angles
- identify, describe and represent the position of a shape following a reflection or translation, using the appropriate language, and know that the shape has not changed
- solve comparison, sum and difference problems using information presented in a line graph
- complete, read and interpret information in tables, including timetables

### Year 6 objectives

- read, write, order and compare numbers up to 10,000,000 and determine the value of each digit
- round any whole number to a required degree of accuracy
- use negative numbers in context, and calculate intervals across 0
- solve number and practical problems that involve all year 6 objectives
- use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy
- multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication
- divide numbers up to 4 digits by a two-digit whole number using the formal written method of long division, and interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the context
- divide numbers up to 4 digits by a two-digit number using the formal written method of short division where appropriate, interpreting remainders according to the context
- perform mental calculations, including with mixed operations and large numbers
- identify common factors, common multiples and prime numbers
- use their knowledge of the order of operations to carry out calculations involving the 4 operations
- solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why
- solve problems involving addition, subtraction, multiplication and division
- use common factors to simplify fractions; use common multiples to express fractions in the same denomination
- compare and order fractions, including fractions >1
- add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions
- multiply simple pairs of proper fractions, writing the answer in its simplest form [for example, 1/4 x 1/2 = 1/8]
- divide proper fractions by whole numbers [for example, 1/3 ÷ 2 = 1/6]
- associate a fraction with division and calculate decimal fraction equivalents [for example, 0.375] for a simple fraction [for example, 3/8]
- identify the value of each digit in numbers given to 3 decimal places and multiply and divide numbers by 10, 100 and 1,000 giving answers up to 3 decimal places
- multiply one-digit numbers with up to 2 decimal places by whole numbers
- use written division methods in cases where the answer has up to 2 decimal places
- solve problems which require answers to be rounded to specified degrees of accuracy
- recall and use equivalences between simple fractions, decimals and percentages, including in different contexts
- solve problems involving the relative sizes of 2 quantities where missing values can be found by using integer multiplication and division facts
- solve problems involving the calculation of percentages [for example, of measures and such as 15% of 360] and the use of percentages for comparison
- solve problems involving similar shapes where the scale factor is known or can be found
- solve problems involving unequal sharing and grouping using knowledge of fractions and multiples
- use simple formulae
- generate and describe linear number sequences
- express missing number problems algebraically
- find pairs of numbers that satisfy an equation with 2 unknowns
- enumerate possibilities of combinations of 2 variables
- draw 2-D shapes using given dimensions and angles
- recognise, describe and build simple 3-D shapes, including making nets
- compare and classify geometric shapes based on their properties and sizes and find unknown angles in any triangles, quadrilaterals, and regular polygons
- illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius
- recognise angles where they meet at a point, are on a straight line, or are vertically opposite, and find missing angles
- describe positions on the full coordinate grid (all 4 quadrants)
- draw and translate simple shapes on the coordinate plane, and reflect them in the axes
- interpret and construct pie charts and line graphs and use these to solve problems
- calculate and interpret the mean as an average
- perform mental calculations, including with mixed operations and large numbers
- use their knowledge of the order of operations to carry out calculations involving the 4 operations
- solve problems involving addition, subtraction, multiplication and division

### Non primary curriculum objectives

### Year 6 objectives

- solve problems involving the calculation and conversion of units of measure, using decimal notation up to 3 decimal places where appropriate
- use, read, write and convert between standard units, converting measurements of length, mass, volume and time from a smaller unit of measure to a larger unit, and vice versa, using decimal notation to up to 3 decimal places
- convert between miles and kilometres
- recognise that shapes with the same areas can have different perimeters and vice versa
- recognise when it is possible to use formulae for area and volume of shapes
- calculate the area of parallelograms and triangles
- calculate, estimate and compare volume of cubes and cuboids using standard units, including cubic centimetres (cm³) and cubic metres (m³), and extending to other units [for example, mm³ and km³]

### Non primary curriculum objectives

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