3rd grade math

Program of study for 3rd grade

The CCSS core curriculum for 3rd grade covers a range of categories, including:

• Number and place value
  Students learn about place value up to 10,000, and how to use this knowledge to solve problems. They learn to compare, order, and round numbers. They explore number patterns and sequences. They also learn how to count forwards and backwards in steps of powers of 10.

• Addition and subtraction
  Students learn how to add and subtract whole numbers with up to 3 digits, including using formal written methods (columnar addition and subtraction). They will also learn how to add and subtract numbers mentally with increasingly large numbers.

• Multiplication and division
  Students learn how to multiply and divide whole numbers by 10 and 100 (keeping to whole number quotients). They also learn how to solve problems involving missing factors and multiples.

• Fractions
  Students learn how to compare and order fractions, and how to express fractions in the same denomination. They also learn how to simplify fractions and add, subtract and multiply fractions.

• Measurement
  Students explore various aspects of measurement, including length, mass, volume, and time. They convert between different units of measurement and approximate equivalence between metric and imperial units.

• Geometry & shapes
  Students study properties of shapes and angles. They learn to identify, classify, and describe 2D shapes such as squares, rectangles, triangles, and circles. They also learn how to calculate the area and perimeter of 2D shapes. They begin to understand basic properties of triangles and quadrilaterals.

• Position & direction
  Students begin to explore simple reflections and translations.

• Statistics
  Students explore different tables and line graphs and use them to identify facts.

• Algebra
  Students learn about basic algebraic concepts, such as variables and equations. They learn how to solve simple algebraic problems.

• Count up in steps of 6
  
  Count up in steps of 6 through 50 using whole numbers
• Count down in steps of 6
  
  Count down in steps of 6 from 60 using whole numbers
• 6 step number line
  
  Identify the missing steps on these 6 step number lines through 60

• Count up in steps of 7
  
  Count up in steps of 7 through 50 using whole numbers
• Count down in steps of 7
  
  Count down in steps of 7 from 60 using whole numbers
• 7 step number line
  
  Identify the missing steps on these 7 step number lines to 70

• Count in steps of 9
  
  Count up in steps of 9 to 90 using whole numbers
• Count down in steps of 9
  
  Count down in steps of 9 from 90 using whole numbers
• 9 step number line
  
  Identify the missing steps on these 9 step number lines to 90

• Steps of 25: to 1000
  
  Count in steps of 25 from 0 to 1000 using whole numbers
• Steps of 25: 1000 to 2000
  
  Count in steps of 25 from 1000 to 2000 using whole numbers

• Count up in steps of 1000 to 20,000
  
  Count in steps of 1000 to 20,000 using whole numbers
• Count down in steps of 1000 from 20,000
  
  Count down in steps of 1000 from 20,000

• Count down in steps of 10 to -100
  
  Count down in steps of 10 from 0 to -100 using whole numbers

• Telling the time: analogue clock
  
  Look at these analogue clock faces and choose the correct time
• Telling the time: 24-hour clock
  
  Choose the correct description for each 24-hour clock time
• Roman numerals to numbers
  
  Convert these Roman numerals into modern day numbers between 12 and 50
• Numbers to Roman numerals
  
  Convert these modern day numbers between 12 and 50 into Roman numerals

• Is city X warmest or coldest?
  
  Use the temperature graphs to determine whether the selected city is the warmest or the coldest
• Difference in temperature
  
  Work out the difference in average March temperatures between pairs of European cities

• Largest 4-digit number
  
  Choose the largest from a set of four 4-digit numbers
• Smallest 4-digit number
  
  Choose the smallest from a selection of four 4-digit numbers
• Middle number
  
  Choose the four-digit number in between the smallest and largest of these four-digit numbers
• 4-digit numbers: ascending
  
  Choose the correct order for sets of 4-digit numbers from smallest to largest (ascending order)
• 4-digit numbers: descending
  
  Choose the correct order of 4-digit numbers from largest to smallest (descending order)

• Decimal numbers: ascending
  
  Choose the correct ascending order for these lists of 4 decimal numbers
• Decimal numbers: descending
  
  Choose the correct descending order for these lists of 4 decimal numbers

• Number in middle: 1 dp decimals
  
  Which number lies halfway between these two 1 decimal place decimals
• Number in middle: 2 dp decimals
  
  Which number lies halfway between these two 2 decimal place decimals?
• Decimal: nearest integer
  
  Decide which integer each of these decimal numbers is nearest to

• Smallest amount
  
  Choose the smallest of 3 amounts of money
• Largest amount
  
  Choose the largest of 3 amounts of money
• Money: order ascending
  
  Choose the correct order of money from smallest to largest
• Convert notes and coins to coins
  
  Choose the amount in coins that is equivalent to the given amount in notes and coins

• 7 minutes fast
  
  If the clock is fast by 7 minutes, what is the correct time?
• 12 minutes slow
  
  If the clock is slow by exactly 12 minutes calculate the correct time

• Add a number each time
  
  Find the missing number in patterns that add the same number each time
• Subtract a number each time
  
  Pick the next term when subtracting the same number each time
• Doubling each time
  
  Pick the next number in these number doubling patterns
• Halving each time
  
  Pick the next number in these halving patterns
• Fraction patterns
  
  Choose the next number in each list of fractions
• Square numbers
  
  Pick the next number in these patterns of square numbers

• Seven times table
  
  Identify the missing numbers in these sections of the 7 times table
• Nine times table
  
  Identify the missing numbers in these sections of the 9 times table
• Eleven times table
  
  Identify the missing numbers in these sections of the 11 times table
• Twelve times table
  
  Identify the missing numbers in these sections of the 12 times table

• 4-digit number: units
  
  Identify the unit digit of these four-digit numbers
• 4-digit number: tens
  
  Identify the tens digit of these four-digit numbers
• 4-digit number: hundreds
  
  Identify the hundreds digit of these four-digit numbers
• 4-digit number: thousands
  
  Identify the thousands digit of these four-digit numbers
• Place value names: 4-digits
  
  Say whether the green digit in each 4-digit number is a unit, a ten, a hundred or a thousand

• Round to nearest 10
  
  Use place values to round numbers up to 1000 to the nearest 10
• Round to nearest 100
  
  Use place values to round numbers to 1000 to nearest 100
• Round to nearest 1000
  
  Use place values to round numbers to 10,000 to nearest 1000
• Round to nearest 10,000
  
  Use place values to round numbers 10k-100k to nearest 10,000

• Change place value: multiply
  
  What do you need to multiply by to make the green digit a hundred? Is it 10 or 100?
• Change place value: divide
  
  What doyou need to divide by to change the green digit to have a tens place value? Is it 1, 10, 100 or 1000?

• Work out the cost
  
  Work out the cost of X packets of goods using place value
• Work out the area
  
  Work out the area of places and things using place value

• Number bonding to 1000
  
  Identify pairs of multiples of 50 with a combined total of 1000
• Number bonding to 200
  
  Identify pairs of multiples of 20 with a total of 200
• Number bonding to 0
  
  Identify the pairs of numbers that bond to 0
• 4-digit numbers + tens
  
  Add multiples of 10 to 4-digit numbers
• 4-digit numbers plus hundreds
  
  Add multiples of one hundred to four-digit numbers

• Bond strings of 3 double-digit numbers
  
  Use mental calculations to bond three double-digit numbers
• Bond strings of 4 double-digit numbers
  
  Use mental calculations to bond four double-digit numbers
• Bond strings of 5 double digit numbers
  
  Use mental calculations to bond five double-digit numbers

• Rounding up to add
  
  Identify the correct adjustment to make after rounding up to add
• Rounding down to add
  
  Identify the correct adjustment to make after rounding down
• Rounding up and down
  
  Use rounding up and down to the nearest 5 or 10 to simplify these additions

• Match additions: single & double-digit
  
  Choose the two additions of a 1-digit and a 2-digit number that give the same answer
• Match additions: 2-digit numbers
  
  Choose the matching additions from sets of 2-digit plus 2-digit sums

• Total number of items
  
  Use addition to find out how many items each person has in total
• Total cost: 2 items
  
  Use addition to find out the total cost of the 2 items
• Total cost: 3 items
  
  Use addition to find out how much the 3 items cost in total

• Formal addition: 2-digit numbers
  
  Choose the correct missing number for these formal 2-digit plus 2-digit columnar additions
• Formal addition: 2-digits plus 3-digits
  
  Find the missing number for these formal 2-digit plus 3-digit columnar additions
• Formal addition: 3-digit numbers
  
  Find the missing number for these formal 3-digit plus 3-digit columnar additions
• Formal addition: 4-digit numbers
  
  Choose the missing number for these formal 4-digit plus 4-digit columnar additions

• Rounding up to subtract
  
  Identify the correct adjustment to make after rounding up to subtract
• Rounding down to subtract
  
  Pick the adjustment required after rounding down to subtract
• Rounding up both numbers
  
  Pick the correct subtraction after rounding up and adjusting

• Match subtractions: 2-digits minus 1-digit
  
  Choose the pair of subtractions that give the same answer from sets of 2-digit minus 1-digit sums
• Match subtractions: 2-digit numbers
  
  Choose the two subtractions that give the same answer for these 2-digit minus 2-digit sums

• Subtract 2-digit numbers
  
  Choose the correct missing number for these columnar 2-digit minus 2-digit subtractions
• Formal subtraction: 3-digits minus 2-digits
  
  Calculate the answer for these 3-digit minus 2-digit formal written subtractions
• Subtract 3-digit numbers
  
  Choose the correct missing number for these formal 3-digit number subtractions

• How many more?
  
  Use subtraction to find how many more items one person has than the other person
• How many are left?
  
  Use subtraction to find out the number of items that are remaining

• Adding 49
  
  Add 49 to a number by first adding 50 and then subtracting 1 from the result
• Adding 59
  
  Add 59 to a number by first adding 60 and then subtracting 1
• Adding 69
  
  Add 69 to a number by first adding 70 and then subtracting 1

• Adding 51
  
  Add 51 to a number by first adding 50 and then adding 1 more
• Adding 61
  
  Add 61 to a number by first adding 60 and then adding 1 more
• Adding 71
  
  Add 71 to a number by first adding 70 and then adding 1 more

• Subtracting 49
  
  Subtract 49 from a number by subtracting 50 and then adding 1 back
• Subtracting 59
  
  Subtract 59 from a number by subtracting 60 and then adding 1
• Subtracting 69
  
  Subtract 69 from a number by subtracting 70 and then adding 1

• Subtracting 51
  
  Subtract 51 from a number by subtracting 50 and then subtracting 1 more
• Subtracting 61
  
  Subtract 61 from a number by subtracting 60 and then subtracting 1 more
• Subtracting 71
  
  Subtract 71 by subtracting 70 and then subtracting 1 more

• Add and subtract
  
  Add to a number and then subtract to find the answer
• Missing addition
  
  Find the missing addition in these add and subtract sums
• Missing subtraction
  
  Find the missing subtraction value in these 2 step add and subtract sums

• Checking subtractions
  
  Choose the correct inverse operation to check the given subtraction
• Checking additions
  
  Choose the inverse operations that correctly check the given additions

• Halving, doubling to 60
  
  Choose the halving and doubling pairs that equal each other
• Repeat additions
  
  Which repeat addition gives the same answer as the multiplication?

• Add then multiply
  
  Work out the answer when you add first and then multiply
• Subtract then multiply
  
  Work out the answer when you subtract first and then multiply
• Multiply then add
  
  Work out the answer when you multiply first and then add
• Multiply then subtract
  
  Work out the answer when you multiply first and then subtract

• Multiples of 6 to 72
  
  Identify the multiple or multiples of 6 in each of the lists of numbers up to 72
• Greatest multiple of 6
  
  Choose the greatest multiple of 6 from these lists of numbers up to 90
• Smallest multiple of 8
  
  Find the smallest multiple of 8 from these lists of numbers
• Greatest multiple of 12
  
  Choose the greatest multiple of 12 from these lists of numbers

• Multiply by 0 and/or 1
  
  Identify the correct answer to multiplications involving 0 and / or 1
• Multiply by 10, 100
  
  Identify the correct answers to multiplications involving 10 or 100

• Multiply 2 single-digit numbers
  
  Use mental arithmetic to multiply two single-digit numbers
• Multiply 3 numbers up to 6
  
  Use mental arithmetic to multiply three single-digit numbers from 1 to 6

• Long Multiplication: 2x1
  
  Calculate the missing number for these two-digit by one-digit long multiplications
• Long Multiplication: 3x1
  
  Calculate the correct answer for these three-digit by one-digit long multiplications

• Distributive method
  
  Turn a x b into a x ( c + d ) e.g. 4 x 8 = 4 ( 6 + 2 )

• Two categories
  
  If there are x cakes and y drinks how many different combinations of cakes and drinks are there?
• Three categories
  
  Given 3 categories of items how many different combinations of items are there?

• Divide by 6
  
  Do these divisions by 6 and choose the correct answer
• Divide by 7
  
  Do these divisions by 7 and choose the correct answer
• Divide by 9
  
  Divide by 9 and choose the correct answer

• Long Division using 3
  
  Choose the correct missing value for these long divisions by 3
• Long division using 4
  
  Choose the correct missing value for these long divisions by 4
• Long Division using 5
  
  Choose the correct missing value for these long divisions by 5

• Reverse times table division
  
  Find the answer for these reverse times table divisions
• Match division to addition
  
  Which divisions and additions give the same answer?
• Match division to subtraction
  
  Which divisions and subtractions give the same answer?
• Match division to multiplication
  
  Which divisions and multiplications give the same answer

• Add then divide
  
  Work out the answer when you add first and then divide
• Subtract then divide
  
  Work out the answer when you subtract first and then divide
• Divide then add
  
  Work out the answer when you divide first and then add
• Divide then subtract
  
  Work out the answer when you divide and then subtract

• Matching divisions
  
  Choose the pairs of division sums that give the same answer
• Matching multiplications
  
  Choose the pairs of multiplications that give the same answer
• Match multiplication to division
  
  Choose the multiplication and division operations that produce the same answer

• Multiply then divide: missing answer
  
  Do a multiplication and a division to find the answer
• Multiply then divide: missing multiple
  
  Work back from the given answer to find the missing multiple in these number machine questions
• Multiply then divide: missing divisor
  
  Work back from the given answer to find the missing divisor in these number machine questions

• Check multiplications: inverse operations
  
  Use inverse operations and divisions to check multiplication answers
• Check divisions: inverse operations
  
  Use inverse operations and multiplication to check division answers
• Are the answers the same
  
  Choose the pairs of operations that give the same answer

• Derive facts: divison
  
  Use the given statements to derive facts about divisions (e.g. 2 x 3 = 6 so 6 ÷ 3 = 2)

• Dividing by 4
  
  Use division by 4 to work out the best value for money item
• Dividing by 5
  
  Use division by 5 to work out the best value for money item
• Best price: divide by 6
  
  Use division by 6 to work out the best value for money item

• What (simplified) fraction is shaded
  
  Count up the parts shaded red to calculate the fraction and reduce the answer to it's simplest form
• Identify unit fractions
  
  Identify unit fractions and fractions that simplify to unit fractions

• Identify equivalent fractions
  
  Choose which two fractions are equivalent
• Which fraction is biggest
  
  Choose the largest fraction from the selection
• Which fraction is smallest
  
  Choose the smallest fraction from the selection

• ⅙ of an amount
  
  Choose the correct answer for 1/6th of a monetary amounts
• ⅐ of an amount
  
  Choose the correct answer for 1/7th of a monetary amounts
• ⅛ of an amount
  
  Choose the correct answer for 1/8th of a monetary amount

• Fractions of a measure
  
  Calculate what the given fraction (¼, ½, ¾) of each decimal amount will be e.g. ¼ of 400 ml

• Number line of fifths
  
  From the one fifths number line choose the correct fraction values
• Number line of tenths
  
  From the 1/10 number line choose the correct fraction value

• Fraction to percent
  
  What is the percentage equivalent of these fractions?

• Add fractions: same denominator below 10
  
  Add fractions with the same denominator below 10
• Add fractions: denominators 10 to 20
  
  Add fractions with the same denominator between 10 & 20
• Add fractions: denominators of 100
  
  Add pairs of fractions with the same denominator of 100
• Add fractions: different denominators
  
  Add fractions by changing the smaller denominator into the larger denominator

• Subtract fractions: denominators below 10
  
  Subtract fractions with the same denominators below 10
• Subtract fractions: denominators 10 to 20
  
  Subtract pairs of fractions with the same denominators between 10 & 20
• Subtract fractions: denominators of 100
  
  Subtract pairs of fractions with the same denominator of 100

• Compare decimals: biggest
  
  Identify the largest of these 1 or 2 decimal place decimals
• Compare decimals: smallest
  
  Identify the smallest of these 1 and 2 decimal place decimals
• Round decimals to the nearest whole number
  
  Round these decimal numbers to the nearest whole number

• Equivalent sizes
  
  Identify the decimals and fractions that are the equivalent size
• Order fractions ascending
  
  Arrange these lists of fractions in ascending order (from smallest to largest)
• Order fractions & decimals
  
  Arrange the fractions and decimals in ascending order

• Estimate time
  
  Estimate or guess the approximate time to complete the tasks
• Estimate heights of things
  
  Estimate or guess the approximate heights of each of the given objects
• Estimate weights
  
  Estimate or guess the approximate weight of each of the given objects
• Estimate the volume
  
  Estimate or guess the approximate volume of the containers in liters or milliliters
• Estimate areas
  
  Estimate or guess the approximate area of each shape or space
• Estimate costs of common items
  
  Estimate or guess the approximate monetary value of the items

• Add centimeters to meters
  
  Add lengths by converting meters into centimeters and then adding the measurements together
• Add kilograms and grams
  
  Add the masses by converting the given kilograms to grams and then adding the weights together
• Subtract grams from kilograms
  
  Subtract masses by converting the given kilograms to grams and then subtracting the weights
• Add liters and milliliters
  
  Add liters and milliliters by converting the liters to milliliters and then adding the volumes together
• Subtract milliliters from liters
  
  Subtract milliliters from liters by converting the liters to milliliters and then subtracting
• Subtract metric lengths
  
  Identify the correct answers for calculations involving subtracting metric lengths
• Calculate perimeters of squares
  
  Calculate the perimeters of squares by adding the lengths of their sides
• Calculate perimeters of rectangles
  
  Calculate the perimeters of rectangles by adding the lengths of their sides
• Calculate area: multiply measurements
  
  Calculate the areas of rectangles by multiplying the given measurements of width and height

• Compare metric lengths: longer item
  
  Compare metric to metric measures of length and decide which of the 2 items is longer
• Compare metric units: longest
  
  For each selection of item lengths given in metric units, choose the item that is the longest
• Compare metric units: shortest
  
  For each selection of item lengths given in metric units, choose the item that is the shortest
• Use symbols to compare lengths
  
  Choose a symbol to say if the first length is longer, shorter or equal to the second length

• Who is heaviest?
  
  Look at the weights in kilograms of 4 pupils and say who is heaviest
• Which is lightest?
  
  Look at the digital weights of 4 items and say which is lightest
• Use symbols to compare weight
  
  Select equality symbols to correctly compare masses in kilograms and grams
• Compare different units
  
  Compare weights in different metric units and choose the heaviest item

• Cheapest option
  
  Use addition or multiplication to work out which of the 2 options costs the least
• Most expensive option
  
  Use addition or multiplication to work out which of the 2 options is more expensive

• Convert liters to milliliters
  
  Convert fractions of liters into milliliters by multiplying the liters by 1000
• Convert milliliters to liters
  
  Convert hundreds and thousands of milliliters to liters by dividing by 1000

• Analogue clock
  
  Using the clock choose the correct description for the time
• Digital clock
  
  Choose the correct description for each of the given digital clock times
• 24-hour to standard time
  
  Choose the correct 12-hour clock descriptions for these 24-hour clock times
• 12-hour to 24-hour clock times
  
  Convert standard 12-hour clock times to 24-hour clock times

• Minutes to hours and minutes
  
  Convert times given in minutes into the equivalent time in hours and minutes
• Hours and minutes to minutes
  
  Convert hours and minutes into the equivalent number of minutes only
• Convert minutes to seconds
  
  Convert durations given in minutes to durations in seconds by multiplying by 60
• Convert years to months
  
  Convert years into the correct number of months and vice versa
• Convert weeks to days
  
  Convert weeks into the correct number of days and vice versa
• Convert kilometers to meters
  
  Convert kilometers into the correct number of meters
• Convert meters to kilometers
  
  Convert meters into the correct number of kilometers

• 2D shapes: name from diagram
  
  Identify the names of these two-dimensional (2D) shapes from the images
• 2D shapes: diagram from name
  
  Identify the correct diagram for each of these names of 2-dimensional (2D) shapes
• 3D shapes: name from diagram
  
  Identify the names of these three-dimensional (3D) shapes in various orientations
• Identify types of triangle
  
  Identify the names of types of triangles: equilateral, isosceles, scalene and right angle
• Identify names of quadrilaterals
  
  Identify the names of these quadrilateral shapes from the pictures shown

• Angles: acute or obtuse
  
  Identify whether the given angles are acute angles, right angles or obtuse angles
• Order angles by size
  
  Order the angles in each list from smallest to largest

• How many sides
  
  Identify the number of sides that each of these named 2-dimensional shapes have
• How many vertices and sides
  
  Count the number of vertices (corners) and sides on the given 2-D shapes
• How many lines of symmetry
  
  Identify the number of lines of symmetry each shape has
• Identify properties of 2-D shapes
  
  Choose the correct set of properties for the given 2-dimensional shapes

• Right up from the origin
  
  From the origin count the number of steps right and up to get to point X

• Right 3, up 3
  
  Identify the shape that has moved 3 squares right and 3 squares up
• Right 3, down 3
  
  Identify the shape that has moved 3 squares right and 3 squares down

• Right and up
  
  Describe the translation of the pink square to the green square using right and up
• Right and down
  
  Describe the translation of the pink square to the green square using right & down
• Left and up
  
  Describe the translation of the red square to the green square using left and up
• Left and down
  
  Describe the translation of the green square to the pink square using left and down

• 90-degree turn clockwise
  
  Pick the shape that has turned 90-degrees clockwise
• 180-degree turn
  
  Pick a shape that has turned 180-degrees
• 90° turn anticlockwise
  
  Pick the shape that has turned 90 degrees anticlockwise

• What polygon is formed
  
  Take the plotted points and the additional point coordinates to identify the polygon that is formed

• Interpret bar charts
  
  Use the bar charts to identify the number of people who prefer different pets
• Bar charts: most, least popular
  
  For each survey result graph, decide which animal is the most or least popular pet
• Bar charts: how many more
  
  Decide how many more people prefer one pet over the number who prefer a different pet

• Interpret tables
  
  Read the tables and interpret the data to answer the questions about how many vehicles were seen
• Tables: most, least frequent
  
  For each table work out which category of vehicle is the most or least frequently seen
• Tables: greatest, least difference
  
  In these tables, which two categories of vehicles have the biggest or smallest difference in frequency?

• Venn diagrams: 2 categories
  
  Use these 2 category Venn diagrams to answer the questions
• Venn diagrams: 2 categories: missing numbers
  
  Use the given information to complete these 2 category Venn diagrams

• Interpret time graphs
  
  Use the time graphs to identify the distance travelled after a certain number of hours
• Time graphs: distance traveled
  
  Use the time graphs to work out the distance traveled or the distance from home at the given times

• One step addition equations
  
  Solve the one-step addition equation to find the value of the unknown variable
• One step subtraction equations
  
  Solve the one-step subtraction equation to find the value of the letter
• One step multiplication equations
  
  Solve the multiplication equation to find the value of the letter
• One step division equations
  
  Solve the one-step division equation to find the value of the letter