2nd grade math

Program of study for 2nd grade

The CCSS core curriculum for 2nd grade covers a range of categories, including:

• Number and place value
  Students develop a solid understanding of place value, including numbers up to 1,000. They also learn how to count forwards and backwards in steps of 4 and 8, and in steps of 10, 20, 30, 40, 50, and 100. They compare 3 digit numbers and distinguish odd and even.

• Addition and subtraction
  Students learn how to add and subtract whole numbers with up to 3 digits. They study number bonding up to 1000. They also learn how to add and subtract numbers mentally including with 3 digit numbers.

• Multiplication and division
  Students learn how to multiply and divide whole numbers by 10 and 100 in addition to multiples of 2, 3 and 5. They learn the area model method of multiplication and reverse times tables for division.

• Fractions
  Students learn about unit fractions and equivalent fractions, and how to compare fractions by size. They learn how to add fractions with the same denominator. They learn to compare simple fractions and decimals.

• Measurement
  Students explore various aspects of measurement, including length, mass and time. They add, subtract and compare measurements with related units. They understand 24 hour times and how to compare durations in different units.

• Geometry & shapes
  Students learn to identify and describe 2D shapes such as squares, rectangles, triangles, and circles. They talk about numbers of corners and sides. They learn by comparing horizontal and vertical lines, and parallel and perpendicular lines.

• Position & direction
  Students begin to explore shapes that turn and simple translations.

• Statistics
  Students explore pictographs, bar charts and tables and use them to identify facts.

In addition to these specific categories, students will also develop their fluency with mathematical concepts and their ability to solve mathematical problems.

• Count up in steps of 4
  
  Count up in steps of 4 through 50 using whole numbers
• Count down in steps of 4
  
  Count down from 48 in steps of 4 using numbers
• 4 step number line
  
  Count up in steps of 4 to 50 using a number line

• Count up in steps of 8
  
  Count up in steps of 8 to 80 using whole numbers
• Count down in steps of 8
  
  Count down in steps of 8 from 80 using whole numbers
• 8 step number line
  
  Count up in steps of 8 through 50 using an 8 step number line

• Count in steps of 20
  
  Count up in steps of 20 from 0 to 200 using whole numbers
• Count in steps of 30
  
  Count up in steps of 30 from 0 through 200 using whole numbers
• Count in steps of 40
  
  Count up in steps of 40 from 0 through 200 using whole numbers

• Count in steps of 100
  
  Count up in steps of 100 from 0 to 1000 using whole numbers
• 100 step number line
  
  Count up in steps of 100 to 1000 using a number line
• Count in steps of 50
  
  Count up in steps of 50 to 500 using whole numbers
• 50 step number line to 500
  
  Count up in steps of 50 to 500 using a number line

• Analogue clock
  
  Look at the clock and choose the correct time
• Tell the time: 24-hour clock
  
  Choose the correct description for each of the 24-hour times shown
• Roman numerals to numbers
  
  Convert these Roman numerals into modern day numbers between 1 and 12
• Numbers to Roman numerals
  
  Convert these modern day numbers between 1 and 12 into Roman numerals
• Convert minutes to hours & minutes
  
  Convert minutes into hours and minutes
• Convert hours and minutes to minutes
  
  Convert hours and minutes into just minutes

• Which city is the warmest?
  
  Use these graphs of average temperatures to identify the warmest city
• Which city is the coldest?
  
  Use these graphs of average temperatures to identify the coldest city

• Largest 3-digit number
  
  From a selection of four 3-digit numbers choose the largest number
• Smallest 3-digit number
  
  Choose the smallest number from a selection of 4 three-digit numbers
• Middle number
  
  Choose the number that is in between the smallest and largest of these 3-digit numbers
• Ascending order
  
  Choose the correct order from smallest to largest for these sets of four 3-digit numbers
• Descending order
  
  Choose the correct order from largest to smallest for these sets of four 3-digit numbers

• Is the number odd or even?
  
  Choose whether these numbers from 20 to 100 are odd or even
• More odds or evens
  
  In these groups are there more odd or even numbers?
• Count even numbers
  
  How many of these numbers from 20 to 100 are even?
• Count odd numbers
  
  How many of these numbers from 20 to 100 are odd?

• Smallest to largest
  
  Put these decimals in ascending order from smallest to largest
• Largest to smallest
  
  Put these decimals in descending order from largest to smallest

• Number in the middle
  
  Say which number lies halfway between these two 1 decimal place decimal numbers

• Convert coins to notes and coins
  
  Convert the given value of coins to the correct amount in notes and coins

• The clock is 10 minutes fast
  
  If the clock is fast by 10 minutes choose the correct time
• The clock is 15 minutes fast
  
  If the clock is fast by 15 minutes choose the correct time
• The clock is 10 minutes slow
  
  If the clock is slow by 10 minutes choose the correct time
• The clock is 15 minutes slow
  
  If the clock is slow by 15 minutes choose the correct time

• Add a number each time
  
  Pick the next number when adding the same number each time
• Subtract a number each time
  
  Pick the next term when subtracting the same number each time
• Fraction patterns
  
  Pick the next correct number in the pattern
• Add or subtract numbers
  
  Identify the 2 missing numbers in each of these patterns

• Three times table
  
  Identify the missing number in these 3x table number patterns
• Four times table
  
  Identify the missing number in these 4x table number patterns
• Eight times table
  
  Identify the missing numbers in these 8x table patterns

• 20 more
  
  Work out the number that is 20 more than the given number between 0 and 100
• 20 less
  
  Work out the number that is 20 less than the given number between 20 and 100

• 40 more
  
  Pick the number that is 40 more than the given number between 0 and 100
• 40 less
  
  Pick the number that is 40 less than the given number between 40 and 100

• From digits to number names
  
  Identify the correct names for these 3-digit numbers
• From number names to digits
  
  Identify each of these 3-digit numbers written as words

• Units place value: 3-digit numbers
  
  Identify the units place value for each of these 3-digit numbers
• Tens place value: 3-digit numbers
  
  Identify the tens place value for these three-digit numbers
• Hundreds place value
  
  Identify the hundreds place value for each of these three-digit numbers

• 3-digit numbers to 500
  
  Is the green digit in these 3-digit numbers to 500 a unit, a ten or a hundred?
• 3-digit numbers to 999
  
  Is the highlighted digit in these 3-digit numbers a unit, a ten or a hundred?

• Round to nearest 10
  
  Use place values to round numbers up to 500 to the nearest 10
• Round to nearest 100
  
  Use place values to round numbers up to 999 up or down to the nearest 100
• Round to nearest 1000
  
  Use place values to round numbers up to 5000 up or down to the nearest 1000

• Place value: 10 times as much
  
  If person A gets some money and person B gets 10 times as much, how much does person B get?
• Place value: 100 times as much
  
  If a person gets some money and another person gets 100 times as much, how much does person 2 get?

• Number bonding to 20
  
  Identify the number that bonds to 20 with each of the given numbers
• Number bonds to 100: multiples of 10
  
  Identify pairs of multiples of 10 with a total of 100
• Number bonds to 100
  
  Identify pairs of numbers that sum to a total of 100
• Number bonding to 1000
  
  Identify pairs of multiples of 100 with a total of 1000
• Number bonding to 200
  
  Identify pairs of multiples of 25 with a total of 200

• 3-digit number plus units
  
  Use mental calculations to add the given number of units to a three-digit number
• 3-digit number plus multiple of 10
  
  Use mental calculations to add the given number of tens to a three-digit number
• 3-digit number plus multiple of 100
  
  Use mental calculations to add the given multiple of 100 to a three-digit number

• Missing number: 3-digit additions
  
  Find the missing number for these three-digit addition sums
• Missing answer: 3-digit numbers
  
  Pick the missing answer for these three-digit addition sums

• Match additions: 1-digit plus 2-digits
  
  Choose the two 1-digit plus 2-digits addition tiles that give the same answer
• Match additions: two 2-digit numbers
  
  Choose the two 2-digit plus 2-digit additions that give the same answer

• Total number of items
  
  Use addition to find out how many items there are in total
• Total cost of 2 items
  
  Use addition to find out how much the 2 items cost in total
• Total cost of 3 items
  
  Use addition and / or multiplication to find out how much the 3 items cost in total

• Subtract single-digit numbers
  
  Subtract a single-digit number from a single-digit number
• Subtract 1-digit from 2-digit numbers
  
  Subtract a single-digit numbers from double-digit numbers
• Subtract 2-digit from 2-digit numbers
  
  Subtract double-digit numbers from double-digit numbers

• Missing number problems
  
  Work out the missing number for these double-digit minus single-digit subtractions
• Missing answer problems
  
  Calculate the missing answer for these double-digit minus single-digit subtractions

• Match subtractions: 2-digits minus 1-digit
  
  Choose the two 2-digits minus 1-digit subtractions that give the same answer
• Match subtractions: 2-digit numbers
  
  Choose the pair of matching 2-digit minus 2-digit subtractions from a choice of 3

• 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 9
  
  Add 9 by first adding 10 to a number and then subtracting 1 from the result
• Adding 19
  
  Add 19 by first adding 20 to a number and then subtracting 1 from the result
• Adding 29
  
  Add 29 by first adding 30 to a number and then subtracting 1 from the result
• Adding 39
  
  Add 39 by first adding 40 to a number and then subtracting 1 from the result

• Adding 11
  
  Add 11 by first adding 10 to a number and then adding 1 more
• Adding 21
  
  Add 21 by first adding 20 to a number and then adding 1 more
• Adding 31
  
  Add 31 by first adding 30 to a number and then adding 1 more
• Adding 41
  
  Add 41 by first adding 40 to a number and then adding 1 more

• Subtracting 9
  
  Subtract 9 by subtracting 10 from a number then adding 1
• Subtracting 19
  
  Subtract 19 by subtracting 20 from a number then adding 1
• Subtracting 29
  
  Subtract 29 by subtracting 30 from a number then adding 1
• Subtracting 39
  
  Subtract 39 by subtracting 40 from a number then adding 1

• Subtracting 11
  
  Subtract 11 by subtracting 10 and then subtracting 1 more
• Subtracting 21
  
  Subtract 21 by subtracting 20 and then subtracting 1 more
• Subtracting 31
  
  Subtract 31 by subtracting 30 and then subtracting an extra 1
• Subtracting 41
  
  Subtract 41 by subtracting 40 and then subtracting 1 more

• Add and subtract
  
  Add and subtract to find the answer
• Missing addition
  
  Find the missing number for the addition
• Missing subtraction
  
  Find the missing subtraction in these add and subtract sums

• Checking subtractions
  
  Choose the inverse operations that check these subtractions
• Checking additions
  
  Choose the inverse operations that correctly check these additions

• Doubling numbers to 100
  
  Calculate the number that is double the given number
• Repeat additions
  
  Which repeat addition gives the same answer as the multiplication?
• Matching answers
  
  Choose the multiplication and addition sums that give the same answer
• Multiply decimals by 10: move the point
  
  Connect multiplying a decimal number by 10 and place value by moving the point 1 place to the right

• Count in steps of 4 or 5
  
  Use counting in steps to work out simple multiplications of 4 and 5
• Multiply by counting: steps of 4
  
  Use counting in steps to work out simple multiplications of 4
• Multiply by counting: steps of 8
  
  Use counting in steps to work out simple multiplications of 8
• Multiply by counting: steps of 50
  
  Use steps to work out simple multiplications of 50
• Multiply by counting: steps of 100
  
  Use counting in steps to work out simple multiplications of 100

• Multiply 1-digit by 1-digit numbers
  
  Use mental arithmetic to multiply two single-digit numbers
• Multiply 1-digit by 2-digit numbers
  
  Use mental arithmetic to multiply a 2-digit number by a 1-digit number

• Area model: 2 by 1-digit
  
  Use the area model method to multiply 2-digit numbers by 1-digit numbers
• Area model: 3-digits by 1-digit
  
  Use the area model method to multiply a 3-digit number by a 1-digit number
• Area model: 2-digits by 2-digits
  
  Find the missing number in these area model multiplications of 2-digit numbers by 2 digit-numbers

• 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 2
  
  Choose the greatest multiple of 2 from the list
• Multiples of 3
  
  Choose the smallest multiple of 3 from the list
• Multiples of 5
  
  Choose the smallest multiple of 5 from the list
• Multiples of 10
  
  Find the multiple of 10, smallest multiple of 10 or largest multiple of 10 from the lists

• Long Multiplication: 2-digits by 1-digit
  
  Pick the missing number in these 2-digit by 1-digit long multiplications
• Long Multiplication: 3-digits by 1-digit
  
  Work out the missing number for these 3-digit by 1-digit long multiplication sums

• Possible choices
  
  Use multiplication to work out how many different combination choices you have
• Scaling problems
  
  Calculate the size an object or model given that a scale model of the object is 10x larger or smaller

• Identify matching sums
  
  Apply the commutative law for multiplication to identify which sums are equal
• Identify the missing number
  
  Use the commutative law for multiplication to identify the missing value

• Divide by 3
  
  Do these divisions by 3 and choose the correct answer
• Divide by 4
  
  Do these divisions by 4 and choose the correct answer
• Divide by 8
  
  Do these divisions by 8 and choose the correct answer

• Division using bus stop method
  
  Use the bus stop method to identify the missing numbers in these divisions

• Reverse times table division
  
  Choose the missing numbers for these reverse times table divisions
• Match division to addition
  
  Which divisions and additions give the same answers
• Match division to subtraction
  
  Which divisions and subtractions give the same answer
• Match division to multiplication
  
  Which division and multiplication sums give the same answer?

• Number machine: add then divide
  
  Work out the answer when you add first and then divide
• Number machine: subtract then divide
  
  Work out the answer when you subtract first and then divide
• Number machine: divide then add
  
  Work out the answer when you divide first and then add
• Number machine: divide then subtract
  
  Work out the answer when you divide first and then subtract

• Matching multiplications
  
  Choose the pairs of multiplications that produce the same answer

• Find the missing answer
  
  Do a multiplication and a division to find the answer
• Find the missing multiple
  
  Work back from the given answer to find the missing multiple in these number machine questions
• Find the 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 division to check multiplication sums
• Check divisions: inverse operations
  
  Use inverse operations and multiplication to check the answers to divisions
• Are the answers the same?
  
  Which of these different multiplication and division operations give the same answer?

• Match doubles and halves to 24
  
  Find the number from 1 to 24 that is half of one number and double another number
• Match doubles and halves to 50
  
  Find numbers up to 50 that are half of one number and double another number

• What fraction of the squares are red?
  
  Count up the red squares to calculate what fraction of the whole they make
• Naming fractions
  
  Select the correct name for these fractions
• Identify unit fractions
  
  Identify unit fractions: fractions where the top number is a one e.g. ½ and ⅓

• Fractions from division by 10
  
  What fractions are made when numbers are divided by 10?

• Which fractions are equivalent
  
  Decide if the pairs of fractions are equivalent / the same size
• Which fraction is bigger?
  
  For each pair of fractions, choose which one would be the bigger share of a whole

• 1/5 of an amount
  
  Choose the correct answer for one fifth of a whole number
• 1/10 of an amount
  
  Choose the correct answer for one tenth of a whole number

• 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

• Add fractions: same denominator
  
  Add two fractions with the same denominator that is below 10
• Add fractions: denominator 10 to 20
  
  Add two fractions with the same denominator between 10 & 20

• Identify fraction operators
  
  Which divisions produce the same results as the given fraction operators?

• Equivalent sizes
  
  Identify the decimals and fractions that are the same size
• Decimal greater than fraction
  
  Identify the decimal that is greater than the fraction
• Decimal less than fraction
  
  Identify the decimal that is less than the fraction
• Order fractions from smallest to largest
  
  Re-arrange each set of fractions so that they are listed from smallest to largest

• Estimate the time
  
  Estimate or guess the approximate time to complete the tasks
• Estimate the weight
  
  Estimate or guess the approximate weight of the objects

• Add lengths in meters
  
  Identify the correct answers when adding 2 lengths given in meters
• Add lengths in centimeters
  
  Identify the correct answers for adding 2 lengths given in centimeters
• Add lengths in millimeters
  
  Identify the correct answers for adding 2 lengths given in millimeters
• Subtract lengths in meters
  
  Identify the correct answers for subtracting lengths given in meters
• Subtract lengths in centimeters
  
  Identify the correct answers when subtracting lengths given in centimeters
• Subtract lengths in millimeters
  
  Identify the correct answers when subtracting lengths given in millimeters
• Add mass: kilograms, grams
  
  Add the given pairs of weights given in either kilograms or grams

• Which is the longer item?
  
  Choose the item that is longer
• Use symbols to compare length
  
  Choose a symbol to say if the first length is longer, shorter or equal to the second length
• Scaling distance by 10
  
  If journey B is ten times longer than journey A, how long is journey B?

• Who is heaviest?
  
  Look at the weights in kilograms of 3 school pupils and say who is heaviest
• Which item is lightest?
  
  Look at the metric weights of 3 items and say which is lightest
• Use symbols to compare weight
  
  Choose a symbol to say if the first mass is greater than, less than or equal to the second mass
• Scaling weight by 10
  
  If an object is ten times heavier than another object, what does it weigh?

• Choose the units
  
  Choose the most likely units to use for taking the measurements described
• Perimeter of a rectangle
  
  Use the diagram to measure the perimeter of the rectangle

• Tell the time: analogue clock
  
  Look at the clock pictures and choose the correct words to describe the time
• Tell the time: Roman numerals
  
  Reading a clock with Roman numerals choose the correct description for the time
• Tell the time: digital clock
  
  Choose the correct description for each of the given digital clock times
• 24-hour clock times
  
  Choose the correct description for each of these 24-hour clock times

• am or pm
  
  Decide whether these 24 hour clock times are am or pm
• Arrival times: first or last
  
  From the given list of arrival times pick the person who arrives first or last
• Compare durations: seconds & minutes
  
  From the race times given in seconds or minutes identify who finished first or last
• Compare durations: minutes & hours
  
  From the journey times given in hours or minutes identify who arrives first or last
• Which durations are the same?
  
  Compare three durations in minutes and hours and pick the two that are the same
• How many of these in that
  
  Identify how many smaller units make up larger unit of time e.g. the number of seconds in a minute is 60

• Subtract coins
  
  Subtract groups of coins of all denominations and say how much is left
• How much change from $5?
  
  Use subtraction to work out how much change you should get from $5

• Add meters to centimeters
  
  Convert meters into centimeters and then add the measures together
• Add kilograms and grams
  
  Convert the given kilograms to grams and then add the weights together
• Add liters and milliliters
  
  Add liters and milliliters by converting the liters to milliliters and then adding the volumes together

• 2D shapes: name from diagram
  
  Identify the names of the two-dimensional (2D) shapes from the pictures
• 2D shapes: diagram from name
  
  Identify the 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
• 3D shapes: diagram from name
  
  Identify the correct diagram from the names of these 3-dimensional (3D) shapes

• How many corners
  
  Count the number of corners on each of these named 2-dimensional shapes
• How many sides
  
  Count the number of sides on each of these named 2-dimensional shapes
• Identify properties of 2-D shapes
  
  Choose the correct set of properties for the given 2-dimensional shapes

• Identify right angles
  
  Identify whether the given angles are right angles or are angles greater than or less than a right angle

• Horizontal and vertical
  
  Identify the horizontal or vertical line from each selection of lines
• Parallel or perpendicular
  
  Identify whether each pair of lines are parallel or perpendicular

• Turn clockwise
  
  Pick the shape after it has done a quarter, a half or a three-quarter turn clockwise
• Turn anticlockwise
  
  Pick the shape after it has done a quarter, a half or a three-quarter turn anticlockwise

• Left 2, up 2
  
  Which shape has moved two squares to the left and two squares up?
• Right and up
  
  Which shape has moved the given number of squares right and up

• Interpret pictographs
  
  Use the pictograph to count the number of children who did different activities
• Many to one correspondence
  
  Use pictographs with a many to one correspondence to see which people like certain fruit
• How many more
  
  Compare how many people like 2 different fruit using pictographs with many to one correspondences

• Interpret bar charts
  
  Use the bar charts to count the number of items in different categories
• Bar charts: most or least
  
  Use the bar charts to identify the most or least popular fruits
• Bar charts: how many more
  
  From the bar charts say how many more items one category has than another

• Interpret tables
  
  Use the data tables to answer questions about how many pupils get to school in different ways
• Most or least frequent
  
  From the frequency tables say which way of getting to school was most or least common
• Tables: how many more
  
  For each table work out how many more pupils got to school by one means rather than another

• Algebra equations: Addition
  
  Solve these one-step addition equations to find the value of b in each equation