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5th grade math

Program of study for 5th grade

The CCSS core curriculum for 5th grade covers a range of categories, including:

  • Number and place value
    Students develop a deep understanding of the number system, including place value, ordering and comparing numbers, and rounding.

  • Addition, subtraction, multiplication, and division
    Students continue to refine their arithmetic skills and mental calculations. They learn efficient methods for addition, subtraction, multiplication, and division of larger numbers, including long multiplication and long division. They also develop strategies for solving multi-step problems involving these operations.

  • Fractions, Decimals, and Percentages
    Students will learn about different types of fractions, such as proper fractions, improper fractions, and mixed numbers. They will also learn how to add, subtract, multiply, and divide fractions. They learn to compare and order fractions and decimals, convert between these forms, and solve problems involving fractions and decimals. They also explore the concept of percentages and their relationship to fractions and decimals.

  • Ratio and proportion
    Students learn about ratios and how to express relationships between quantities using ratios. They will also learn how to use ratio and proportion to solve problems including scaling and finding equivalent ratios.

  • Measurement
    Students will learn about different units of measurement, such as length, mass, volume, and time. They will also learn how to convert between different units of measurement.

  • Geometry & shapes
    Students will learn about the properties of 2D and 3D shapes. They will also learn how to calculate the area and perimeter of 2D shapes, and the volume of 3D shapes.

  • Position & direction
    Students study properties of lines including angles, lines of symmetry, and parallel and perpendicular lines. They also explore transformations, such as reflections, rotations, and translations.

  • Statistics
    Students will learn about how to collect, organize, and interpret data. Students begin to analyze and interpret data using various graphs and charts, such as bar charts, line graphs, and pictograms. They learn to calculate the mean, median and mode of data sets.

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

  • Problem-solving
    Students will learn how to solve mathematical problems using a variety of methods. They will also learn how to apply mathematical concepts to real-world problems.

In addition to these specific topics, students will also develop their fluency with mathematical concepts and their ability to solve mathematical problems. They will be able to use mathematical reasoning to solve problems in other areas of their lives, such as science, technology, and engineering.

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Math topic index for 5th grade

Below is the complete list of topics for 5th grade arranged by category. Click on a topic to view more information.

Counting
Read large numbers
Write large numbers
Steps of powers of 10
Order negative numbers
Negative coordinates
Temperature graph
Roman numerals

Comparing numbers
Order decimal numbers
Order positives & negatives
Using inequality symbols
Money
Naming numbers

Pattern
Next number
Missing term
Describing a pattern

Place value
Identify the place value
Rounding numbers
Change the place value
Describe the place value
  • Multiply by 100
    What will the place value of the highlighted green digit be after multiplying by 100?
  • Multiply by 1000
    What will the place value of the highlighted green digit be after multiplying by 1000?
  • Multiply by 0.1
    What will the place value of the highlighted green digit be after multiplying by 0.1?
  • Dividing by 10
    What will the place value of the highlighted green digit be after dividing by 10?
  • Dividing by 100
    What will the place value of the highlighted green digit be after dividing by 100?
  • Dividing by 0.1
    What will the place value of the highlighted green digit be after dividing by 0.1?

Addition
Number bonding
Strings of numbers
Round + adjust to add
Estimate to add
Word problems
Formal written method

Subtraction
Estimate to subtract
Formal written method
Word problems
Money left

Add + Subtract
Add 109, 119, 129
Add 101, 111, 121
Subtract 89, 99, 109
Subtract 101, 111, 121
  • Subtract 101
    Subtract 101 from a number by subtracting 100 and then subtracting 1 more
  • Subtract 111
    Subtract 111 from a number by subtracting 110 and then subtracting 1 more
  • Subtract 121
    Subtract 121 from a number by subtracting 120 and then subtracting 1 more
Number machine
  • Add and subtract
    Add and subtract to find the answer to these 2 step problems
  • Missing addition
    Find the missing addition in these 2 step add and subtract number machine operations
  • Missing subtraction
    Find the missing subtraction value in these 2 step add and subtract operations
Checking answers

Multiplication
Identifying multiples
Mental Method
Formal written method
Mixed operations

Division
Mental method
Formal short method
Formal long method
Formal short with remainder
Formal long with remainder
Mixed operations
  • Add then divide
    Use mental calculations to answer questions where you add first and then divide
  • Subtract then divide
    Use mental calculations to answer questions where you subtract first and then divide
  • Divide then add
    Use mental calculations to answer questions where you divide first and then add
  • Divide then subtract
    Use mental calculations to answer questions where you divide and then subtract
  • BIDMAS - 4 operations
    Use order of operations (BIDMAS) to find the correct answers

Multiply + Divide
Matching Pairs
Order of operations
Factors
Distributive laws
Solving problems
Best Price
  • Best price - divide by 7
    Use division by 7 to work out the saving made by purchasing a packet of 7 rather than individual items
  • Best price - divide by 9
    Use division by 9 to work out the saving made by purchasing a packet of 9 rather than individual items
Money and people

Fractions
Compare fractions
Order fractions
Fractions of a quantity
Convert fractions
Add fractions
Subtract fractions
Multiply fractions
Divide proper fractions
Reverse fraction of quantity
Fractions and decimals
Word problems

Decimals
Writing decimals
Value of a digit
Round decimals
Add decimals
  • Add decimals
    Add decimal numbers by arranging them in columns and lining up the decimal points
Subtract decimals
  • Subtract decimals
    Subtract decimal numbers by arranging them in columns and lining up the decimal points
Multiply decimals
Divide decimals

Ratio + proportion
Relative sizes
  • Double the size
    Use multiplication and division to get double the size of the objects or values
  • Triple the size
    Use multiplication and division to find triple the given values and measures
  • Five times the size
    Use multiplication and division to find five times the given sizes
  • Half the size
    Use multiplication and division to find half of the given quantities and measures
  • A third of the size
    Use multiplication and division to find a third of the size of the given values and measures
  • A fifth of the size
    Use multiplication and division to find a fifth of the given values and measures
  • Calculate total size
    Use multiplication and division to calculate the whole value or measure from the given decimal portion
  • Relative size: find scale factor
    Use multiplication and division to find the scale factor given original and final sizes
Percent: no calculator
  • Find 10%
    From 100% find out what 10% is using division (without using your calculator)
  • Find 30%
    Find 30% by breaking up each given value into 3 lots of 10% (no calculator)
  • Find 15%
    Find 15% by breaking up each given value into a 10% and a 5% and adding them together
Percent: with calculator
Express as a percentage
Compare proportions
Similar shape problems

Measurements
Volume
Standard units
Convert units: large to small
Convert units: small to large
Approximate equivalence
Formulae for area
Solving problems

Shapes
Identifying shapes
Properties of 2-D shapes
  • Most vertices
    For each pair of shapes, identify which one has the greater number of vertices
  • Most sides
    For each pair of shapes, identify which one has the greater number of sides
  • Lines of symmetry
    For each pair of shapes, identify which shape has more lines of symmetry
  • Identify 2D shapes from properties
    Choose the shape to which the given set of properties (sides, angles, lines of symmetry) apply
  • Parts of a circle
    Identify parts of a circle including radius, diameter, circumference, chord, tangent etc.
Angles
  • Acute angles
    For each of these lists, identify the largest angle that is acute
  • Obtuse angles
    Identify the smallest or largest angle in each of these sets which is obtuse
  • Reflex angles
    Identify the smallest or largest angle in each of these sets that is reflex
Angle problems

Position + Direction
Describe the translation
Lines
Position on a full grid
Translate a shape
  • Left and up
    Identify the square that is the result of translating the pink square left and up
  • Right and down
    Identify the square that is the result of translating the pink square right and down

Statistics
Interpret
Mean mode median
  • Mode
    Identify the mode or most frequent in each data set
  • Median
    Identify the median by placing numbers in order and striking
  • Mean
    Calculate the mean by finding the total and dividing by the number of data points
  • Range
    Identify the range for each of these sets of numbers
  • Outliers
    Identify the outlier in each of these sets of numbers

Algebra
Equations
Formulae: perimeter
Formulae: area
  • Area of squares
    Calculate the area of squares using the formula area A = length L times L
  • Area of rectangles
    Calculate the area of rectangles using the formula area A = length L x width W
Missing angles
Express the missing angle
Missing lengths & numbers
Simplify
Linear Sequences
Enumerate possibilities
  • Two variables
    Identify the pair of numbers that satisfy a statement
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