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Grade 5 Math

Concepts, unit by unit

Every topic in the course and the concepts it is about, in the order the units teach them. A numbered card opens the idea on its own page; a concept with its big idea opens its topic.

Unit 1 of 5

Number

How big? How close? How much?

6 topics · 138 concepts · Open the unit

  1. Where fractions livePut fractions on the line. Watch equal ones share a spotThe lesson
    1. Equal parts make a fraction
    2. Top number, bottom number
    3. A fraction of a group of things
    4. A fraction is a spot on the number line
    5. Compare fractions of the same whole
    6. Split the parts: same amount, new name
    7. Equivalent fractions share one spot
    8. Multiply the top and bottom by the same number
    9. Fractions that make one whole
    10. Fractions can be more than 1
    11. From improper fraction to mixed number
    12. From mixed number back to improper fraction
    13. Same bottom number: compare the tops
    14. Same top number: more parts means smaller parts
    15. Use 1/2 as a landmark
    16. Which is closer to 1?
    17. Rename to the same bottom number to compare
    18. Ordering mixed numbers and improper fractions
    19. Add fractions with the same bottom number
    20. When a sum goes past one whole
    21. Subtract fractions with the same bottom number
    22. Tenths and hundredths as decimals
    23. Percent means out of 100
    24. One amount, three names: fraction, decimal, percent
  2. The closer neighbourWatch a decimal pick its closer neighbourThe lesson
    1. Tenths: one whole cut into 10
    2. Hundredths: each tenth cut into 10
    3. Read a decimal by its last place
    4. Decimals live between whole numbers
    5. A metre stick counts in hundredths
    6. A zero holds the place
    7. Decimals in expanded form
    8. Decimals as money
    9. A zero at the end changes nothing
    10. After 0.99 comes 1.00
    11. One place right: one tenth as much
    12. More digits is not more
    13. Put decimals in order
    14. Rounding picks the closer tenth
    15. Count the hundredths to each side
    16. Exactly halfway rounds up
    17. The hundredths digit is a shortcut
    18. Rounding up into the next whole
    19. Nearest tenth or nearest whole?
    20. Rounding measurements in real life
    21. Round up to have enough
    22. Rounded numbers can hide a difference
    23. Which numbers round to 4.3?
  3. Big Numbers, Adding & SubtractingOpen numbers into places, regroup them, add and subtractThe lesson
    1. A digit is worth its place
    2. Ten of a place make one of the next
    3. Read a big number in two parts
    4. A zero holds an empty place
    5. Expanded form shows each digit's value
    6. Build a number more than one way
    7. One more than 99 999
    8. More digits means a greater number
    9. Compare from the biggest place
    10. Put big numbers in order
    11. Big numbers on a number line
    12. Add in any order
    13. Group to make a friendly number
    14. Split a number to multiply it
    15. Subtraction undoes addition
    16. Count up to subtract
    17. Use a friendly number, then fix it
    18. The little 1 is a ten moved up
    19. Unpack a ten to subtract
    20. Subtract across zeros
    21. Line up the places in decimals
    22. Estimate to check an answer
    23. Solve a problem in two steps
  4. Multiplication & DivisionSee the structure, split it apart, flip it to divideThe lesson
    1. Rows times columns
    2. Turn the array, keep the product
    3. Times 0 and times 1
    4. Double, then double again
    5. Split a fact into two you know
    6. Nines from tens
    7. Share out, or make groups
    8. One array, four facts
    9. Times 0.1 is one tenth
    10. Times 0.01 is one hundredth
    11. Times 0.1 makes a number smaller
    12. Estimate a decimal sum
    13. Estimate the change
    14. Tens times tens make hundreds
    15. The area model for 23 × 14
    16. Partial products in a column
    17. The algorithm in two rows
    18. Estimate to check a product
    19. Division finds a missing side
    20. Divide in friendly chunks
    21. What is left over
    22. Round up, or leave the remainder out
    23. Share the remainder too
    24. Check a division by multiplying
  5. How Many Pieces?Four ribbons cut into thirds gives twelve pieces — and still four ribbonsThe lesson
    1. A unit fraction is one equal piece
    2. A bigger bottom number means a smaller piece
    3. Count in thirds
    4. 4 × 1/3 is 4 groups of one third
    5. Multiplying is adding the same piece again
    6. The whole number becomes the numerator
    7. 4/3 is one whole and one third
    8. Sometimes the pieces make whole numbers
    9. Jumps of 1/4 on a number line
    10. 4 ÷ 1/3: how many thirds fit in 4?
    11. Same pieces in every whole
    12. 12 thirds is still 4 wholes
    13. Smaller pieces fit more times
    14. Dividing by 1/3 is not dividing by 3
    15. Count the jumps from 0 to 2
    16. One egg is 1/6 of a carton
    17. × and ÷ undo each other
    18. 4 × 1/3 and 4 ÷ 1/3 ask different questions
    19. Ribbon for 5 bows
    20. How many 1/2-cup scoops?
    21. How many people get 1/6 of a pizza?
    22. × or ÷? Read what the story gives you
  6. Ratios & RatesScale both quantities together — the relationship survivesThe lesson
    1. A ratio compares two amounts
    2. Part to part
    3. Part to whole
    4. Three ways to write a ratio
    5. The order of a ratio matters
    6. Equal groups keep the ratio
    7. A ratio table, group by group
    8. Scale up: multiply both terms
    9. Scale down: divide both terms
    10. Adding the same to both breaks a ratio
    11. Are two ratios equivalent?
    12. Find a missing term
    13. Add two columns to make a third
    14. Ratios on a double number line
    15. A rate compares different units
    16. Beats per minute from 15 seconds
    17. The unit rate is the amount for one
    18. Use the unit rate for any amount
    19. Scale a recipe up or down
    20. A map scale is a ratio
    21. From kilometres back to the map
    22. Use the whole to find a part

Unit 2 of 5

Data

What do the numbers really say?

5 topics · 110 concepts · Open the unit

  1. Same Data, Three StoriesSame numbers, three very different graphsThe lesson
    1. A graph needs a title and labels
    2. A source says where the data came from
    3. A scale counts in equal steps
    4. Pick a scale that fits the data
    5. A pictograph's key counts for many
    6. A bar graph compares groups
    7. A double-bar graph compares two groups
    8. A stacked bar shows parts of a whole
    9. Read one part of a stacked bar
    10. A line graph shows change over time
    11. Match the graph to the question
    12. Same data, two graphs, two answers
    13. Same numbers, different pictures
    14. Bars need a scale that starts at 0
    15. Watch for uneven steps on a scale
    16. Bigger pictures can fool the eye
    17. 3-D bars are hard to read
    18. Fix a misleading graph
    19. Ask questions at three levels
    20. A conclusion the data supports
    21. Test an idea with data
    22. Make a decision with data
  2. Spinner LabGuess first. Then spin 1000 times and see what happensThe lab
    1. Outcomes and events
    2. Equal sections are equally likely
    3. Probability as a fraction
    4. Every section goes on the bottom
    5. Split unequal sections into equal parts
    6. Impossible is 0, certain is 1
    7. Unlikely, even chance, likely
    8. Put a probability on the line
    9. Happening and not happening make 1
    10. Which spinner gives the better chance?
    11. Same chance, different spinners
    12. Predict how many times
    13. Tally the spins
    14. What should happen and what did happen
    15. Small experiments wander
    16. More trials settle closer
    17. The spinner has no memory
    18. Streaks happen by chance
    19. A big gap after many trials
    20. Is the game fair?
    21. Make an unfair game fair
    22. Use probability to decide
  3. What's Typical?One group of numbers. Three honest answersThe lesson
    1. One number for a whole group
    2. The mode: the value that appears most
    3. No mode, or two modes
    4. The mode works for words
    5. The median: the middle value in order
    6. An even count has a middle pair
    7. Finding the number halfway
    8. Put decimals in order by place value
    9. A decimal median can land on hundredths
    10. The mean: level the stacks
    11. Add, then divide by how many
    12. A zero still counts
    13. The mean can be a number not in the data
    14. Above and below the mean balance
    15. The mean of decimal data
    16. A value far from the rest
    17. An outlier pulls the mean
    18. Mode, median and mean on a line plot
    19. Use the mode for the most popular
    20. Use the median when a value is far off
    21. Use the mean for a fair share
    22. What each measure tells you
  4. Who did we ask?Same school, same question, two very different answersThe lesson
    1. The question decides the data
    2. Data in words or in numbers
    3. Collect it yourself, or look it up
    4. Survey, observe or experiment
    5. A survey question that does not push
    6. The population and the sample
    7. Ask everyone, or ask some?
    8. Whoever is nearby is not everyone
    9. More people won't fix it
    10. A sample with the school's mix
    11. Names in a hat
    12. Split into groups first
    13. Every 4th name on the list
    14. Ask everyone the same way
    15. Two fair samples can differ a little
    16. Tally, then count
    17. How many out of how many
    18. As a fraction, a decimal or a percent
    19. The parts make 100%
    20. Out of the number asked
    21. Compare shares, not counts
    22. A sample predicts the group
  5. Tell the StoryBuild an infographic — then check whether it says what the data saysThe lesson
    1. An infographic tells one story
    2. Decide the one message first
    3. Made for a reader
    4. Count out of the whole group
    5. Shares as decimals
    6. The shares make one whole
    7. Compare shares, not counts
    8. Parts stacked in one bar
    9. Read a middle piece
    10. Stretch each bar to one whole
    11. Pick the display for the question
    12. One big number
    13. Pictures sized honestly
    14. Icons with a key
    15. Put the parts in reading order
    16. Titles, labels and a source
    17. Leave out what does not help
    18. “Most” means more than half
    19. Check where the scale starts
    20. The story fits who was asked
    21. Revise the draft
    22. Build an infographic from data

Unit 3 of 5

Algebra

What's the rule behind the pattern?

3 topics · 67 concepts · Open the unit

  1. Patterns & RulesCatch the rule behind a pattern and make it work for youThe lesson
    1. Repeat, grow or shrink
    2. Patterns around you
    3. One staircase, three patterns
    4. Find the missing term
    5. Which shape is 20th?
    6. Patterns with decimals
    7. Patterns that times by 10
    8. Number strings for 7
    9. Say the rule
    10. From tiles to a table
    11. Growing by adding a core
    12. Extend it backwards
    13. Input, rule, output
    14. Week 0 comes first
    15. The rule as 5x + 15
    16. Jump ahead with the rule
    17. Which figure has 41 tiles?
    18. Make a pattern, then prove it
    19. Graph the savings
    20. Between and beyond the dots
    21. Spending down, four ways
  2. Variables & EquationsCrack the = sign's secret and free the mystery numberThe lesson
    1. A letter holds a number
    2. A variable can change
    3. 3n means 3 times n
    4. Words into an expression
    5. A picture into an expression
    6. Same value, different look
    7. Put a number in for the letter
    8. Multiply first, then add
    9. An expression in a story
    10. Expression or equation?
    11. Equals means the same value
    12. Do the same to both sides
    13. Guess, check and revise
    14. Work backwards to the unknown
    15. Solve it on the balance
    16. Put it back to check
    17. The unknown can be on either side
    18. Undo a take-away
    19. An equation from a story
    20. An inequality has many solutions
    21. Less than or equal to
    22. Graph the solutions
    23. An inequality in a story
  3. Rule MachinesWrite a rule that asks a question — then watch it decideThe lesson
    1. Code is exact steps in order
    2. Swap two lines, change the output
    3. A variable holds one number
    4. Same code, new input
    5. A loop repeats the lines inside it
    6. Counting with a loop
    7. A loop can make a pattern
    8. Trace code in a table
    9. A condition is yes or no
    10. IF … THEN runs only on a yes
    11. IF … ELSE picks one of two paths
    12. Greater than, less than, equal to
    13. Sort numbers with an IF
    14. A question inside a question
    15. A loop with an IF inside
    16. Predict before you run
    17. Change one number, see what changes
    18. Find the bug, fix the line
    19. Test the number on the edge
    20. It runs, but is the math right?
    21. Reuse code for a new job
    22. Write code for a savings plan
    23. Write an IF for a rule

Unit 4 of 5

Spatial

What can shapes and space do?

6 topics · 118 concepts · Open the unit

  1. Area & PerimeterSame area, different fence — reshape it and seeThe lesson
    1. Area counts the squares inside
    2. Perimeter is the distance around
    3. Fence or floor: which measure?
    4. Length × width gives the area
    5. Two lengths and two widths
    6. Square units for area, plain units for perimeter
    7. Split a shape into rectangles
    8. Find the missing sides first
    9. Work back from the area
    10. A parallelogram becomes a rectangle
    11. The height goes straight up
    12. Two triangles make a parallelogram
    13. A triangle's height can land outside it
    14. Any side can be the base
    15. Same base, same height, same area
    16. Same area, different perimeters
    17. Close to a square needs the least fence
    18. Same perimeter, different areas
    19. Move a tile, change the perimeter
    20. Carpet and baseboard for a room
    21. A fence on three sides
    22. A wall with a triangle on top
  2. Triangles & AnglesMove a corner — every angle changes, one number never doesThe lesson
    1. An angle is a turn
    2. Lay one angle on another
    3. Count wedges to measure an angle
    4. A degree is a tiny turn
    5. Benchmark angles for estimating
    6. Acute, right, obtuse or straight
    7. Put the protractor on the vertex
    8. Two scales: start at the 0
    9. Draw an angle with a protractor
    10. Every triangle has three angles
    11. Name a triangle by its sides
    12. Equal sides face equal angles
    13. Name a triangle by its angles
    14. One triangle, two names
    15. A triangle's angles make 180°
    16. Find the missing angle
    17. Inside and outside angles
    18. Outside angles make a full turn
    19. Build a triangle from three sides
    20. Two sides must beat the third
    21. Build from a base and two angles
    22. Congruent means an exact copy
    23. Same angles can differ in size
    24. Congruent rectangles and parallelograms
  5. How Big Is It, Really?One ribbon, four units — the ribbon never moves, the number doesThe lesson
    1. Length, mass, capacity or area?
    2. Pick a unit that fits the size
    3. Rough or exact: the job picks the unit
    4. Benchmarks for length
    5. Benchmarks for mass and capacity
    6. Could that really be its size?
    7. Estimate first, then measure
    8. Count the spaces from the start
    9. 10 millimetres make 1 centimetre
    10. Area is measured in squares
    11. Smaller unit, more of them
    12. Metres, centimetres and millimetres
    13. A kilometre is 1000 metres
    14. Kilo, centi, milli: one pattern for every unit
    15. Grams and kilograms
    16. Millilitres and litres
    17. Big unit to small unit: multiply
    18. Decimals in measurements
    19. Move the digits to change the unit
    20. Small unit to big unit: divide
    21. Compare in the same unit
    22. Solve a measuring problem
  6. From Every SideOne object, three drawings — and none of them look alikeThe lesson
    1. A view shows one side, drawn flat
    2. The front view: the tallest in each column
    3. The side view: standing at the right
    4. The top view: looking straight down
    5. Where you stand sets the view
    6. The back view is the front view flipped
    7. A view cannot show how deep
    8. Hidden cubes still count
    9. Numbers on the top view give the heights
    10. Shading on the top view shows height
    11. Different buildings can share a view
    12. Each view rules out more buildings
    13. Build a building from its three views
    14. The most cubes that fit two views
    15. The fewest cubes that fit two views
    16. Draw a view on grid paper
    17. An isometric drawing shows three sides at once
    18. Turn the building to check a view
    19. Views of an everyday object: a mug
    20. A line in a view shows where the height changes
    21. Match the views to the object
    22. Builders call them plans and elevations

Unit 5 of 5

Financial

How can math help you choose?

3 topics · 69 concepts · Open the unit

  1. Money, Transactions & BudgetsBuild a plan, watch what's left, fix it when it breaksThe lesson
    1. Who pays whom
    2. Debit takes it from the account
    3. One account down, one account up
    4. Gift cards and cheques
    5. Pick the way that fits
    6. Estimate a total by rounding
    7. Multiply each line, then add
    8. Count up to make change
    9. Cash rounds to 5 cents
    10. 13% sales tax
    11. Estimate the tax and the change
    12. A budget plans money in and out
    13. Needs come before wants
    14. Values shape a budget
    15. Surplus, balanced or deficit
    16. Fix a budget that is over
    17. Save a set amount each week
    18. Keep a record of money
    19. Budget for a class sale
    20. Credit is borrowed money
    21. A debt is paid back over time
    22. Interest is the cost of borrowing
    23. Pay now or pay later
  2. Smart ShoppingFind the rate for ONE — then let the goal make the callThe lesson
    1. The price for one is the unit price
    2. Price ÷ how many, not the other way
    3. Halve the price table down to one
    4. The price for 100 g
    5. The price for one litre
    6. Estimate to check a unit price
    7. Compare the price for one
    8. Bigger is not always cheaper
    9. Compare the same amount
    10. Change kilograms to grams first
    11. Change litres to millilitres first
    12. Read the unit price on the shelf tag
    13. 3 for $5.00: check the deal
    14. Buy one, get one free
    15. Percent off is a fraction off
    16. A sale, or a bigger pack?
    17. The price for one hour
    18. Pay monthly or pay yearly?
    19. When a pass pays off
    20. Less today, or less for each?
    21. Food you throw away is not a saving
    22. The best value must fit your budget
    23. Lasting longer can cost less
  3. Where Does It Come From?Nobody pays at the door — so follow the money that keeps a town goingThe lesson
    1. A tax pays for shared things
    2. A tax, a fee or a price
    3. Revenue is all the tax collected
    4. Federal, provincial and municipal
    5. Band councils collect tax too
    6. Each government pays for its own jobs
    7. Income tax comes off the pay
    8. Sales tax is added at the till
    9. 13% is 10% plus 3%
    10. Add the prices, then the tax
    11. HST has a federal part and an Ontario part
    12. Basic groceries have no sales tax
    13. Property tax comes from a home's value
    14. Gas tax is counted by the litre
    15. No tax belongs to one government
    16. Taxes join in one revenue
    17. A town budget in 100 squares
    18. Read a spending bar graph
    19. Health care is Ontario's biggest part
    20. A property tax bill has a school part
    21. Public and private services
    22. More pay means a bigger share of tax
    23. Taxes help even people who never use a service