Mathematics 5

Course Outline

Number

  • read, write, represent, and describe numbers to 1 000 000 using concrete materials, pictures,  expressions, expanded notation, words, place-value charts, and symbols 
  • describe numbers to 1 000 000 in two or more parts (partition)
  • explore place value (ones, tens, hundreds, thousands, ten thousands, hundred thousands, millions)
  • use place-value patterns to understand numbers up to  1 000 000
  • compare and order large numbers to 1 000 000
  • represent and describe decimal numbers (tenths, hundredths, thousandths) using concrete materials, pictures, money, expressions, words, and symbols
  • read, write, and recognize decimal number symbols (to thousandths)
  • compare and order decimal numbers (to thousandths)
  • represent, interpret, model, and rename fractions using concrete materials, pictures, and symbols 
  • compare and order fractions (use benchmarks, compare numerators and denominators)
  • rename fractions (one halfone quarter, and three quarters and with denominators of 10, 100, and 1000) as decimals
  • rename decimals as fractions (e.g., 0.25 = twenty-five over one hundred)
  • estimate sums, differences, products, and quotients (involving whole numbers) using appropriate mental mathematics strategies
  • estimate the answers to addition and subtraction questions that use decimals to the thousandths
  • explain the reasons for our estimates
  • choose appropriate estimates
  • solve and create addition and subtraction problems that involve whole numbers and decimals
  • use personal strategies to calculate sums and differences involving whole numbers and decimals to the thousandths
  • represent multiplication and division problems concretely, pictorially, and symbolically
  • quickly recall multiplication and division basic facts 
  • mentally multiply by 10, 100, and 1000 and their multiples
  • use mental mathematics strategies to make multiplication more efficient
  • continue to use personal strategies to multiply one-, two-, and three-digit numbers by a one-digit number
  • use personal strategies to multiply two two-digit numbers
  • use personal strategies to divide two- and three-digit numbers by a one-digit number
  • solve and create multiplication and division story problems that involve whole numbers 
  • explain the treatment of a remainder in a division story problem

 

Patterns and Relations (PR)

  • identify and describe (orally and in writing) patterns 
  • identify and describe patterns found in charts and tables using an expression
  • use an expression to represent a pattern
  • extend an increasing or decreasing pattern and describe how the terms in the pattern change from one step to the next
  • determine missing or subsequent elements in a pattern
  • identify errors in a pattern
  • use a pattern rule to continue a pattern
  • use patterns to solve problems
  • create a table or chart from a pattern shown concretely
  • create a pattern concretely from a table or chart
  • use a letter variable to represent the unknown in an addition, subtraction, multiplication, or division problem (e.g., 24 ÷ n = 6, 24 = 6 × n or 24 = 6 × n)
  • write an equation with a variable to represent a given story problem
  • create a story problem for a given equation with one unknown
  • solve a one-step equation with one variable 
  • represent addition, subtraction, multiplication, and division situations with an equation having one variable

  

Measurement

  • draw rectangles for a given perimeter (distance around the outside)
  • draw rectangles for a given area 
  • recognize and demonstrate that different objects can have the same area (inside space)
  • recognize and demonstrate that objects with the same area can have different perimeters (distance around the outside)
  • determine the shape that will result in the least or the greatest area for a given perimeter
  • estimate and measure area in square centimetres and square metres
  • solve simple problems involving the perimeter and/or area of polygons
  • identify a referent for one millimetre, one centimetre, and one metre
  • understand that 10 millimetres is equal to 1 centimetre and 1000 millimetres is equal to 1 metre
  • estimate and measure length in millimetres, centimetres, and metres
  • determine which unit of measurement is appropriate to use in a given situation
  • identify a referent for a cubic centimetre and a cubic metre
  • estimate and measure volume (the amount of space occupied by a 3-D object) using standard units (cubic centimetres and cubic metres)
  • estimate and then determine the volume of rectangular prisms using centimetre cubes
  • construct a rectangular prism for a given volume using cubes
  • provide a referent for one litre and one millilitre
  • understand that 1000 millilitres is equal to 1 litre
  • estimate and measure capacity (the amount a container is capable of holding) using materials that take on the shape of the inside of a container, and using standard units (millilitre and litre)
  • solve measurement problems (area, perimeter, length, volume, and capacity)

  

Geometry

  • recognize, name, and describe parallel, intersecting, perpendicular, vertical, and horizontal edges and faces on 3-D objects
  • recognize, name, and describe parallel, intersecting, perpendicular, vertical, and horizontal sides on 2-D shapes
  • draw 2-D shapes with sides that are parallel, intersecting, perpendicular, vertical, and horizontal 
  • build 3-D objects with edges and faces that are parallel, intersecting, perpendicular, vertical, and horizontal 
  • identify, name, and sort quadrilaterals according to their attributes
  • identify a translation (slide) of a 2-D shape
  • identify a rotation (turn) of a 2-D shape
  • identify a reflection (flip) of a 2-D shape
  • describe the direction and magnitude of a translation (slide)
  • describe the direction of turn of a rotation (turn)
  • describe the line of reflection (e.g., horizontal, vertical) and the distance from the line of reflection (flip)
  • identify transformations (flips, slides, and turns) found in the everyday world 
  • perform a translation (slide) of a 2-D shape
  • perform a rotation (turn) of a 2-D shape
  • perform a reflection (flip) of a 2-D shape
  • predict the result of a transformation (a flip, a slide, or a turn) and verify the prediction
  • identify and sketch right angles
  • identify angles that are greater than and less than a right angle

  

Statistics and Probability 

  • explain the difference between first-hand data and second-hand data
  • ask questions that can be answered using first-hand data
  • ask questions that can be answered using second-hand data 
  • create, read, and interpret double bar graphs 
  • solve problems by constructing and interpreting double bar graphs
  • make predictions about whether particular events are certain, impossible, possible, less likely, more likely, or equally likely to occur
  • identify events that are certain, impossible, possible, less likely, more likely, or equally likely to occur
  • design and conduct a probability experiment in which the likelihood of an outcome occurring is either possible, impossible, or certain
  • design and conduct a probability experiment in which the likelihood of an outcome occurring is less likely, more likely, or equally likely to occur as another outcome
  • conduct simple experiments to determine probabilities

Updated January 31, 2022