Math Games

Say the number sequence forward and backward from 0 to 1000 by:
• 5s, 10s or 100s using any starting point
• 3s using starting points that are multiples of 3
• 4s using starting points that are multiples of 4
• 25s using starting points that are multiples of 25.

• Achievement Indicators
• Students who have achieved this outcome(s) should be able to:
- Extend a given skip counting sequence by 5s, 10s or 100s, forward and backward, using a given starting point.
- Extend a given skip counting sequence by 3s, forward and backward, starting at a given multiple of 3.
- Extend a given skip counting sequence by 4s, forward and backward, starting at a given multiple of 4.
- Extend a given skip counting sequence by 25s, forward and backward, starting at a given multiple of 25.
- Identify and correct errors and omissions in a given skip counting sequence.
- Determine the value of a given set of coins (nickels, dimes, quarters, loonies) by using skip counting.
- Identify and explain the skip counting pattern for a given number sequence.

Apply mental mathematics strategies and number properties, such as:
• using doubles
• making 10
• using the commutative property
• using the property of zero
• thinking addition for subtraction
to recall basic addition facts to 18 and related subtraction facts.

• Achievement Indicators
• Students who have achieved this outcome(s) should be able to:
- Describe a mental mathematics strategy that could be used to determine a given basic fact, such as:
• doubles, e.g., for 6 + 8, think 7 + 7
• doubles plus one, e.g., for 6 + 7, think 6 + 6 + 1
• doubles take away one, e.g., for 6 + 7, think 7 + 7 – 1
• doubles plus two, e.g., for 6 + 8, think 6 + 6 + 2
• doubles take away two, e.g., for 6 + 8, think 8 + 8 – 2
• making 10, e.g., for 6 + 8, think 6 + 4 + 4 or 8 + 2 + 4
• commutative property, e.g., for 3 + 9, think 9 + 3
• addition to subtraction, e.g., for 13 – 7, think 7 + ? = 13.
- Provide a rule for determining answers for adding and subtracting zero.
- Recall basic addition facts to 18 and related subtraction facts to solve problems.

Demonstrate an understanding of multiplication to products of 36 with single digit factors by:
• representing and explaining multiplication using equal grouping and arrays
• creating and solving problems in context that involve multiplication
• modelling multiplication using concrete and visual representations, and recording the process symbolically
• relating multiplication to repeated addition
• relating multiplication to division.

• Achievement Indicators
• Students who have achieved this outcome(s) should be able to:
- Identify events from experience that can be described as multiplication.
- Represent a given story problem (orally, shared reading, written) using manipulatives or diagrams and record in a number sentence.
- Represent a given multiplication expression as repeated addition.
- Represent a given repeated addition as multiplication.
- Create and illustrate a story problem for a given number sentence, e.g., given 2 × 3, create and illustrate a story problem.
- Represent, concretely or pictorially, equal groups for a given number sentence.
- Represent a given multiplication expression using an array.
- Create an array to model the commutative property of multiplication.
- Relate multiplication to division by using arrays and writing related number sentences.
- Solve a given problem in context involving multiplication.

Demonstrate an understanding of division by:
• representing and explaining division using equal sharing and equal grouping
• creating and solving problems in context that involve equal sharing and equal grouping
• modeling equal sharing and equal grouping using concrete and visual representations, and recording the process symbolically
• relating division to repeated subtraction
• relating division to multiplication.
(limited to division related to multiplication facts up to products of 36 with single digit factors)

• Achievement Indicators
• Students who have achieved this outcome(s) should be able to:
- Identify events from experience that can be described as equal sharing.
- Identify events from experience that can be described as equal grouping.
- Illustrate, with counters or a diagram, a given story problem involving equal sharing, presented orally or through shared reading and solve the problem.
- Illustrate, with counters or a diagram, a given story problem involving equal grouping, presented orally or through shared reading, and solve the problem.
- Listen to a story problem, represent the numbers using manipulatives or a sketch and record the problem with a number sentence.
- Create and illustrate with counters, a story problem for a given number sentence, e.g., given 6 ÷ 3, create and illustrate a story problem.
- Represent a given division expression as repeated subtraction.
- Represent a given repeated subtraction as a division expression.
- Relate division to multiplication by using arrays and writing related number sentences.

Demonstrate an understanding of fractions by:
• explaining that a fraction represents a part of a whole
• describing situations in which fractions are used
• comparing fractions of the same whole with like denominators.

• Achievement Indicators
• Students who have achieved this outcome(s) should be able to:
- Identify common characteristics of a given set of fractions.
- Describe everyday situations where fractions are used.
- Cut or fold a whole into equal parts, or draw a whole in equal parts; demonstrate that the parts are equal and name the parts.
- Sort a given set of diagrams of regions into those that represent equal parts and those that do not, and explain the sorting.
- Represent a given fraction concretely or pictorially.
- Name and record the fraction represented by the shaded and non-shaded parts of a given region.
- Compare given fractions with the same denominator using models.
- Identify the numerator and denominator for a given fraction.
- Model and explain the meaning of numerator and denominator.

Represent and describe numbers to 1000, concretely, pictorially and symbolically.
• Achievement Indicators
• Students who have achieved this outcome(s) should be able to:
- Read a given three-digit numeral without using the word “and,” e.g., 321 is three hundred twenty one, not three hundred AND twenty one.
- Read a given number word (0 to 1000).
- Represent a given number as an expression, e.g., 300 – 50 for 250 or 230 + 20
- Represent a given number using manipulatives, such as base ten materials, in multiple ways.
- Represent a given number pictorially.
- Write number words for given multiples of ten to 90.
- Write number words for given multiples of hundred to 900.

Compare and order numbers to 1000.
• Achievement Indicators
• Students who have achieved this outcome(s) should be able to:
- Place a given set of numbers in ascending or descending order and verify the result by using a hundred chart, e.g., a one hundred chart, a two hundred chart, a three hundred chart, a number line or by making references to place value.
- Create as many different 3-digit numerals as possible, given three different digits. Place the numbers in ascending or descending order.
- Identify errors in a given ordered sequence.
- Identify missing numbers in isolated parts of a given hundred chart (include charts beyond 100).
- Identify errors in a given hundred chart (include charts beyond 100).

Estimate quantities less than 1000 using referents.
• Achievement Indicators
• Students who have achieved this outcome(s) should be able to:
- Estimate the number of groups of ten in a given quantity using 10 as a referent (known quantity).
- Estimate the number of groups of a hundred in a given quantity using 100 as a referent.
- Estimate a given quantity by comparing it to a referent.
- Select an estimate for a given quantity by choosing among three possible choices.
- Select and justify a referent for determining an estimate for a given quantity.

Illustrate, concretely and pictorially, the meaning of place value for numerals to 1000.
• Achievement Indicators
• Students who have achieved this outcome(s) should be able to:
- Record, in more than one way, the number represented by given proportional and non-proportional concrete materials.
- Represent a given number in different ways using proportional and non-proportional concrete materials and explain how they are equivalent, e.g., 351 can be represented as three 100s, five 10s and one 1s, or two 100s, fifteen 10s and one 1s, or three 100s, four 10s and eleven 1s.
- Explain, and show with counters, the meaning of each digit for a given 3-digit numeral with all digits the same, e.g., for the numeral 222, the first digit represents two hundreds (two hundred counters) the second digit represents two tens (twenty counters) and the third digit represents two ones (two counters).
- Record a number represented by base ten blocks arranged informally (not grouped L to R from highest to lowest values).

Describe and apply mental mathematics strategies for adding two 2-digit numerals, such as:
• adding from left to right
• taking one addend to the nearest multiple of ten and then compensating
• using doubles.

• Achievement Indicators
• Students who have achieved this outcome(s) should be able to:
- Add two given 2-digit numbers using a mental mathematics strategy and explain or illustrate the strategy.
- Explain how to use the “adding from left to right” strategy, e.g., to determine the sum of 23 + 46, think 20 + 40 and 3 + 6.
- Explain how to use the “taking one addend to the nearest multiple of ten” strategy, e.g., to determine the sum of 28 + 47, think 30 + 47 – 2 or 50 + 28 – 3.
- Explain how to use the “using doubles” strategy, e.g., to determine the sum of 24 + 26, think 25 + 25; to determine the sum of 25 + 26, think 25 + 25 + 1 or doubles plus 1.
- Apply a mental mathematics strategy for adding two given 2-digit numerals.

Describe and apply mental mathematics strategies for subtracting two 2-digit numerals, such as:
• taking the subtrahend to the nearest multiple of ten and then compensating
• thinking of addition
• using doubles

• Achievement Indicators
• Students who have achieved this outcome(s) should be able to:
- Subtract two given 2-digit numerals using a mental mathematics strategy and explain or model the strategy used.
- Explain how to use the “taking the subtrahend to the nearest multiple of ten” and then compensating strategy, e.g., to determine the difference of 48 – 19, think 48 – 20 + 1.
- Explain how to use the “thinking of addition” strategy, e.g., to determine the difference of 62 – 45, a student might think 45 + 5, then 50 + 12 and then 5 + 12. Using an open number line is helpful with this strategy.
- Explain how to use the “using doubles” strategy, e.g., to determine the difference of 24 – 12, think 12 + 12.
- Apply a mental mathematics strategy for subtracting two given 2-digit numerals.

Apply estimation strategies to predict sums and differences of two 2-digit numerals in a problem solving context.
• Achievement Indicators
• Students who have achieved this outcome(s) should be able to:
- Estimate the solution for a given story problem involving the sum of two 2-digit numerals, e.g., to estimate the sum of 43 + 56, use 40 + 50; the sum is close to 90.
- Estimate the solution for a given story problem involving the difference of two 2-digit numerals, e.g., to estimate the difference of 56 - 23, use 50 - 20; the difference is close to 30.

Demonstrate an understanding of addition and subtraction of numbers with answers to 1000 (limited to 1, 2 and 3-digit numerals) by:
• using personal strategies for adding and subtracting with and without the support of manipulatives
• creating and solving problems in contexts that involve addition and subtraction of numbers concretely, pictorially and symbolically.

• Achievement Indicators
• Students who have achieved this outcome(s) should be able to:
- Model the addition of two or more given numbers using concrete or visual representations and record the process symbolically.
- Model the subtraction of two given numbers using concrete or visual representations and record the process symbolically.
- Create an addition or subtraction story problem for a given solution.
- Determine the sum of two given numbers using a personal strategy, e.g., for 326 + 48, record 300 + 60 + 14.
- Determine the difference of two given numbers using a personal strategy, e.g., for 127 – 38, record 38 + 2 + 80 + 7 or 127 – 20 – 10 – 8.
- Solve a given problem involving the sum or difference of two given numbers.

Relate the passage of time to common activities using non-standard and standard units (minutes, hours, days, weeks, months, years).
• Achievement Indicators
• Students who have achieved this outcome(s) should be able to:
- Select and use a non-standard unit of measure, such as television shows or pendulum swings, to measure the passage of time and explain the choice.
- Identify activities that can or cannot be accomplished in minutes, hours, days, months and years.
- Provide personal referents for minutes and hours.

Relate the number of seconds to a minute, the number of minutes to an hour and the number of days to a month in a problem-solving context.
• Achievement Indicators
• Students who have achieved this outcome(s) should be able to:
• Determine the number of days in any given month using a calendar.
• Solve a given problem involving the number of minutes in an hour or the number of days in a given month.
• Create a calendar that includes days of the week, dates and personal events.

Demonstrate an understanding of measuring length (cm, m) by:
• selecting and justifying referents for the units cm and m
• modeling and describing the relationship between the units cm and m
• estimating length using referents
• measuring and recording length, width and height.

• Achievement Indicators
• Students who have achieved this outcome(s) should be able to:
- Provide a personal referent for one centimetre and explain the choice.
- Provide a personal referent for one metre and explain the choice.
- Match a given standard unit to a given referent.
- Show that 100 centimetres is equivalent to 1 metre by using concrete materials.
- Estimate the length of an object using personal referents.
- Determine and record the length and width of a given 2-D shape.
- Determine and record the length, width or height of a given 3-D object.
- Draw a line segment of a given length using a ruler.
- Sketch a line segment of a given length without using a ruler.

Demonstrate an understanding of measuring mass (g, kg) by:
• selecting and justifying referents for the units g and kg
• modeling and describing the relationship between the units g and kg
• estimating mass using referents
• measuring and recording mass.

• Achievement Indicators
• Students who have achieved this outcome(s) should be able to:
- Provide a personal referent for one gram and explain the choice.
- Provide a personal referent for one kilogram and explain the choice.
- Match a given standard unit to a given referent.
- Explain the relationship between 1000 grams and 1 kilogram using a model.
- Estimate the mass of a given object using personal referents.
- Determine and record the mass of a given 3-D object.
- Measure, using a scale, and record the mass of given everyday objects using the units g and kg.
- Provide examples of 3-D objects that have a mass of approximately 1 g, 100 g and 1 kg.
- Determine the mass of two given similar objects with different masses and explain the results.
- Determine the mass of an object, change its shape, re-measure its mass and explain the results.

Demonstrate an understanding of perimeter of regular and irregular shapes by:
• estimating perimeter using referents for centimetre or metre
• measuring and recording perimeter (cm, m)
• constructing different shapes for a given perimeter (cm, m) to demonstrate that many shapes are possible for a perimeter.

• Achievement Indicators
• Students who have achieved this outcome(s) should be able to:
- Measure and record the perimeter of a given regular shape, and explain the strategy used.
- Measure and record the perimeter of a given irregular shape, and explain the strategy used.
- Construct a shape for a given perimeter (cm, m).
- Construct or draw more than one shape for the same given perimeter.
- Estimate the perimeter of a given shape (cm, m) using personal referents.

Describe 3-D objects according to the shape of the faces, and the number of edges and vertices.
• Achievement Indicators
• Students who have achieved this outcome(s) should be able to:
- Identify the faces, edges and vertices of given 3-D objects, including cubes, spheres, cones, cylinders, pyramids and prisms.
- Identify the shape of the faces of a given 3-D object.
- Determine the number of faces, edges and vertices of a given 3-D object.
- Construct a skeleton of a given 3-D object and describe how the skeleton relates to the 3-D object.
- Sort a given set of 3-D objects according to the number of faces, edges or vertices.

Sort regular and irregular polygons, including:
• triangles
• quadrilaterals
• pentagons
• hexagons
• octagons
according to the number of sides.

• Achievement Indicators
• Students who have achieved this outcome(s) should be able to:
- Classify a given set of regular and irregular polygons according to the number of sides.
- Identify given regular and irregular polygons having different dimensions.
- Identify given regular and irregular polygons having different orientations.

Collect first-hand data and organize it using tally marks, line plots, charts, and lists to answer questions.
• Achievement Indicators
• Students who have achieved this outcome(s) should be able to:
- Record the number of objects in a given set using tally marks.
- Determine the common attributes of line plots by comparing line plots in a given set.
- Organize a given set of data using tally marks, line plots, charts or lists.
- Collect and organize data using tally marks, line plots, charts and lists.
- Answer questions arising from a given line plot, chart or list.
- Answer questions using collected data.

Construct, label and interpret bar graphs to solve problems.
• Achievement Indicators
• Students who have achieved this outcome(s) should be able to:
- Determine the common attributes, title and axes, of bar graphs by comparing bar graphs in a given set.
- Create bar graphs from a given set of data including labelling the title and axes.
- Draw conclusions from a given bar graph to solve problems.
- Solve problems by constructing and interpreting a bar graph.

Demonstrate an understanding of increasing patterns by describing, extending, comparing, and creating patterns using manipulatives, diagrams, sounds and actions (numbers to 1000).
• Achievement Indicators
• Students who have achieved this outcome(s) should be able to:
- Describe a given increasing pattern by stating a pattern rule that includes the starting point and a description of how the pattern continues.
- Identify the pattern rule of a given increasing pattern and extend the pattern for the next three terms.
- Identify and explain errors in a given increasing pattern.
- Locate and describe various increasing patterns found on a hundred chart, such as horizontal, vertical and diagonal patterns.
- Compare numeric patterns of counting by 2s, 5s, 10s, 25s and 100s.
- Create a concrete, pictorial or symbolic representation of an increasing pattern for a given pattern rule.
- Create a concrete, pictorial or symbolic increasing pattern and describe the pattern rule.
- Solve a given problem using increasing patterns.
- Identify and describe increasing patterns in the environment.
- Identify and apply a pattern rule to determine missing elements for a given pattern.
- Describe the strategy used to determine missing elements in a given increasing pattern.

Demonstrate an understanding of decreasing patterns by describing, extending, comparing, and creating patterns using manipulatives, diagrams, sounds and actions (numbers to 1000).
• Achievement Indicators
• Students who have achieved this outcome(s) should be able to:
- Describe a given decreasing pattern by stating a pattern rule that includes the starting point and a description of how the pattern continues.
- Identify the pattern rule of a given decreasing pattern and extend the pattern for the next three terms.
- Identify and explain errors in a given decreasing pattern.
- Identify and describe various decreasing patterns found on a hundred chart, such as horizontal, vertical and diagonal patterns.
- Compare decreasing numeric patterns of counting backward by 2s, 5s, 10s, 25s and 100s.
- Create a concrete, pictorial or symbolic decreasing pattern for a given pattern rule.
- Create a concrete, pictorial or symbolic decreasing pattern and describe the pattern rule.
- Solve a given problem using decreasing patterns.
- Identify and describe decreasing patterns in the environment.
- Identify and apply a pattern rule to determine missing elements for a given pattern.
- Describe the strategy used to determine missing elements in a given decreasing pattern.

Solve one-step addition and subtraction equations involving symbols representing an unknown number.
• Achievement Indicators
• Students who have achieved this outcome(s) should be able to:
- Explain the purpose of the symbol, such as a triangle or a circle, in a given addition and in a given subtraction equation with one unknown.
- Create an addition or subtraction equation with one unknown to represent a given combination or separation action.
- Provide an alternative symbol for the unknown in a given addition or subtraction equation.
- Solve a given addition or subtraction equation that represents combining or separating actions with one unknown using manipulatives.
- Solve a given addition or subtraction equation with one unknown using a variety of strategies including guess and test.
- Explain why the unknown in a given addition or subtraction equation has only one value.