Math Games

Determine the pattern rule to make predictions about subsequent elements.
• Achievement Indicators:
- 5PR1.1 Extend a given pattern with and without concrete materials, and explain how each element differs from the preceding one.
- 5PR1.2 Describe, orally or in writing, a given pattern, using mathematical language, such as one more, one less, five more.
- 5PR1.3 Predict subsequent elements in a given pattern.
- 5PR1.4 Represent a given pattern visually to verify predictions.
- 5PR1.5 Solve a given problem by using a pattern rule to determine subsequent elements.
- 5PR1.6 Determine and explain why a given number is or is not the next element in a pattern.
- 5PR1.7 Write a mathematical expression to represent a given pattern.
- 5PR1.8 Describe the relationship in a given table or chart, using a mathematical expression.

Solve problems involving single-variable, one-step equations with whole number coefficients and whole number solutions.
• Achievement Indicators:
- 5PR2.1 Express a given problem as an equation where the unknown is represented by a letter variable.
- 5PR2.2 Solve a given single-variable equation with the unknown in any of the terms; e.g., n + 2 = 5, 4 + a = 7, 6 = r – 2, 10 = 2c.
- 5PR2.3 Identify the unknown in a problem; represent the problem with an equation; and solve the problem concretely, pictorially or symbolically.
- 5PR2.4 Create a problem for a given equation.

Design and construct different rectangles, given either perimeter or area, or both (whole numbers), and draw conclusions.
• Achievement Indicators:
- 5SS1.1 Construct or draw two or more rectangles for a given perimeter in a problem-solving context.
- 5SS1.2 Construct or draw two or more rectangles for a given area in a problem-solving context.
- 5SS1.3 Illustrate that for any given perimeter, the square or shape closest to a square will result in the greatest area.
- 5SS1.4 Illustrate that for any given perimeter, the rectangle with the smallest possible width will result in the least area.
- 5SS1.5 Provide a real-life context for when it is important to consider the relationship between area and perimeter.

Demonstrate an understanding of measuring length (mm and km) by:
• selecting and justifying referents for the unit mm
• modelling and describing the relationship between mm and cm units, and between mm and m units.
• selecting and justifying referents for the unit km.
• modelling and describing the relationship between m and km units.

• Achievement Indicators:
- 5SS2.1 Show that 10 millimetres is equivalent to one centimetre, using concrete materials.
- 5SS2.2 Show that 1 000 millimetres is equivalent to one metre, using concrete materials.
- 5SS2.3 Provide examples of when millimetres are used as the unit of measure.
- 5SS2.4 Provide a referent for one kilometre, and explain the choice.
- 5SS2.5 Know that 1 000 metres is equivalent to one kilometre.
- 5SS2.6 Provide examples of when kilometres are used as the unit of measure.
- 5SS2.7 Explore and generalize the measurement relationships between and among millimetres, centimetres, metres and kilometres.
- 5SS2.8 Provide a referent for one millimetre, and explain the choice.
- 5SS2.9 Provide a referent for one centimetre, and explain the choice.
- 5SS2.10 Provide a referent for one metre, and explain the choice.

Demonstrate an understanding of volume by:
• selecting and justifying referents for cm³ or m³ units
• estimating volume, using referents for cm³ or m³
• measuring and recording volume (cm³ or m³)
• constructing right rectangular prisms for a given volume.

• Achievement Indicators:
- 5SS3.1 Identify the cube as the most efficient unit for measuring volume, and explain why.
- 5SS3.2 Determine the volume of a given 3-D object, using manipulatives, and explain the strategy.
- 5SS3.3 Construct a right rectangular prism for a given volume.
- 5SS3.4 Explain that many rectangular prisms are possible for a given volume by constructing more than one right rectangular prism for the same given volume.
- 5SS3.5 Provide a referent for a cubic centimetre, and explain the choice.
- 5SS3.6 Provide a referent for a cubic metre, and explain the choice.
- 5SS3.7 Determine which standard cubic unit is represented by a given referent.
- 5SS3.8 Estimate the volume of a given 3-D object, using personal referents.

Demonstrate an understanding of capacity by:
• describing the relationship between mL and L
• selecting and justifying referents for mL or L units
• estimating capacity, using referents for mL or L
• measuring and recording capacity (mL or L).

• Achievement Indicators:
- 5SS4.1 Demonstrate that 1 000 millilitres is equivalent to 1 litre by filling a 1 litre container using a combination of smaller containers.
- 5SS4.2 Determine the capacity of a given container, using materials that take the shape of the inside of the container, and explain the strategy.
- 5SS4.3 Relate mL and L in problem solving situations.
- 5SS4.4 Provide a referent for a litre, and explain the choice.
- 5SS4.5 Provide a referent for a millilitre, and explain the choice.
- 5SS4.6 Determine which capacity unit is represented by a given referent.
- 5SS4.7 Estimate the capacity of a given container, using personal referents.

Describe and provide examples of edges and faces of 3-D objects, and sides of 2-D shapes that are:
• parallel
• intersecting
• perpendicular
• vertical
• horizontal.

• Achievement Indicators:
- 5SS5.1 Identify parallel, intersecting, perpendicular, vertical and horizontal sides on 2-D shapes.
- 5SS5.2 Identify that perpendicular lines meet to form right angles.
- 5SS5.3 Describe the sides of a given 2-D shape, using terms such as parallel, intersecting, perpendicular, vertical or horizontal.
- 5SS5.4 Draw 2-D shapes that have sides that are parallel, intersecting, perpendicular, vertical or horizontal.
- 5SS5.5 Identify parallel, intersecting, perpendicular, vertical and horizontal edges and faces on 3-D objects.
- 5SS5.6 Describe the faces and edges of a given 3-D object, using terms such as parallel, intersecting, perpendicular, vertical or horizontal.
- 5SS5.7 Draw 3-D objects that have edges and faces that are parallel, intersecting, perpendicular, vertical or horizontal.
- 5SS5.8 Provide examples from the environment that show parallel, intersecting, perpendicular, vertical and horizontal line segments.
- 5SS5.9 Find examples of edges, faces and sides that are parallel, intersecting, perpendicular, vertical and horizontal in print and electronic media, such as newspapers, magazines and the Internet.

Identify and sort quadrilaterals, including:
• rectangles
• squares
• trapezoids
• parallelograms
• rhombi (or rhombuses)
according to their attributes.

• Achievement Indicators:
- 5SS6.1 Identify and describe the characteristics of a pre-sorted set of quadrilaterals.
- 5SS6.2 Sort a given set of quadrilaterals according to the lengths of the sides.
- 5SS6.3 Sort a given set of quadrilaterals according to whether or not opposite sides are parallel.
- 5SS6.4 Sort a given set of quadrilaterals, and explain the sorting rule.

Perform a single transformation (translation, rotation or reflection) of a 2-D shape, and draw and describe the image.
• Achievement Indicators:
- 5SS7.1 Translate a given 2-D shape horizontally, vertically or diagonally, and draw and describe the position and orientation of the image.
- 5SS7.2 Draw a 2-D shape, translate the shape, and record the translation by describing the direction and magnitude of the movement.
- 5SS7.3 Reflect a given 2-D shape in a line of reflection, and describe the position and orientation of the image.
- 5SS7.4 Draw a 2-D shape, reflect the shape, and identify the line of reflection and the distance of the image from the line of reflection.
- 5SS7.5 Rotate a given 2-D shape about a vertex, and describe the direction of rotation (clockwise or counter clockwise) and the fraction of the turn (limited to 1/4. 1/2, 3/4 or full turn).
- 5SS7.6 Draw a 2-D shape, rotate the shape about a vertex, and describe the direction of the turn (clockwise or counter clockwise), the fraction of the turn (limited to 1/4, 1/2, 3/4 or full turn and point of rotation.
- 5SS7.7 Predict the result of a single transformation of a 2-D shape, and verify the prediction.

Identify and describe a single transformation, including a translation, rotation and reflection of 2-D shapes.
• Achievement Indicators:
- 5SS8.1 Describe a given translation by identifying the direction and magnitude of the movement.
- 5SS8.2 Describe a given reflection by identifying the line of reflection and the distance of the image from the line of reflection.
- 5SS8.3 Describe a given rotation about a vertex by the direction of the turn (clockwise or counter clockwise).
- 5SS8.4 Provide an example of a translation, a rotation and a reflection.
- 5SS8.5 Identify a given single transformation as a translation, rotation or reflection.

Represent and describe whole numbers to 1 000 000.
• Achievement Indicators:
- 5N1.1 Write a given numeral, using proper spacing without commas.
- 5N1.2 Write a given numeral to 1 000 000 in words.
- 5N1.3 Describe the pattern of adjacent place positions moving from right to left.
- 5N1.4 Describe the meaning of each digit in a given numeral.
- 5N1.5 Express a given numeral in expanded notation.
- 5N1.6 Write the numeral represented by a given expanded notation.
- 5N1.7 Provide examples of large numbers used in print or electronic media.

Compare and order decimals (to thousandths) by using:
• benchmarks
• place value
• equivalent decimals.

• Achievement Indicators:
- 5N10.1 Order a given set of decimals including only tenths, using place value.
- 5N10.2 Order a given set of decimals including only hundredths, using place value.
- 5N10.3 Order a given set of decimals including only thousandths, using place value.
- 5N10.4 Order a given set of decimals by placing them on a number line (vertical or horizontal) that contains the benchmarks 0.0, 0.5 and 1.0.
- 5N10.5 Order a given set of decimals including tenths, hundredths and thousandths, using equivalent decimals.
- 5N10.6 Explain what is the same and what is different about 0.2, 0.20 and 0.200.

Demonstrate an understanding of addition and subtraction of decimals (limited to thousandths).
• Achievement Indicators:
- 5N11.1 Predict sums and differences of decimals, using estimation strategies.
- 5N11.2 Place the decimal point in a sum or difference, using estimation.
- 5N11.3 Correct errors of decimal point placement in sums and differences without using paper and pencil.
- 5N11.4 Explain why keeping track of place value positions is important when adding and subtracting decimals.
- 5N11.5 Create and solve problems that involve addition and subtraction of decimals, limited to thousandths.
- 5N11.6 Correct errors of decimal point placements in sums and difference without using pencil and paper

Use estimation strategies, including:
• front-end estimation
• compensation
• compatible numbers
• rounding
in problem-solving contexts.

• Achievement Indicators:
- 5N2.1 Round decimals to the nearest whole number, nearest tenth or nearest hundredth.
- 5N2.2 Determine the approximate solution to a given problem not requiring an exact answer.
- 5N2.3 Estimate a sum or product, using compatible numbers.
- 5N2.4 Apply front-end rounding to estimate:
• sums
• differences
• products
• quotients
- 5N2.5 Estimate the solution to a given problem, using compensation, and explain the reason for compensation.
- 5N2.6 Select and use an estimation strategy for a given problem.
- 5N2.7 Provide a context for when estimation is used to:
• make predictions
• check the reasonableness of an answer
• determine approximate answers.
- 5N2.8 Describe contexts in which overestimating is important.

Apply mental mathematics strategies and number properties, such as:
• skip counting from a known fact
• using doubling or halving
• using patterns in the 9s facts
• using repeated doubling or halving
in order to understand, apply and recall basic multiplication facts to 9 x 9 and related division facts.

• Achievement Indicators:
- 5N3.1 Describe the mental mathematics strategy used to determine a given basic fact, such as:
• skip count up by one or two groups from a known fact
• skip down down by one or two groups from a known fact
• doubling
• patterns when multiplying by 9
• repeated doubling
• repeated halving
- 5N3.2 Explain why multiplying by zero produces a product of zero.
- 5N3.3 Demonstrate recall of multiplication facts to 9 × 9 and related division facts.
- 5N3.4 Explain why division by zero is not possible or is undefined.

Apply mental mathematics strategies for multiplication, such as:
• annexing (adding) zero
• halving and doubling
• using the distributive property.

• Achievement Indicators:
- 5N4.1 Determine the products when one factor is a multiple of 10, 100 or 1 000 by annexing (adding) zeros.
- 5N4.2 Apply halving and doubling when determining a given product
- 5N4.3 Apply the distributive property to determine a given product involving multiplying factors that are close to multiples of 10.

Demonstrate, with and without concrete materials, an understanding of multiplication (two-digit by two-digit) to solve problems.
• Achievement Indicators:
- 5N5.1 Model the steps for multiplying two-digit factors, using an array and base ten blocks, and record the process symbolically.
- 5N5.2 Describe a solution procedure for determining the product of two given two-digit factors, using a pictorial representation such as an area model.
- 5N5.3 Solve a given multiplication problem in context, using personal strategies, and record the process.
- 5N5.4 Illustrate partial products in expanded notation for both factors.
- 5N5.5 Represent both two-digit factors in expanded notation to illustrate the distributive property.
- 5N5.6 Refine personal strategies to increase their efficiency.
- 5N5.7 Create and solve a multiplication problem, and record the process.

Demonstrate, with and without concrete materials, an understanding of division (three-digit by one-digit), and interpret remainders to solve problems.
• Achievement Indicators:
- 5N6.1 Students investigate a variety of stategies and become proficient in at least one appropriate and efficient strategy that they understand.
- 5N6.2 Model the division process as equal sharing, using base ten blocks, and record it symbolically.
- 5N6.3 Explain that the interpretation of a remainder depends on the context:
• ignore the remainder
• round up the quotient
• express remainders as fractions
• express remainders as decimals
- 5N6.4 Solve a given division problem in context, using personal strategies, and record the process.
- 5N6.5 Refine personal strategies to increase their efficiency.
- 5N6.6 Create and solve a division problem, and record the process.

Demonstrate an understanding of fractions by using concrete, pictorial and symbolic representations to:
• create sets of equivalent fractions
• compare fractions with like and unlike denominators.

• Achievement Indicators:
- 5N7.1 Create a set of equivalent fractions; and explain, using concrete materials, why there are many equivalent fractions for any given fraction.
- 5N7.2 Model and explain that equivalent fractions represent the same quantity.
- 5N7.3 Determine if two given fractions are equivalent, using concrete materials or pictorial representations.
- 5N7.4 Identify equivalent fractions for a given fraction.
- 5N7.5 Formulate and verify a rule for developing a set of equivalent fractions.
- 5N7.6 Compare two given fractions with unlike denominators by creating equivalent fractions.
- 5N7.7 Position a given set of fractions with like and unlike denominators on a number line (horizontal or vertical), and explain strategies used to determine the order.

Describe and represent decimals (tenths, hundredths, thousandths) concretely, pictorially and symbolically.
• Achievement Indicators:
- 5N8.1 Express orally and in written form the decimal for a given symbolic, concrete or pictorial representation of part of a set, part of a region or part of a unit of measure.
- 5N8.2 Describe the value of each digit in a given decimal.
- 5N8.3 Represent a given decimal, using concrete materials, pictorial representation, or a grid.
- 5N8.4 Express a given tenth as an equivalent hundredth and thousandth.
- 5N8.5 Express a given hundredth as an equivalent thousandth.
- 5N8.6 Represent an equivalent tenth, hundredth or thousandth for a given decimal, using a grid.

Relate decimals to fractions and fractions to decimals (to thousandths).
• Achievement Indicators:
- 5N9.1 Express orally and in written form, a given decimal as a fraction with a denominator of 10, 100 or 1 000.
- 5N9.2 Express orally and in written form, a given fraction with a denominator of 10, 100 or 1 000 as a decimal.
- 5N9.3 Express a given pictorial or concrete representation as a fraction or decimal.

Differentiate between firsthand
and second-hand data.
• Achievement Indicators:
- 5SP1.1 Explain the difference between first-hand and secondhand data.
- 5SP1.2 Formulate a question that can best be answered using first-hand data, and explain why.
- 5SP1.3 Formulate a question that can best be answered using second-hand data, and explain why.
- 5SP1.4 Find examples of second-hand data in print and electronic media, such as newspapers, magazines and the Internet.

Construct and interpret double bar graphs to draw conclusions.
• Achievement Indicators:
- 5SP2.1 Determine the attributes (title, axes, intervals and legend) of double bar graphs by comparing a given set of double bar graphs.
- 5SP2.2 Draw conclusions from a given double bar graph to answer questions.
- 5SP2.3 Provide examples of double bar graphs used in a variety of print and electronic media, such as newspapers, magazines and the Internet.
- 5SP2.4 Represent a given set of data by creating a double bar graph, label the title and axes, and create a legend without the use of technology.
- 5SP2.5 Solve a given problem by constructing and interpreting a double bar graph.

Describe the likelihood of a single outcome occurring, using words such as:
• impossible
• possible
• certain.

• Achievement Indicators:
- 5SP3.1 Provide examples of events, from personal contexts, that are impossible, possible or certain.
- 5SP3.2 Classify the likelihood of a single outcome occurring in a probability experiment as impossible, possible or certain.
- 5SP3.3 Design and conduct a probability experiment in which the likelihood of a single outcome occurring is impossible, possible or certain.
- 5SP3.4 Conduct a given probability experiment a number of times, record the outcomes, and explain the results.

Compare the likelihood of two possible outcomes occurring, using words such as:
• less likely
• equally likely
• more likely.

• Achievement Indicators:
- 5SP4.1 Identify outcomes from a given probability experiment that are less likely, equally likely or more likely to occur than other outcomes.
- 5SP4.2 Design and conduct a probability experiment in which one outcome is less likely to occur than the other outcome.
- 5SP4.3 Design and conduct a probability experiment in which one outcome is equally likely to occur as the other outcome.
- 5SP4.4 Design and conduct a probability experiment in which one outcome is more likely to occur than the other outcome.