 • 3
Top Mathematicians
• Shape and Space
• 3.SS.1
Relate the passage of time to common activities, using nonstandard and standard units (minutes, hours, days, weeks, months, years).
Select and use a nonstandard 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, weeks, months and years.
Provide personal referents for minutes and hours.
• 3.SS.2
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.
Determine the number of days in any given month, using a calendar.
Solve a given problem involving the number of seconds in a minute, minutes in an hour or days in a given month.
Create a calendar that includes days of the week, dates and personal events.
• 3.SS.3
Demonstrate an understanding of measuring length (cm, m) by:
selecting and justifying referents for the units cm and m.
modelling and describing the relationship between the units cm and m.
estimating length, using referents.
measuring and recording length, width and height.
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 cm is equivalent to 1 m 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.
• 3.SS.4
Demonstrate an understanding of measuring mass (g, kg) by:
selecting and justifying referents for the units g and kg.
modelling and describing the relationship between the units g and kg.
estimating mass, using referents.
measuring and recording mass.
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 g and 1 kg, 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, using the units g and kg, the mass of given everyday objects.
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.
• 3.SS.5
Demonstrate an understanding of perimeter of regular and irregular shapes by:
estimating perimeter, using referents for cm or m.
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.
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 a given perimeter.
Estimate the perimeter of a given shape (cm, m), using personal referents.
• 3.SS.6
Describe 3-D objects according to the shape of the faces and the number of edges and vertices.
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.
• 3.SS.7
Sort regular and irregular polygons, including:
triangles according to the number of sides.
quadrilaterals according to the number of sides.
pentagons according to the number of sides.
hexagons according to the number of sides.
octagons according to the number of sides.
Classify a given set of regular and irregular polygons according to the number of sides.
Identify given regular and irregular polygons that have different dimensions.
Identify given regular and irregular polygons that have different orientations.
• Statistics & Probability
• 3.SP.1
Collect first-hand data and organize it using:
tally marks to answer questions.
line plots to answer questions.
charts to answer questions.
lists to answer questions.
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.
• 3.SP.2
Construct, label and interpret bar graphs to solve problems.
Determine the common attributes, titles and axes of bar graphs by comparing bar graphs in a given set.
Create a bar graph, labelling the title and axes, to represent a given set of data.
Draw conclusions from a given bar graph to solve problems.
Solve problems by constructing and interpreting a bar graph.
• Patterns and Relations
• 3.PR.1
Demonstrate an understanding of increasing patterns by:
describing numerical (numbers to 1000) and non-numerical patterns using manipulatives, diagrams, sounds and actions.
extending numerical (numbers to 1000) and non-numerical patterns using manipulatives, diagrams, sounds and actions.
comparing numerical (numbers to 1000) and non-numerical patterns using manipulatives, diagrams, sounds and actions.
creating numerical (numbers to 1000) and non-numerical patterns using manipulatives, diagrams, sounds and actions.
Describe a given increasing pattern by stating a pattern rule that includes the starting point and a description of how the pattern continues; e.g., for 42, 44, 46 the pattern rule is start at 42 and add 2 each time.
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 relationship, using a 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.
• 3.PR.2
Demonstrate an understanding of decreasing patterns by:
describing numerical (numbers to 1000) and non-numerical patterns using manipulatives, diagrams, sounds and actions.
extending numerical (numbers to 1000) and non-numerical patterns using manipulatives, diagrams, sounds and actions.
comparing numerical (numbers to 1000) and non-numerical patterns using manipulatives, diagrams, sounds and actions.
creating numerical (numbers to 1000) and non-numerical patterns using manipulatives, diagrams, sounds and actions.
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 relationship, using a 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.
• 3.PR.3
Sort objects or numbers, using one or more than one attribute.
Classify a given set of numbers according to the number of digits.
Classify a given set of numbers as odd or even.
Classify a given set of numbers as fractions or whole numbers.
Determine the difference between two given pre-sorted sets of objects that have been sorted based on two attributes, and explain a possible sorting rule used to sort them.
Record the sorting of a set of objects, using tools such as Venn diagrams.
Sort a given set of objects or numbers in more than one way, and explain how the sorting rules are different.
• 3.PR.4
Solve one-step addition and subtraction equations involving a symbol to represent an unknown number.
Explain the purpose of the symbol in a given addition or subtraction equation with one unknown; e.g., in the equation 3 + ? = 10, the triangle represents the number that would make the equation true.
Create an addition or subtraction equation with one unknown to represent a given combining or separating action.
Provide an alternative symbol for the unknown in a given addition or subtraction equation.
Solve, using manipulatives, a given addition or subtraction equation with one unknown that represents combining or separating actions.
Solve a given addition or subtraction equation with one unknown, using a variety of strategies, including guess and test.
Solve a given addition or subtraction equation when the unknown is on the left or the right side of the equation.
Explain why the unknown in a given addition or subtraction equation has only one value.
• Number
• 3.N.1
Say the number sequence 0 to 1000 forward and backward 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.
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.
• 3.N.10
Apply mental mathematics strategies and number properties in order to understand and recall basic addition facts and related subtraction facts to 18.
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 for subtraction; e.g., for 13 – 7, think 7 + ? = 13.
Apply the property of zero to determine a given sum or difference when adding or subtracting zero; e.g., 5 + 0 = 5 and 5 – 0 = 5.
Provide a rule for determining answers when adding and subtracting zero.
Apply a mental mathematics strategy to provide a solution to a given basic addition fact up to and including 9 + 9 or a related subtraction fact.
Demonstrate understanding, recall/memorization and application of addition facts up to and including 9 + 9 and related subtraction facts.
• 3.N.11
Demonstrate an understanding of multiplication to 5 × 5 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.
Identify events from experience that can be described as multiplication.
Represent a given story problem, using manipulatives or diagrams, and record the problem 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., 2 × 3 = 6.
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 multiplication problem.
Demonstrate understanding and recall/memorization of multiplication facts to 5 × 5.
• 3.N.12
Demonstrate an understanding of division (limited to division related to multiplication facts up to 5 × 5) by:
representing and explaining division using equal sharing and equal grouping.
creating and solving problems in context that involve equal sharing and equal grouping.
modelling equal sharing and equal grouping using concrete and visual representations, and recording the process symbolically.
relating division to repeated subtraction.
relating division to multiplication.
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, presented orally, that involves equal sharing; and solve the problem.
Illustrate, with counters or a diagram, a given story problem, presented orally, that involves equal grouping; 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., 6 ÷ 3 = 2.
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.
Solve a given problem involving division.
Demonstrate understanding and recall/memorization of division facts related to multiplication facts to 5 × 5.
• 3.N.13
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 that have like denominators.
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 shaded 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.
• 3.N.2
Represent and describe numbers to 1000, concretely, pictorially and symbolically.
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 – 44 or 20 + 236 for 256.
Represent a given number, using manipulatives such as base ten materials.
Represent a given number pictorially.
Write number words for given multiples of ten to 90.
Write number words for given multiples of a hundred to 900.
• 3.N.3
Compare and order numbers to 1000.
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 and explain errors in a given ordered sequence.
Identify missing numbers in parts of a given hundred chart.
Identify errors in a given hundred chart.
• 3.N.4
Estimate quantities less than 1000, using referents.
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.
• 3.N.5
Illustrate, concretely and pictorially, the meaning of place value for numerals to 1000.
Record, in more than one way, the number represented by given proportional materials (e.g., base-ten materials) and non-proportional materials (e.g., money).
Represent a given number in different ways, using proportional and non-proportional materials, and explain how the representations are equivalent; e.g., 351 can be represented as three 100s, five 10s and one 1; or two 100s, fifteen 10s and one 1; 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).
Explain, using concrete materials, the meaning of zero as a place holder in a given number.
• 3.N.6
Describe and apply mental mathematics strategies for adding two 2-digit numerals.
Add two given 2-digit numerals, 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 and then compensating" 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.
• 3.N.7
Describe and apply mental mathematics strategies for subtracting two 2-digit numerals.
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 "adding on" strategy; e.g., to determine the difference of 62 – 45, think 45 + 5, then 50 + 12 and then 5 + 12.
Explain how to use the "using doubles" strategy; e.g., to determine the difference of 24 – 12, think 12 + 12 = 24.
Apply a mental mathematics strategy for subtracting two given 2-digit numerals.
• 3.N.8
Apply estimation strategies to predict sums and differences of two 2-digit numerals in a problem-solving context.
Estimate the solution for a given 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 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).
• 3.N.9
Demonstrate an understanding of addition and subtraction of numbers with answers to 1000 (limited to 1-, 2- and 3-digit numerals), concretely, pictorially and symbolically, by:
using personal strategies for adding and subtracting with and without the support of manipulatives.
creating and solving problems in context that involve addition and subtraction of numbers.
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.
Refine personal strategies to increase their efficiency.
Solve a given problem involving the sum or difference of two given numbers.
Solve a given problem using the standard/traditional addition algorithm.
Solve a given problem using the standard/traditional subtraction algorithm.