Unit 1: Numeration I can write a number using proper spacing without commas. e.g., 934 567. I can write a number to 1 000 000 in words. I can show my understanding of place value in a given number. I can give examples of large numbers used in newspapers, magazines or online. I can write a number in expanded form. I can change a number from expanded form to standard form. I can explain when I use over-estimating. I can give an approximate answer to a given problem. I can estimate a sum or product, using compatible numbers. I can estimate and explain the answer to a problem using compensation. I can choose and use an estimation strategy for a problem. I can use front-end rounding to estimate; -sums; e.g., 253 + 615 is more than 200 + 600 = 800 -differences; e.g., 974 250 is close to 900 200 = 700 -products; e.g., the product of 23 x 24 is greater than 20 x 20 (400) and less than 25 x 25 (625) I can write the decimal for a given number or picture for a set of numbers, part of a region or part of a unit of measure. I can represent a given decimal, using manipulatives or pictures. I can represent an equivalent tenth, hundredth or thousandth for a given decimal, using graph paper. I can show a given tenth as an equivalent hundredth and thousandth.
I can show a given hundredth as an equivalent thousandth. I can describe the value of each digit in a given decimal. I can represent a decimal number as a fraction. I can represent a fraction with a denominator of 10, 100 or 1000 as a decimal number. I can identify a picture or model as a fraction or decimal, e.g., 250 shaded squares on a thousandth grid can be expressed as 0.250 or 250/1000. I can 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. I can order a given set of decimals using tenths, in a place value chart. I can order a given set of decimals using hundredths, in a place value chart. I can order a given set of decimals using thousandths, in a place value chart. I can explain what is the same and what is different about 0.2, 0.20 and 0.200. I can order a given set of decimals including tenths, hundredths and thousandths, using equivalent decimals; e.g., 0.92, 0.7, 0.9, 0.876, 0.925 in order is: 0.700, 0.876, 0.900, 0.920, 0.925
Unit 2: Adding and Subtracting Decimals I can place the decimal point in the correct position in a sum or difference, using front-end estimation; e.g., for 6.3 + 0.25 + 306.158, think 6 + 306 = 312, so the sum must be greater than 312. I can find incorrect decimal point placements in sums and differences without using paper and pencil. I can explain why it is important to keep track of place value positions when adding and subtracting decimals. I can use estimation to predict sums and differences of decimals. I can solve problems using the addition and subtraction of decimals. I can create and solve problems using addition and subtraction of decimals.
Unit 3: Data Relationships I can explain the difference between first-hand and second-hand data. I can create a question that can be answered using first-hand data and explain why. I can create a question that can be answered using second-hand data and explain why. I can find examples of second-hand data in newspapers, magazines and online. I can compare double bar graphs using the title, axes, intervals and legend. I can represent a set of data by creating a double bar graph, labeling the title and axes and creating a legend. I can answer questions about a double bar graph. I can give examples of double bar graphs that are used in newspapers, magazines and online. I can solve a problem by constructing and interpreting a double bar graph.
Unit 4: Motion Geometry I can translate a 2-D shape horizontally, vertically or diagonally, and describe the position of the image. I can rotate a 2-D shape about a vertex, and describe the direction of rotation (clockwise or counter clockwise) and the fraction of the turn (limited to ¼, ½, ¾ or full turn). I can reflect a 2-D shape across a line of reflection, and describe the position of the image. I can draw a 2-D shape, translate the shape, and describe the distance and direction of the shape s movement. I can 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 ¼, ½, ¾ or full turn) and point of rotation. I can 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. I can predict the result of a single transformation of a 2-D shape, and then confirm my prediction by translating the shape. I can give an example of a translation, a rotation and a reflection. I can identify a transformation as a translation, rotation or reflection. I can describe a rotation about a vertex by the direction of the turn (clockwise or counter clockwise). I can describe a reflection by identifying the line of reflection and the distance of the image from the line of reflection. Describe a given translation using distance and direction of the movement.
Unit 5: Multiplication I can provide examples of when to use estimation strategies to make predictions and check my answer. I can decide when to overestimate. I can estimate. I can estimate a sum or product, using compatible numbers. I can choose and use an estimation strategy for a problem. I can use front-end rounding to estimate; sums; e.g., 253 + 615 is more than 200 + 600 = 800 differences; e.g., 974 250 is close to 900 200 = 700 products; e.g., the product of 23 x 24 is greater than 20 x 20 (400) and less than 25 x 25 (625) I can solve multiplication problems using the following mental math strategies: I can skip count up by one or two groups from a known fact; e.g., if 5 x 7 = 35, then 6 x 7 is equal to 35 + 7 and 7 x 7 is equal to 35 + 7 + 7 I can skip count down by one or two groups from a known fact; e.g., if 8 x 8 = 64, then 7 x 8 is equal to 64 8 and 6 x 8 is equal to 64 8 8 I can use doubling; e.g., for 8 x 3 think 4 x 3 = 12, so 8 x 3 = 12 + 12 I can use a simple rule when multiplying by 9; E.g. The sum of the two digits in the product is always 9. For 7 x 9, think: 1 less than 7 is 6, 6 and 3 make 9, so the answer is 63. I can use repeated doubling; e.g., if 2 x 6 is equal to 12, then 4 x 6 is equal to 24 and 8 x 6 is equal to 48 I can use repeated halving; e.g., for 60 x 4, think 60 x 2 = 30 and 30 x 2 = 15. I can explain why multiplying by zero gives a product of zero (Zero groups of ).
I can find answers to multiplication and related division facts to 81; e.g., 9x9=81 & 81 9 = 9 I can remove or add zeros to find the product when one factor is a multiple of 10, 100, or 1000; e.g., for 3 200 think 3 2 and then add two zeros. I can use halving and doubling to find a given product; e.g., 4 x 5 is the same as 2 x 10. I can use the distributive property to find a product using factors that are close to multiples of 10; e.g., 98 x 7 = (100 x 7) (2 x 7). I can write factors in expanded notation (e.g. 36 x 42 = (30 + 6) x (40 + 2)) I can use expanded notation to show my understanding of the distributive property 36 42, (30 + 6) (40 + 2) = 30 40 + 30 2 + 6 40 + 6 2 = 1200 + 60 + 240 + 12 = 1512. I can multiply two digit factors using an array and base ten blocks. I can explain my answer to a multiplication problem (two digit by two digit) using numbers, pictures, and words. I can use a strategy that works best for me to solve a multiplication problem. I can create and solve a multiplication problem and explain my answer.
Unit 6: Patterns I can extend a number pattern with and without models, and explain how each number is different from the one before it. I can describe a pattern using mathematical language, e.g., one more, one less, five more. I can write a mathematical expression to represent a pattern, e.g., r + 1, r 1, r + 5. I can use a mathematical expression to describe the relationship between numbers in a given table or chart. I can determine when a number is or is not the next number in a pattern and explain why. I can predict the next numbers in a pattern. I can solve a problem by using a pattern rule to predict the next numbers in the pattern. I can represent a pattern with pictures or models to confirm my predictions about the next numbers in the pattern. I can express a problem as an equation where the unknown is represented by a letter, e.g., n+2=5 I can solve an equation with one unknown; e.g., n + 2 = 5, 4 + a = 7, 6 = r 2, 10 = 2c.
I can identify the unknown in a problem, represent the unknown by a letter in an equation, and show the solution using models, pictures or numbers. I can create a problem for a given equation.
Unit 7: Fractions I can use pictures and models to create and compare equivalent fractions. I can explain equivalent fractions using pictures and models. I can show that two fractions are equivalent using pictures and models. I can create a rule for making a set of equivalent fractions and make sure it works. I can identify equivalent fractions for a given fraction. I can compare two fractions with different denominators by creating equivalent fractions. I can position a set of fractions with like and unlike denominators on a number line and explain why I placed them where I did. I can represent a decimal number as a fraction. I can represent a fraction with a denominator of 10, 100 or 1000 as a decimal number. I can identify a picture or model as a fraction or decimal, e.g., 250 shaded squares on a thousandth grid can be expressed as 0.250 or 250/1000. I can explain what is the same and what is different about 0.2, 0.20 and 0.200. I can order a given set of decimals including tenths, hundredths and thousandths, using equivalent decimals; e.g., 0.92, 0.7, 0.9, 0.876, 0.925 in order is: 0.700, 0.876, 0.900, 0.920, 0.925
Unit 8: Measurement I can draw or construct two or more different rectangles that have the same perimeter. I can draw or construct two or more rectangles that have the same area. I can show that for any perimeter, the square or rectangle closest to a square will have the greatest area. I can show that for any perimeter, the rectangle with the smallest width will result in the least area. I can talk about how the relationship between area and perimeter can be important in real-life situations. I can give an example of something that is one illimetre in size. I can give an example of something that is one centimetre in size. I can give an example of something that is one metre in size. I can show that 10 millimetres is equivalent to 1 centimetre, using concrete materials; e.g., a ruler. I can show that 1000 millimetres is equivalent to 1 metre, using concrete materials; e.g., a metre stick. I can give examples of when millimetres, centimetres or kilometres would be used. I can show the relationship between millimetres, centimetres and metres. I can explain why the cube is the best unit for measuring volume. I can give an example of something that is one cubic centimetre. I can give an example of something that is one cubic metre. I can give examples of when cubic millimetres, centimetres or kilometres would be used.
I can estimate the volume of a 3-D object. I can find the volume of a 3-D object using models and explain how I did it. I can build a right rectangular prism for a given volume. I can show that many rectangular prisms are possible for a given volume by constructing more than one right rectangular prism for the same volume. I can show that 1000 millilitres is equivalent to 1 litre by filling a 1 litre container using a combination of smaller containers. I can show how millilitres and litres are related. I can give an example of something that is one litre. I can give an example of something that is one millilitre. I can give examples of when millilitres and litres would be used. I can estimate the capacity of a container. I can show the capacity of container using materials that take the shape of the inside of the container (e.g., water, rice, sand, beads) and explain how.
Unit 9: Division I can provide examples of when to use estimation strategies to make predictions and check my answer. I can decide when to overestimate. I can estimate. I can choose and use an estimation strategy for a problem. I can use front-end rounding to estimate; sums; e.g., 253 + 615 is more than 200 + 600 = 800 differences; e.g., 974 250 is close to 900 200 = 700 products; e.g., the product of 23 x 24 is greater than 20 x 20 (400) and less than 25 x 25 (625) I can solve multiplication problems using the following mental math strategies: I can skip count up by one or two groups from a known fact; e.g., if 5 x 7 = 35, then 6 x 7 is equal to 35 + 7 and 7 x 7 is equal to 35 + 7 + 7 I can skip count down by one or two groups from a known fact; e.g., if 8 x 8 = 64, then 7 x 8 is equal to 64 8 and 6 x 8 is equal to 64 8 8 I can use doubling; e.g., for 8 x 3 think 4 x 3 = 12, so 8 x 3 = 12 + 12 I can use a simple rule when multiplying by 9; E.g. The sum of the two digits in the product is always 9. For 7 x 9, think: 1 less than 7 is 6, 6 and 3 make 9, so the answer is 63. I can use repeated doubling; e.g., if 2 x 6 is equal to 12, then 4 x 6 is equal to 24 and 8 x 6 is equal to 48 I can use repeated halving; e.g., for 60 x 4, think 60 x 2 = 30 and 30 x 2 = 15. I can explain why division by zero is not possible. e.g., 8 x 0. I can find answers to multiplication and related division facts to 81; e.g., 9x9=81 & 81 9 = 9 I can model the division process by showing equal groups using base ten blocks. I can explain that a remainder is shown in different ways: I can ignore the remainder; e.g., making teams of 4 from 22 people = 5 teams
I can round up the quotient; e.g., the number of five passenger cars required to transport 13 people = 3 cars I can show remainders as fractions; e.g., five apples shared by two people = 2 ½ each I express remainders as decimals; e.g., measurement and money. 1.5 cm or $2.75 I can solve a division problem using my favourite strategies and show my workings. I can practice my strategies so I can solve division problems more quickly. I can create a division problem, solve it, and show my workings.
Unit 10: Probability I can provide examples of events that are impossible, possible or certain. I can predict whether the outcome of a probability experiment is impossible, possible or certain. I can plan and carry out a probability experiment where the outcome is impossible, possible or certain. I can carry out a probability experiment a number of times, record the outcomes, and explain the results. I can predict whether the outcomes of a probability experiment that are less likely, equally likely or more likely to occur than others. I can plan and carry out a probability experiment where one outcome is less likely to occur than the other(s). I can plan and carry out a probability experiment where one outcome is equally likely to occur as the other(s). I can plan and carry out a probability experiment where one outcome is more likely to occur than the other(s).
Unit 11: 2D and 3D Geometry I can identify parallel, intersecting, perpendicular, vertical and horizontal edges and faces on 3-D objects. I can show that perpendicular lines meet to form 90 degree angles. I can identify parallel, intersecting, perpendicular, vertical and horizontal sides on 2-D shapes. I can give examples of parallel, intersecting, perpendicular, vertical and horizontal line segments from my environment. I can find examples of edges, faces and sides that are parallel, intersecting, perpendicular, vertical and horizontal in newspapers, magazines and online. I can draw 2-D shapes with sides that are parallel, intersecting, perpendicular, vertical or horizontal. I can draw 3-D objects with edges and faces that are parallel, intersecting, perpendicular, vertical or horizontal. I can describe the faces and edges of a given 3-D object as parallel, intersecting, perpendicular, vertical or horizontal. I can describe the sides of a given 2-D shape, using terms such as parallel, intersecting, perpendicular, vertical or horizontal. I can describe the characteristics of a set of quadrilaterals. I can sort quadrilaterals into groups based on their characteristics and explain my sorting rule. I can sort quadrilaterals according to the lengths of their sides. I can sort quadrilaterals according to whether or not their opposite sides are parallel.