1 Grade 4 Long Range Outline Grade 42 Legend On the term-at-a-glance pages, the main focus of instruction is in darker blue and is linked to a page wi...

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Grade 4

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On the term-at-a-glance pages, the main focus of instruction is in darker blue and is linked to a page with the relevant expectations.

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Connected topics appear on the term-at-a-glance pages in lighter blue boxes. Expectations related to those connected topics appear on the focus of instruction pages beside the focus of instruction expectations.

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A solid line on the term-at-a-glance page suggests the topic should be developed over the time period in a gradual fashion.

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A dashed line suggests the topic should be visited periodically over that time span.

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Images of resources are links to those resources.

Timelines are meant to be guidelines only and teachers are encouraged to take into consideration the diverse needs of the students in the classroom in determining the flow through the curriculum.

Main Focus

Connected Concepts

Fractions

September

Number Sense and Numeration

October

Numbers: read, represent, order and compare to 10 000 Place value Introduce tenths-counting by tenths Counting with unit fractions

November

December

January Multiplication/Division

Addition/Subtraction Whole numbers and extend to decimal tenths Fractions

Measurement

Linear measurement to reinforce place value concepts ,including tenths , and relative magnitudes of numbers.

Perimeter in addition and subtraction situations. Elapsed time as a difference situation in a linear representation.

Area and perimeter relationships.

Unit Relationships

Introduce time and relative temperature. Integrate in a variety of contexts through the year.

Geometry and Spatial Sense

2-D Properties Angles Symmetry

Pattern and Algebra Review of addition and subtraction properties from grade 3

Data Management and Probability

Repeating patterns, geometric patterns.

Inverse relationship of multiplication and division. Missing number in multiplication. Commutative property of multiplication. Distributive property of multiplication over addition.

Median Charts, tables and graphs (Stem & leaf plots, double bar graphs, median) - cross curricular in Social Studies and Science

Grade 4

February

Number Sense and Numeration

March

April

May Review

Fractions Proportional Relationships: Simple whole-number multiplicative relationships

Fractions

Measurement

Area in multiplication and division contexts. Unit relationships.

Estimate/measure mass, capacity using standard units.

Time and relative temperature. Integrate in a variety of subject areas through the year.

Geometry and Spatial Sense

3-D Properties

Pattern and Algebra

Data Management and Probability

June

Location and Movement.

Patterns with reflections.

Charts, tables and graphs( stem & leaf plots, double bar graphs, median) - cross curricular in Social Studies and Science

Grade 4

Probability: Fairness, Simple Experiments

Quantity Relationships Instructional Focus: Number Sense

Connected Concepts

Overall Expectation • read, represent, compare, and order whole numbers to 10 000, decimal numbers to tenths, and simple fractions, and represent money amounts to $100. • demonstrate an understanding of magnitude by counting forward and backwards by 0.1 and by fractional amounts. Specific Expectations – represent, compare, and order whole numbers to 10 000, using a variety of tools (e.g., drawings of base ten materials, number lines with increments of 100 or other appropriate amounts). – demonstrate an understanding of place value in whole numbers and decimal numbers from 0.1 to 10 000, using a variety of tools and strategies (e.g., use base ten materials to represent 9307 as 9000 + 300 + 0 + 7) (Sample problem: Use the digits 1, 9, 5, 4 to create the greatest number and the least number possible, and explain your thinking.). – read and print in words whole numbers to one thousand, using meaningful contexts (e.g., books, highway distance signs). – read and represent money amounts to $100 (e.g., five dollars, two quarters, one nickel, and four cents is $5.59); – round four-digit whole numbers to the nearest ten, hundred, and thousand, in problems arising from real-life situations. – represent, compare, and order decimal numbers to tenths, using a variety of tools (e.g., concrete materials such as paper strips divided into tenths and base ten materials, number lines, drawings) and using standard decimal notation (Sample problem: Draw a partial number line that extends from 4.2 to 6.7, and mark the location of 5.6.). – count forward by tenths from any decimal number expressed to one decimal place, using concrete materials and number lines (e.g., use base ten materials to represent 3.7 and count forward: 3.8, 3.9, 4.0, 4.1, …; “Three and seven tenths, three and eight tenths, three and nine tenths, four, four and one tenth, …”) (Sample problem: What connections can you make between counting by tenths and measuring lengths in millimetres and in centimetres?).

Measurement Specific Expectations – estimate, measure, and record length, height, and distance, using standard units (i.e., millimetre, centimetre, metre, kilometre) (e.g., a pencil that is 75 mm long). – draw items using a ruler, given specific lengths in millimetres or centimetres (Sample problem: Use estimation to draw a line that is 115 mm long. Beside it, use a ruler to draw a line that is 115 mm long. Compare the lengths of the lines.).

– describe, through investigation, the relationship between various units of length (i.e., millimetre, centimetre, decimetre, metre, kilometre). – estimate, measure, and record the mass of objects (e.g., apple, baseball, book), using the standard units of the kilogram and the gram. – estimate, measure, and record the capacity of containers (e.g., a drinking glass, a juice box), using the standard units of the litre and the millilitre. – compare and order a collection of objects, using standard units of mass (i.e., gram, kilogram) and/or capacity (i.e., millilitre, litre).

Consider… • using various measures to establish relative magnitudes of numbers when comparing and ordering numbers. • using a metric rulers to establish tenths as suggested in the sample problem and them for partial number lines. • reviewing fractional names from grade 3 in measurement contexts (e.g.. fractions of a litre of kilogram). • connecting linear measures to number lines.

Measurement Grade 4 Learning Activity: The First Decade of My Life

See J/I Modules 3,4 and 7. Volume 6 : Decimal Numbers Grade 4 Learning Activity: Decimal Game and Learning Connections 1-4

Set Tool, Relational Rods, Number Line Tool, Money Tool,

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Data Management Specific Expectations – demonstrate, through investigation, an understanding of median (e.g.,“The median is the value in the middle of the data. If there are two middle values, you have to calculate the middle of those two values.”), and determine the median of a set of data (e.g.,“I used a stem-and-leaf plot to help me find the median.”); Consider… • developing the concept of median when comparing and ordering numbers.

Grade 4

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Addition/Subtraction Instructional Focus: Number Sense

Connected Concepts

Overall Expectation • solve problems involving the addition, subtraction, multiplication, and division of single- and multi-digit whole numbers, and involving the addition and subtraction of decimal numbers to tenths and money amounts, using a variety of strategies. Specific Expectations – solve problems that arise from real-life situations and that relate to the magnitude of whole numbers up to 10 000 (Sample problem: How high would a stack of 10 000 pennies be? Justify your answer.). – add and subtract two-digit numbers, using a variety of mental strategies (e.g., one way to calculate 73 – 39 is to subtract 40 from 73 to get 33, and then add 1 back to get 34). – solve problems involving the addition and subtraction of four-digit numbers, using student-generated algorithms and standard algorithms (e.g.,“I added 4217 + 1914 using 5000 + 1100 + 20 + 11.”). – add and subtract decimal numbers to tenths, using concrete materials (e.g., paper strips divided into tenths, base ten materials) and student-generated algorithms (e.g., “When I added 6.5 and 5.6, I took five tenths in fraction circles and added six tenths in fraction circles to give me one whole and one tenth. Then I added 6 + 5 + 1.1, which equals 12.1.”). – add and subtract money amounts by making simulated purchases and providing change for amounts up to $100, using a variety of tools (e.g., currency manipulatives, drawings). – use estimation when solving problems involving the addition, subtraction, and multiplication of whole numbers, to help judge the reasonableness of a solution (Sample problem: A school is ordering pencils that come in boxes of 100. If there are 9 classes and each class needs about 110 pencils, estimate how many boxes the school should buy.).

See J/I Module 6. Volume 2 : Addition and Subtraction Grade 4 Learning Activity: Grade 4 Learning Activity Rising Waters and Learning Connections 1-4

Measurement Specific Expectations – estimate and determine elapsed time, with and without using a time line, given the durations of events expressed in five-minute intervals, hours, days, weeks, months, or years (Sample problem: If you wake up at 7:30 a.m., and it takes you 10 minutes to eat your breakfast, 5 minutes to brush your teeth, 25 minutes to wash and get dressed, 5 minutes to get your backpack ready, and 20 minutes to get to school, will you be at school by 9:00 a.m.?). – describe, through investigation, the relationship between various units of length (i.e., millimetre, centimetre, decimetre, metre, kilometre). – select and justify the most appropriate standard unit (i.e., millimetre, centimetre, decimetre, metre, kilometre) to measure the side lengths and perimeters of various polygons. Consider… • modelling elapsed time as difference on a number line. • using measurement contexts to support help students develop algorithms. (Eg. One piece of ribbon is 6.5 cm and another is 5.6 cm. What is the total length of the ribbon? ) • using measurement contexts where units can be renamed to draw parallels between whole number and decimal strategies and algorithms. Eg.. 12.4 cm – 8.1 cm can be renamed as 124 mm - 81 mm and the strategies or algorithms carried out in the same ways. • using missing side questions in perimeter contexts to reinforce subtraction as difference. Algebra Consider… • reviewing the inverse relationship between addition and subtraction developed in grade 3. • reviewing missing number equations from grade 3 like 25 - 4 = 15 + ___. • reviewing the associative property of addition developed in grade 3.

Set Tool, Relational Rods, Number Line Tool, Money Tool,

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Grade 4

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Patterns Instructional Focus: Patterning

Connected Concepts

Overall Expectation • describe, extend, and create a variety of numeric and geometric patterns, make predictions related to the patterns, and investigate repeating patterns involving reflections. Specific Expectations – extend, describe, and create repeating, growing, and shrinking number patterns (e.g., “I created the pattern 1, 3, 4, 6, 7, 9, …. I started at 1, then added 2, then added 1, then added 2, then added 1, and I kept repeating this.”). – connect each term in a growing or shrinking pattern with its term number (e.g., in the sequence 1, 4, 7, 10, …, the first term is 1, the second term is 4, the third term is 7, and so on), and record the patterns in a table of values that shows the term number and the term. – create a number pattern involving addition, subtraction, or multiplication, given a pattern rule expressed in words (e.g., the pattern rule “start at 1 and multiply each term by 2 to get the next term” generates the sequence 1, 2, 4, 8, 16, 32, 64, …). – make predictions related to repeating geometric and numeric patterns (Sample problem: Create a pattern block train by alternating one green triangle with one red trapezoid. Predict which block will be in the 30th place.).

Number Sense Specific Expectations – demonstrate an understanding of simple multiplicative relationships involving unit rates, through investigation using concrete materials and drawings (e.g., scale drawings in which 1 cm represents 2 m) (Sample problem: If 1 book costs $4, how do you determine the cost of 2 books? … 3 books? … 4 books?). Patterns that are generated by adding a constant are related to skip counting, and multiplication tables developed in earlier grades as are simple rates. Consider… • connecting skip counting that starts with the first multiple of a number and multiplication tables to patterns like 2, 4, 6, 8,… to connect term number and term value. The first term is 2 x 1 or 2 . The second term is 2 x 2 or 4 and so on. • building models and tables of values of simple rate problems like the one in the sample problem above.

Patterning and Algebra Grade 4 Learning Activities : Picnic Partners and What’s My Rule?

Set Tool, Relational Rods, Number Line Tool, Pattern Maker

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Grade 4

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2D Geometry Instructional Focus: Geometry

Connected Concepts

Overall Expectation • identify quadrilaterals and classify them by their geometric properties, and compare various angles to benchmarks; and three-dimensional figures. Specific Expectations – draw the lines of symmetry of two dimensional shapes, through investigation using a variety of tools (e.g., Mira, grid paper) and strategies (e.g., paper folding) (Sample problem: Use paper folding to compare the symmetry of a rectangle with the symmetry of a square.). – identify and compare different types of quadrilaterals (i.e., rectangle, square, trapezoid, parallelogram, rhombus) and sort and classify them by their geometric properties (e.g., sides of equal length; parallel sides; symmetry; number of right angles). – identify benchmark angles (i.e., straight angle, right angle, half a right angle), using a reference tool (e.g., paper and fasteners, pattern blocks, straws), and compare other angles to these benchmarks (e.g.,“The angle the door makes with the wall is smaller than a right angle but greater than half a right angle.”) (Sample problem: Use paper folding to create benchmarks for a straight angle, a right angle, and half a right angle, and use these benchmarks to describe angles found in pattern blocks.). – relate the names of the benchmark angles to their measures in degrees (e.g., a right angle is 90º).

Number Sense Specific Expectations – represent fractions using concrete materials, words, and standard fractional notation,. – compare fractions to the benchmarks of 0, 1/2 and 1. (e.g., 1/8 is closer to 0 than to 1/2 ). – demonstrate and explain the relationship between equivalent fractions, using concrete materials (e.g., fraction circles, fraction strips, pattern blocks) and drawing (e.g., “I can say that of my cubes are 3 /6 means that white, or half of the cubes are white. This 3/ 6 and 1 /2 are equal.”). Consider… • discussing fractions created when creating lines of symmetry. • discussing benchmark angles in terms of fractions of a full rotation of 360 degrees. • discussing equivalent fractions in angle benchmark term. ( Two quarter turns is the same as one half turn so 2/4 is the same as 1/2.)

Geometry and Spatial Sense See pages 38-52 Grade 4 Learning Activity: Two-Dimensional Shapes: Comparing Angles

Pattern Blocks

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Grade 4

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Area/Perimeter Instructional Focus: Measurement

Connected Concepts

Overall Expectation • determine the relationships among units and measurable attributes, including the area and perimeter of rectangles. Specific Expectations – determine, through investigation, the relationship between the side lengths of a rectangle and its perimeter and area (Sample problem: Create a variety of rectangles on a geoboard. Record the length, width, area, and perimeter of each rectangle on a chart. Identify relationships.). – pose and solve meaningful problems that require the ability to distinguish perimeter and area (e.g., “I need to know about area when I cover a bulletin board with construction paper. I need to know about perimeter when I make the border.”). – compare, using a variety of tools (e.g., geoboard, patterns blocks, dot paper), twodimensional shapes that have the same perimeter or the same area (Sample problem: Draw, using grid paper, as many different rectangles with a perimeter of 10 units as you can make on a geoboard.).

Grade 4 Learning Activity: Measurement Relationships, pages 32 – 39. Designing a Kindergarten Play Enclosure

Coloured Tiles, Number Line

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Number Sense – multiply to 9 x 9 and divide to 81 ÷ 9, using a variety of mental strategies (e.g., doubles, doubles plus another set, skip counting). – solve problems involving the multiplication of one-digit whole numbers, using a variety of mental strategies (e.g., 6 x 8 can be thought of as 5 x 8 + 1 x 8).* Algebra – determine, through investigation, the inverse relationship between multiplication and division (e.g., since 4 x 5 = 20, then 20 ÷ 5 = 4; since 35 ÷ 5 = 7, then 7 x 5 = 35). – determine the missing number in equations involving multiplication of one- and twodigit numbers, using a variety of tools and strategies (e.g., modelling with concrete materials, using guess and check with and without the aid of a calculator) (Sample problem: What is the missing number in the equation ___ x 4 = 24?). – identify, through investigation (e.g., by using sets of objects in arrays, by drawing area models), and use the commutative property of multiplication to facilitate computation with whole numbers . – identify, through investigation (e.g., by using sets of objects in arrays, by drawing area models), and use the distributive property of multiplication over addition to facilitate computation with whole numbers.* Consider… • developing and using above expectations in a variety of area contexts. * These two expectations are essentially the same.

Grade 4

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Multiplication/Division Instructional Focus: Number Sense

Connected Concepts

Overall Expectation • solve problems involving the addition, subtraction, multiplication, and division of single- and multi-digit whole numbers, and involving the addition and subtraction of decimal numbers to tenths and money amounts, using a variety of strategies. Specific Expectations – solve problems that arise from real-life situations and that relate to the magnitude of whole numbers up to 10 000 (Sample problem: How high would a stack of 10 000 pennies be? Justify your answer.). – multiply to 9 x 9 and divide to 81 ÷ 9, using a variety of mental strategies (e.g., doubles, doubles plus another set, skip counting). – solve problems involving the multiplication of one-digit whole numbers, using a variety of mental strategies (e.g., 6 x 8 can be thought of as 5 x 8 + 1 x 8). – multiply whole numbers by 10, 100, and 1000, and divide whole numbers by 10 and 100, using mental strategies (e.g., use a calculator to look for patterns and generalize to develop a rule). – multiply two-digit whole numbers by one-digit whole numbers, using a variety of tools (e.g., base ten materials or drawings of them, arrays), student-generated algorithms, and standard algorithms. – divide two-digit whole numbers by one-digit whole numbers, using a variety of tools (e.g., concrete materials, drawings) and student-generated algorithms. Volume Three: Multiplication Multiplication in the Junior Grades: Pages 11-27 Grade 4 Learning Activity: Chairs, Chairs, and More Chairs! Volume Four: Division Division in the Junior Grades, pages 11 – 25. Grade 4 Learning Activity: Intramural Dilemmas

Measurement – solve problems involving the relationship between years and decades, and between decades and centuries (Sample problem: How many decades old is Canada?). Consider… • continuing to use area context and the area model of multiplication to develop and extend multiplication and division work. • using year, decade and century relationships to develop and reinforce multiplication of a whole number by 10 and 100. • using linear measurement contexts to develop and reinforce multiplication of a whole number by 10, 100, and 1000. (How many millimetres long would a 4 cm piece of ribbon be?) Algebra Specific Expectations – determine, through investigation, the inverse relationship between multiplication and division (e.g., since 4 x 5 = 20, then 20 ÷ 5 = 4; since 35 ÷ 5 = 7, then 7 x 5 = 35). – determine the missing number in equations involving multiplication of one- and twodigit numbers, using a variety of tools and strategies (e.g., modelling with concrete materials, using guess and check with and without the aid of a calculator) (Sample problem: What is the missing number in the equation ___ x 4 = 24?). – identify, through investigation (e.g., by using sets of objects in arrays, by drawing area models), and use the commutative property of multiplication to facilitate computation with whole numbers . – identify, through investigation (e.g., by using sets of objects in arrays, by drawing area models), and use the distributive property of multiplication over addition to facilitate computation with whole numbers. Consider… • developing and using above expectations in a variety of area contexts.

Set Tool, Relational Rods, Number Line Tool, Coloured Tiles

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Grade 4

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Fractions/Proportional Relationships Instructional Focus: Number Sense

Connected Concepts

Overall Expectation • read, represent, compare, and order whole numbers to 10 000, decimal numbers to tenths, and simple fractions, and represent money amounts to $100. • demonstrate an understanding of proportional reasoning by investigating whole-number unit rates. Specific Expectations – represent fractions using concrete materials, words, and standard fractional notation, and explain the meaning of the denominator as the number of the fractional parts of a whole or a set, and the numerator as the number of fractional parts being considered. – compare and order fractions (i.e., halves, thirds, fourths, fifths, tenths) by considering the size and the number of fractional parts (e.g., 4/5 is greater than 3 /5 there are more parts in 4/5; 1/4 is greater than 1/5 because the size of the part is larger in 1/4. – compare fractions to the benchmarks of 0, 1/2 and 1. (e.g., 1/8 is closer to 0 than to 1/2). – demonstrate and explain the relationship between equivalent fractions, using concrete materials (e.g., fraction circles, fraction strips, pattern blocks) and drawing (e.g., “I can say that of my cubes are 3 /6 means that white, or half of the cubes are white. This 3/ 6 and 1 /2 are equal.”). – count forward by halves, thirds, fourths, and tenths to beyond one whole, using concrete materials and number lines (e.g., use fraction circles to count fourths: “One fourth, two fourths, three fourths, four fourths, five fourths, six fourths, …”). – describe relationships that involve simple whole-number multiplication (e.g.,“If you have 2 marbles and I have 6 marbles, I can say that I have three times the number of marbles you have.”); – determine and explain, through investigation, the relationship between fractions (i.e., halves, fifths, tenths) and decimals to tenths, using a variety of tools (e.g., concrete materials, drawings, calculators) and dividing each fifth into two equal parts to show that 2/5 can be represented as 0.4). – demonstrate an understanding of simple multiplicative relationships involving unit rates, through investigation using concrete materials and drawings (e.g., scale drawings in which 1 cm represents 2 m)

Geometry – identify benchmark angles (i.e., straight angle, right angle, half a right angle), using a reference tool (e.g., paper and fasteners, pattern blocks, straws), and compare other angles to these benchmarks (e.g.,“The angle the door makes with the wall is smaller than a right angle but greater than half a right angle.”) (Sample problem: Use paper folding to create benchmarks for a straight angle, a right angle, and half a right angle, and use these benchmarks to describe angles found in pattern blocks.). – relate the names of the benchmark angles to their measures in degrees (e.g., a right angle is 90º). Consider… • connecting benchmark angles to benchmark fractions . (Eg. A straight angle is a half turn. A right angle is a quarter turn.). Algebra – connect each term in a growing or shrinking pattern with its term number (e.g., in the sequence 1, 4, 7, 10, …, the first term is 1, the second term is 4, the third term is 7, and so on), and record the patterns in a table of values that shows the term number and the term. Consider… • representing unit rates in tables to see the multiplicative relationships between term number and term value.

Volume Five: Fractions Learning about Fractions in the Junior Grades , pages 11 – 23. Grade 4 Learning Activity: Every Vote Counts!

(Sample problem: If 1 book costs $4, how do you determine the cost of 2 books? … 3 books? … 4 books?).

Fraction lessons and research background supporting those lessons. Cells in the first two columns address junior fraction expectations.

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Partitioning Sets, Pouring Containers, Fraction Strips, Relational Rods

Grade 4

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Properties of 3-D Shapes Instructional Focus: Geometry Overall Expectation • identify quadrilaterals and three-dimensional figures and classify them by their geometric properties, and compare various angles to benchmarks. • construct three-dimensional figures, using two-dimensional shapes. Specific Expectations – identify and describe prisms and pyramids, and classify them by their geometric properties (i.e., shape of faces, number of edges, number of vertices), using concrete materials. – construct a three-dimensional figure from a picture or model of the figure, using connecting cubes (e.g., use connecting cubes to construct a rectangular prism). – construct skeletons of three-dimensional figures, using a variety of tools (e.g., straws and modelling clay, toothpicks and marshmallows, Polydrons), and sketch the skeletons. – draw and describe nets of rectangular and triangular prisms (Sample problem: Create as many different nets for a cube as you can, and share your results with a partner.). – construct prisms and pyramids from given nets. – construct three-dimensional figures (e.g., cube, tetrahedron), using only congruent shapes.

Geometry Grade 4 Learning Activity: Three-Dimensional Figures: Construction Challenge

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Grade 4

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3-D Measurement Instructional Focus: Measurement

Connected Concepts

Overall Expectations • estimate, measure, and record length, perimeter, area, mass, capacity, volume, and elapsed time, using a variety of strategies. • determine the relationships among units and measurable attributes, including the area and perimeter of rectangles. Specific Expectations – estimate, measure, and record the mass of objects (e.g., apple, baseball, book), using the standard units of the kilogram and the gram. – estimate, measure, and record the capacity of containers (e.g., a drinking glass, a juice box), using the standard units of the litre and the millilitre. – compare and order a collection of objects, using standard units of mass (i.e., gram, kilogram) and/or capacity (i.e., millilitre, litre). – determine, through investigation, the relationship between grams and kilograms (Sample problem: Use centimetre cubes with a mass of one gram, or other objects of known mass, to balance a one-kilogram mass.). – estimate, measure using concrete materials, and record volume, and relate volume to the space taken up by an object (e.g., use centimetre cubes to demonstrate how much space a rectangular prism takes up) (Sample problem: Build a rectangular prism using connecting cubes. Describe the volume of the prism using the number of connecting cubes.). – determine, through investigation, the relationship between millilitres and litres (Sample problem: Use small containers of different known capacities to fill a one litre container.). – select and justify the most appropriate standard unit to measure mass (i.e., milligram, gram, kilogram) and the most appropriate standard unit to measure the capacity of a container (i.e., millilitre, litre).

Number Sense Consider… • reviewing addition and subtraction when exploring the relationship between millilitres and litres, as well as grams and kilograms. • reviewing multiplication by 1000. • describing the relationship between smaller containers and larger containers with fractional language.

Measurement Measurement Relationships , pages 35 -37.

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Grade 4

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Probability Instructional Focus: Probability

Connected Concepts

Overall Expectation • predict the results of a simple probability experiment, then conduct the experiment and compare the prediction to the results. Specific Expectations – predict the frequency of an outcome in a simple probability experiment, explaining their reasoning; conduct the experiment; and compare the result with the prediction (Sample problem: If you toss a pair of number cubes 20 times and calculate the sum for each toss, how many times would you expect to get 12? 7? 1? Explain your thinking. Then conduct the experiment and compare the results with your predictions.). – determine, through investigation, how the number of repetitions of a probability experiment can affect the conclusions drawn (Sample problem: Each student in the class tosses a coin 10 times and records how many times tails comes up. Combine the individual student results to determine a class result, and then compare the individual student results and the class result.).

Number Sense – compare fractions to the benchmarks of 0, 1/2 and 1. (e.g., 1/8 is closer to 0 than to 1/2 ). – demonstrate and explain the relationship between equivalent fractions, using concrete materials (e.g., fraction circles, fraction strips, pattern blocks) and drawing (e.g., “I can say that of my cubes are 3 /6 means that white, or half of the cubes are white. This 3/ 6 and 1 /2 are equal.”). – demonstrate an understanding of simple multiplicative relationships involving unit rates, through investigation using concrete materials and drawings (e.g., scale drawings in which 1 cm represents 2 m) (Sample problem: If 1 book costs $4, how do you determine the cost of 2 books? … 3 books? … 4 books?).

Data Management and Probability Grade 4 Learning Activity: Heads or Tails?

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Grade 4

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Location and Movement/Patterns with Reflections Instructional Focus: Geometry

Connected Concepts

Overall Expectation • identify and describe the location of an object, using a grid map, and reflect twodimensional shapes. Specific Expectations – identify and describe the general location of an object using a grid system (e.g.,“The library is located at A3 on the map.”). – identify, perform, and describe reflections using a variety of tools (e.g., Mira, dot paper, technology). – create and analyse symmetrical designs by reflecting a shape, or shapes, using a variety of tools (e.g., pattern blocks, Mira, geoboard, drawings), and identify the congruent shapes in the designs.

Number Sense Consider… • using fractional language as appropriate to describe relationships in symmetrical designs.

Instructional Focus: Patterning Overall Expectation • describe, extend, and create a variety of numeric and geometric patterns, make predictions related to the patterns, and investigate repeating patterns involving reflections; Specific Expectations – extend and create repeating patterns that result from reflections, through investigation using a variety of tools (e.g., pattern blocks, dynamic geometry software, dot paper).

Geometry and Spatial Sense Grade 4 Learning Activity: Location: Check Mate Grade 4 Learning Activity: Movement: Hit the Target

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Grade 4

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Data Management Overall Expectations • collect and organize discrete primary data and display the data using charts and graphs, including stem-and-leaf plots and double bar graphs. • read, describe, and interpret primary data and secondary data presented in charts and graphs, including stem-and-leaf plots and double bar graphs. *Integrating Data Management may not be possible for different teachers and in different school contexts. Learning activities are available in The Guides to Effective Instruction . (Data Management and Probability: Grade 4 Learning Activity Too Much TV) Collection and Organization of Data – collect data by conducting a survey (e.g., “Choose your favourite meal from the following list: breakfast, lunch, dinner, other.”) or an experiment to do with themselves, their environment, issues in their school or the community, or content from another subject, and record observations or measurements; – collect and organize discrete primary data and display the data in charts, tables, and graphs (including stem-and-leaf plots and double bar graphs) that have appropriate titles, labels (e.g., appropriate units marked on the axes), and scales (e.g., with appropriate increments) that suit the range and distribution of the data, using a variety of tools (e.g., graph paper, simple spreadsheets, dynamic statistical software).

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Investigations in Science class offer the opportunity to collect, organize and display data. As these investigations can take place regularly in many strands of Science, there are many opportunities to revisit key concepts throughout the year. Displaying class data for an investigation, recorded in a spreadsheet and displayed on a projector can allow for manipulation of type of graph, scale and labels that serves the clear purpose of working with the data at hand. Consider doing focused teaching of a specific type of data display in math class so it can be applied in Science class.

Social Studies The inquiry process as laid out in the front matter of curriculum document includes the elements below. • • • • •

formulating questions gathering and organizing information, evidence, and/or data interpreting and analysing information, evidence, and/or data evaluating information, evidence, and/or data and drawing conclusions communicating findings

See grade-level expectations for specific examples.

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Grade 4

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Data Management Overall Expectations • collect and organize discrete primary data and display the data using charts and graphs, including stem-and-leaf plots and double bar graphs. • read, describe, and interpret primary data and secondary data presented in charts and graphs, including stem-and-leaf plots and double bar graphs.

*Integrating Data Management may not be possible for different teachers and in different school contexts. Learning activities are available in The Guides to Effective Instruction . (Data Management and Probability: Grade 4 Learning Activity Too Much TV) Data Relationships – read, interpret, and draw conclusions from primary data (e.g., survey results, measurements, observations) and from secondary data (e.g., temperature data in the newspaper, data from the Internet about endangered species), presented in charts, tables, and graphs (including stem-and-leaf plots and double bar graphs); – demonstrate, through investigation, an understanding of median (e.g.,“The median is the value in the middle of the data. If there are two middle values, you have to calculate the middle of those two values.”), and determine the median of a set of data (e.g.,“I used a stem-and-leaf plot to help me find the median.”); – describe the shape of a set of data across its range of values, using charts, tables, and graphs (e.g. “The data values are spread out evenly.”; “The set of data bunches up around the median.”); – compare similarities and differences between two related sets of data, using a variety of strategies (e.g., by representing the data using tally charts, stem-and-leaf plots, or double bar graphs; by determining the mode or the median; by describing the shape of a data set across its range of values).

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Science • Investigations in Science class offer the opportunity to read, interpret and draw conclusions from data. As these investigations can take place regularly in many strands of Science, there are many opportunities to revisit key concepts throughout the year. • Displaying class data for an investigation, recorded in a spreadsheet and displayed on a projector can allows students to see the results of a number of trials. Meaningful opportunities to determine and discuss measures of central tendency can take place in that context. • Consider doing focused teaching of a specific type of data display in math class so it can be applied in Science class. • Many of the relationships investigated in Science class will allow students to identify and describe trends in a graph.

Social Studies The inquiry process as laid out in the front matter of curriculum document includes the elements below. • • • • •

formulating questions gathering and organizing information, evidence, and/or data interpreting and analysing information, evidence, and/or data evaluating information, evidence, and/or data and drawing conclusions communicating findings

See grade-level expectations for specific examples.

Grade 4

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Fractions All fraction expectations are accounted for in the long -range outline. However, recent research by Cathy Bruce and colleagues suggests that punctuating instruction in fractions throughout the year is effective. Teachers are encouraged to include fractional language when opportunities arise incidentally and to regularly incorporate fraction lessons into units that may not have a fractional focus. She also outlines seven other critical components of fraction teaching. Those are listed below. •

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Emphasize unit fractions Unit fractions (i.e., a fraction with a numerator of 1) are foundational to fractions understanding. This understanding is built through tasks such as counting by unit fractions and composing/decomposing fractions. Use number lines and rectangles/ribbons Linear models allow students to make sense of and solve mathematical tasks as well as explain their thinking. These models have longevity across grades, mathematical number systems, and contexts. Have students partition figures and paper fold The action of partitioning figures, through drawing and paper folding, supports students in understanding the role of the denominator, and the relationship between unit fractions and the whole. Read a fraction as a number not two numbers A fraction is a number and should be read as such. For example, 2 is ‘two thirds’ (not ‘two over three’).

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Punctuate instruction Allocating time differently, rather than allocating more time, benefited students. A few days every few weeks on fraction concepts and skills, resulted in enhanced student understanding.

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Find a common unit rather than a common denominator If the denominator is considered the fractional unit, then ‘finding a common denominator’ is more aptly named ‘finding a common unit’. This terminology allows students to connect to their knowledge of unit in other contexts, such as place value, money and measurement. Mix proper and improper fractions in tasks Improper fractions include the whole. Mixing the two reduces the incorrect generalizations that students may make about fractions when only presented with proper fractions. Annotate fractions to clarify A single representation can be interpreted multiple ways. Adding information about the characteristics (such as shaded equal regions for the numerator) ensures that students are attending to the same characteristics.

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These recommendations and further research on teaching fractions are available here. She and her colleagues have laid out a progression for learning fractions. Each cell in the pathway is linked to an elaboration of the fraction idea and most have lessons attached. The pathway can be found by clicking on the image below.

Grade 5

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Time and Relative Temperature Expectations Grade 3 – read time using analogue clocks, to the nearest five minutes, and using digital clocks (e.g., 1:23 means twenty-three minutes after one o’clock), and represent time in 12-hour notation. – estimate, read (i.e., using a thermometer), and record positive temperatures to the nearest degree Celsius (i.e., using a number line; using appropriate notation) (Sample problem: Record the temperature outside each day using a thermometer, and compare your measurements with those reported in the daily news.). – identify benchmarks for freezing, cold, cool, warm, hot, and boiling temperatures as they relate to water and for cold, cool, warm, and hot temperatures as they relate to air (e.g., water freezes at 0°C; the air temperature on a warm day is about 20°C, but water at 20°C feels cool). – solve problems involving the relationships between minutes and hours, hours and days, days and weeks, and weeks and years, using a variety of tools (e.g., clocks, calendars, calculators).

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Grade 4 – estimate, measure (i.e., using an analogue clock), and represent time intervals to the nearest minute; – estimate and determine elapsed time, with and without using a time line, given the durations of events expressed in five-minute intervals, hours, days, weeks, months, or years (Sample problem: If you wake up at 7:30 a.m., and it takes you 10 minutes to eat your breakfast, 5 minutes to brush your teeth, 25 minutes to wash and get dressed, 5 minutes to get your backpack ready, and 20 minutes to get to school, will you be at school by 9:00 a.m.?). – solve problems involving the relationship between years and decades, and between decades and centuries (Sample problem: How many decades old is Canada?). Grade 5

– estimate, measure (i.e., using an analogue clock), and represent time intervals to the nearest second. – estimate and determine elapsed time, with and without using a time line, given the durations of events expressed in minutes, hours, days, weeks, months, or years (Sample problem: You are travelling from Toronto to Montreal by train. If the train departs Toronto at 11:30 a.m. and arrives in Montreal at 4:56 p.m., how long will you be on the train?). – measure and record temperatures to determine and represent temperature changes over time (e.g., record temperature changes in an experiment or over a season) (Sample problem: Investigate the relationship between weather, climate, and temperature changes over time in different locations.).

Grade 3

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Review-June Number Sense • read, represent, compare, and order whole numbers to 10 000, decimal numbers to tenths, and simple fractions, and represent money amounts to $100. • demonstrate an understanding of magnitude by counting forward and backwards by 0.1 and by fractional amounts. • solve problems involving the addition, subtraction, multiplication, and division of single- and multi-digit whole numbers, and involving the addition and subtraction of decimal numbers to tenths and money amounts, using a variety of strategies. • demonstrate an understanding of proportional reasoning by investigating whole-number unit rates. Measurement • estimate, measure, and record length, perimeter, area, mass, capacity, volume, and elapsed time, using a variety of strategies. • determine the relationships among units and measurable attributes, including the area and perimeter of rectangles. Geometry and Spatial Sense • identify quadrilaterals and three-dimensional figures and classify them by their geometric properties, and compare various angles to benchmarks; • construct three-dimensional figures, using two-dimensional shapes; • identify and describe the location of an object, using a grid map, and reflect two-dimensional shapes. Data Management and Probability • collect and organize discrete primary data and display the data using charts and graphs, including stem-and-leaf plots and double bar graphs; • read, describe, and interpret primary data and secondary data presented in charts and graphs, including stem-and-leaf plots and double bar graphs; • predict the results of a simple probability experiment, then conduct the experiment and compare the prediction to the results. Patterning and Algebra • describe, extend, and create a variety of numeric and geometric patterns, make predictions related to the patterns, and investigate repeating patterns involving reflections. • demonstrate an understanding of equality between pairs of expressions, using addition, subtraction, and multiplication.

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Consider using the assessment questions in D2L throughout the month of June for each strand and address overall expectations that students still find challenging. Questions are matched to each overall expectation across the 5 strands and are varied in their achievement chart focus, addressing thinking, application, and knowledge. Once students complete a set of questions, the D2L generates instant data on overall performance, individual student performance, performance by question, and question detail that shows the percentage of students answering each of the incorrect options and the correct option. To gain access to these questions, you may contact the eLearning/Blended Learning Assistant, Vicky Grewal, and request access to the Math Diagnostic Assessment. Her email is [email protected] Please include your school, grade and TVDSB employee number in the email. If you teach a class that is not your homeroom, please include the name of the teacher who is attached to that class in Trillium.

Grade 4

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