GRADE 5 UNIT PLANS LINKED TO THE BIG IDEAS

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1 GRADE 5 UNIT PLANS LINKED TO THE BIG IDEAS STRAND: Patterning and Algebra TERM: 1 First Instructional Strand Patterns and Relationships 1. Experience with a wide variety of patterns helps students recognize relationships within and between patterns. 2. Growing and shrinking patterns involve an increase or a decrease in elements as the pattern continues. The increase or decrease in elements can be described numerically. Chapter 1, Patterns in Building Chapter 1, Diagnostic Assessment: Getting Started-Patterns in Phone Chains Determine, through investigation using a table of values, relationships in growing and shrinking patterns, and investigate repeating patterns involving translations. Create, identify, and extend numeric and geometric patterns, using a variety of tools (e.g., concrete materials, paper and pencil, calculators, spreadsheets). Build a model to represent a number pattern presented in a table of values that shows the term number and the term. Make a table of values for a pattern that is generated by adding or subtracting a number (i.e., a constant) to get the next term, or by multiplying or dividing by a constant to get the next term, given either the sequence or the pattern rule in words. Make predictions related to growing and shrinking geometric and numeric patterns. Extend and create repeating patterns that result from translations, through investigation using a variety of tools. Lesson 1 Two Dimensional Patterns Lesson 2 Patterns and Tables Ontario Supplement Lesson A: Building a Model, p. 24 Lesson 3 Solving Problems Using Patterns 3D Patterns Super Source Grades 3-4: Pattern Blocks Spiney and Other Creatures, p. 58 What s Next, p. 78 Teaching Student Centered Mathematics, Grades 3-5 Volume 2 by John Van De Walle Repeating Patterns, p. 291 Growing Patterns, p

2 STRAND: Number Sense and Numeration TERM: 1 Second Instructional Strand Quantity Relationships 1. Having a sense of quantity involves understanding the howmuchness of whole numbers and decimal numbers. 2. Experiences with numbers in meaningful contexts help to develop a sense of quantity. Representation 1. Words, numbers, models, symbols (e.g., decimal point) and placement are used to indicate quantity and relationships (e.g., place value mat, number line, base ten models, money). Chapter 2, Reporting Numbers Chapter 2, Diagnostic Assessment: Getting Started, Modelling and Comparing Numbers Read, represent, compare, and order whole numbers to and decimal numbers to hundredths. Demonstrate an understanding of magnitude by counting forward and backwards by Represent, compare, and order whole numbers and decimal numbers from 0.01 to , using a variety of tools. Demonstrate an understanding of place value in whole numbers and decimal numbers from 0.01 to , using a variety of tools and strategies. Read and print in words whole numbers to ten thousand, using meaningful contexts. Count forward by hundredths from any decimal number expressed to two decimal places, using concrete materials and number lines. Round decimal numbers to the nearest tenth, in problems arising from real-life situations. Solve problems that arise from real-life situations and that relate to the magnitude of whole numbers up to Lesson 1 Estimating 50 Thousand Lesson 2 Reading and Writing Numbers Lesson 3 Renaming Numbers Lesson 4 Comparing and Ordering Numbers Lesson 5 Rounding Numbers Lesson 7 Decimal Hundredths. Lesson 8 Exploring Equivalent Decimals Lesson 9 Rounding Decimals Lesson 10 Comparing and Ordering Decimals Teaching Student Centered Mathematics Grades 3-5 by John Van de Walle, p SuperSource Grades 3-4: Base Ten Blocks Clear the Mat, p. 26 Place It, p. 62 SuperSource Grades 5-6: Base 10 Blocks Nearest Ten, p

3 STRAND: Data Management and Probability TERM: 1 Third Instructional Strand Collection and Organization of Data Data Relationships: 1. Collect and organize primary and secondary data. 1. Interpret and use charts and graphs, including continuous line graphs. 2. Explain relationships between data sets and draw inferences from data. Chapter 3, Swimsuit Sales Chapter 3, Diagnostic Assessment: Getting Started-Graphing Favourite Authors Collect and organize discrete or continuous primary data and secondary data and display the data using charts and graphs, including broken-line graphs. Read, describe, and interpret primary data and secondary data presented in charts and graphs, including broken-line graphs. Distinguish between discrete data (i.e., data organized using numbers that have gaps between them, such as whole numbers, and often used to represent a count, such as the number of times a word is used) and continuous data (i.e., data organized using all numbers on a number line that fall within the range of the data, and used to represent measurements such as heights or ages of trees). Collect data by conducting a survey or an experiment to do with themselves, their environment, issues in their school or community, or content from another subject, and record observations or measurements. Collect and organize discrete or continuous primary data and secondary data and display the data in charts, tables, and graphs (including broken-line graphs) that have appropriate titles, labels and scales that suit the range and distribution of the data. Read, interpret, and draw conclusions from primary data and from secondary data, presented in charts, tables, and graphs including broken-line graphs. Calculate the mean for a small set of data and use it to describe the shape of the data set across its range of values, using charts, tables, and graphs. Compare similarities and differences between two related sets of data, using a variety of strategies. Demonstrate that sets of data can be samples of larger populations. Describe, through investigation, how a set of data is collected and explain whether the collection method is appropriate. Lesson 1 Evaluating Survey Results Lesson 2 Broken Line Graphs Lesson 5 Pictographs Lesson 6 Changing the Appearance of a Graph Lesson 8 Mean and Mode Ontario Supplement Lesson A: Collecting Data, p.35 Lesson 9 Communicate About Graphs Teaching Student Centered Mathematics, Grades 3-5, Volume 2 by John Van de Walle Exploring Mean, p. 326 Leveling the Bars The Mean Foot Bar Graphs to Pie Graphs, p. 337 A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6: Data Management and Probability, Grades 4 to 6, 2008 Daily Physical Activity, p SuperSource Grades 5-6: Pattern Blocks How Many Can Sit, p

4 STRAND: Measurement Attributes, Units and Measurement Sense 1. Investigate measurement problems in real-life settings. 2. Extend their knowledge of measurement units and their relationships. 3. Extend their knowledge of time and temperature measurement. Estimate, measure, and record perimeter, temperature change, and elapsed time, using a variety of strategies. Determine the relationships among units and measurable attributes. 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. Measure and record temperatures to determine and represent temperature changes over time. Estimate and measure the perimeter of regular and irregular polygons, using a variety of tools and strategies. Select and justify the most appropriate standard unit (i.e., millimetre, centimetre, decimetre, metre, kilometre) to measure length, height, width, and distance, and to measure the perimeter of various polygons. Solve problems requiring conversion from metres to centimetres and from kilometres to metres. Solve problems involving the relationship between a 12-hour clock and 24-hour clock. TERM: 2 First Instructional Strand Chapter 5, Perimeter Walk and Ontario Supplement Chapter Review (time) Chapter 5, Diagnostic Assessment: Getting Started-Measuring Length and Time Lesson 1 Using Measurements to Describe Objects Lesson 2 Measuring Lengths Ontario Supplement Lesson A: Metric Relationships, p Lesson 4 Measuring Perimeter Lesson 5 Measuring the Perimeter of a Rectangle Lesson 6 Solve Problems Using Tables Lesson 7 Measuring Time Ontario Supplement Lesson B: Lengths of Time, p Ontario Supplement Lesson C: 24 Hour Clocks, p Teaching Student Centered Mathematics, Grades 3-5, Volume 2 by John Van de Walle Changing Units (length), p. 258 One Handed Clocks (time), p. 269 Elapsed Time, p A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6: Measurement, Grades 4 to 6, 2008 Weather or Not (time), p. 67 Hiking the Bruce Trail (measurement relations), p. 89 SuperSource Grades 5-6: Pattern Blocks All Possible Perimeters, p

5 STRAND: Number Sense and Numeration TERM: 2 A Second Instructional Strand Operational Sense 1. Operational sense depends on an understanding of addition and subtraction, the properties of these operations, and the relationships among them. 2. Students demonstrate operational sense when they can work flexibly with a variety of computational strategies, including those of their own devising. 3. Solving problems and using models are key instructional components that allow students to develop conceptual and procedural understanding of the operations. Chapter 4, Counting Calories Chapter 2, Diagnostic Assessment: Getting Started, Going to the Movies Chapter 4 Solve problems involving the addition and subtraction of whole numbers and decimal numbers to hundredths, using a variety of strategies. Solve problems involving the addition, subtraction, using a variety of mental strategies. Add and subtract decimal numbers to hundredths, including money amounts, using concrete materials, estimation, and algorithms. Use estimation when solving problems involving the addition, subtraction, of whole numbers, to help judge the reasonableness of a solution. Read and write money amounts to $1000. Lesson 1 Addition and Subtraction Using Mental Math Lesson 2 Estimating Sums and Difference Lesson 3 Adding Whole Numbers Lesson 5 Communicate About a Choice of Calculation Method Lesson 6 Adding Decimals Lesson 7 Adding Money Lesson 8 Making Change Lesson 9 Subtracting Decimals Teaching Student Centered Mathematics Grades 3-5 by John Van de Walle, Strategies for Whole Number Computation, p A Guide to Effective Instruction in Mathematics K-6: Number Sense and Numeration, Grades 4-6, Volume 2, 2006, p SuperSource Grades 3-4: Base Ten Blocks Even It Up, p , More or Less, p. 58 SuperSource Grades 5-6: Base 10 Blocks Closest to 1, p

6 STRAND: Number Sense and Numeration TERM: 2 B Second Instructional Strand Operational Sense 1. Operational sense depends on an understanding of multiplication and division, the properties of these operations, and the relationships among them. 2. Students demonstrate operational sense when they can work flexibly with a variety of computational strategies, including those of their own devising. 3. Solving problems and using models are key instructional components that allow students to develop conceptual and procedural understanding of the operations. Chapter 6, Raising Money and Ontario Supplement p. 59 Chapter 2, Diagnostic Assessment: Making Dream Catchers and Ontario Supplement p.46 Chapter 6 Lesson 1 Multiplying 10 s Solve problems involving the multiplication and division of multi-digit whole numbers, using a variety of strategies. Demonstrate an understanding of proportional reasoning by investigating whole-number rates. Solve problems involving the multiplication of whole numbers, using a variety of mental strategies. Multiply two-digit whole numbers by two-digit whole numbers, using estimation, student-generated algorithms, and standard algorithms. Divide three-digit whole numbers by one-digit whole numbers, using concrete materials, estimation, studentgenerated algorithms, and standard algorithms. Multiply decimal numbers by 10, 100, 1000, and and divide decimal numbers by 10 and 100, using mental strategies. Use estimation when solving problems involving multiplication and division of whole numbers, to help judge the reasonableness of a solution. Demonstrate an understanding of simple multiplicative relationships involving whole-number rates, through investigation using concrete materials and drawings. Lesson 2 Estimating Products Lesson 4 Multiplying by Regrouping Lesson 5 Multiply With Arrays Lesson 6 Dividing Hundreds by One Digit Numbers Ontario Supplement Lesson A: Estimating Quotients, p Ontario Supplement Lesson B: Dividing Three Digit Numbers, p Teaching Student Centered Mathematics Grades 3-5 by John Van de Walle, p A Guide to Effective Instruction in Mathematics K-6: Number Sense and Numeration, Grades 4-6, Volumes 3 and 4, 2006 Multiplication, Volume 3, p Division, Volume 4, p Multiplication SuperSource Grades 3-4: SuperSource Grades 5-6: Snap Cubes Base Ten Blocks Grab Bag Math, p. 30 Modelling Multiplication, p. 54 Loose Caboose, p. 34 Fair Shares, p. 42 Base Ten Blocks It s in the Bag, p. 46 Even It Up, p

7 STRAND: Geometry and Spatial Sense TERM: 2 Third Instructional Strand Geometric Properties of Two-Dimensional Shapes 1. Two dimensional shapes have properties that allow them to be identified, sorted and classified. 2. Angles are measures of turn, and can be classified by degree of rotation. 3. An understanding of polygons and their properties allows students to explore and investigate concepts in geometry and measurement. Chapter 7, Design a Logo Chapter 7, Diagnostic Assessment: Getting Started Shape Hunt Ontario Supplement Lesson A : Constructing Triangles, p Overall Expectations(s): Identify and classify two-dimensional shapes by side and angle properties. Distinguish among polygons, regular polygons, and other two-dimensional shapes. Identify and classify acute, right, obtuse, and straight angles. Measure and construct angles up to 90 degrees, using a protractor. Identify triangles (i.e., acute, right, obtuse, scalene, isosceles, equilateral), and classify them according to angle and side properties. Construct triangles, using a variety of tools. Lesson 3 Classifying Triangles by Angles Lesson 4 Classifying Triangles by Side Lengths Lesson 5 Measuring Angles in Polygons Lesson 6 Properties of Polygons Lesson 7 Sorting Polygons Lesson 8 Communication About Shapes Teaching Student Centered Mathematics, Grades 3-5, Volume 2 by John Van De Walle Geometric Thinking and Geometric Concepts, p Measuring Angles, p SuperSource Grades 5-6: Pattern Blocks Building Hexagons, p. 26 A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6:Geometry and Spatial Sense, Grades 4 to 6, 2008 Triangle Sort, p

8 STRAND: Patterning and Algebra TERM: 2 Fourth Instructional Strand Patterns and Relationships 1. An understanding of patterns in numbers and operations contributes to the development of algebraic thinking. Expressions and Equality 1. Equations express the equality between quantities. 2. Variables are used to represent unknown quantities, to represent quantities that vary, and to generalize number properties. A Guide to Effective Instruction in Mathematics K-6: Patterning and Algebra, Grades 4-6, 2008 Balancing Act, p. 77 Demonstrate, through investigation, an understanding of the use of variables in equations. Demonstrate, through investigation, an understanding of variables as changing quantities, given equations with letters or other symbols that describe relationships involving simple rates. Demonstrate, through investigation, an understanding of variables as unknown quantities represented by a letter or other symbol. Determine the missing number in equations involving addition, subtraction, multiplication, or division and one- or two digit numbers, using a variety of tools and strategies. Ontario Supplement Lesson B : Variables in Expressions, p Ontario Supplement Lesson C: Solving Equations, p Teaching Student Centered Mathematics, Grades 3-5, Volume 2 by John Van de Walle, p and p A Guide to Effective Instruction in Mathematics K-6: Patterning and Algebra, Grades 4-6, 2008 Growing Weave Designs, p

9 STRAND: Number Sense and Numeration TERM: 3 First Instructional Strand Proportional Relationships 1. Can be expressed using fractions, ratios, and percents. 2. Involves recognizing comparisons between ratios. Quantity Relationships 1. Having a sense of quantity involves understanding the howmuchness of whole numbers, decimal numbers, fractions, and percents. Relationships 2. Fractions, decimal numbers, and percents are all representations of fractional relationships. Chapter 12, Fractions in Your LIfe Chapter 2, Diagnostic Assessment: Getting Started, Zoomobiles and Rides Chapter 12 Demonstrate an understanding of proportional reasoning by investigating whole-number rates. Read, represent, compare and order proper and improper fractions, and mixed numbers. Represent, compare, and order fractional amounts with like denominators, including proper and improper fractions and mixed numbers, using a variety of tools and using standard fractional notation. Demonstrate and explain equivalent representations of a decimal number, using concrete materials and drawings. Demonstrate and explain the concept of equivalent fractions, using concrete materials. Describe multiplicative relationships between quantities by using simple fractions and decimals. Determine and explain, through investigation using concrete materials, drawings, and calculators, the relationship between fractions (i.e., with denominators of 2, 4, 5, 10, 20, 25, 50, and 100) and their equivalent decimal forms. Lesson 1 Fraction Puzzles Lesson 2 Equivalent Fractions Lesson 4 Improper Fractions and Mixed Fractions Ontario Supplement Lesson A: Comparing and Ordering Fractions, p.72 Lesson 5 Relating Fractions to Decimals Lesson 6 Solve Problems by Making Models Teaching Student Centered Mathematics Grades 3-5 by John Van de Walle, p A Guide to Effective Instruction in Mathematics K-6: Number Sense and Numeration, Grades 4-6, Volume 5, 2006, p SuperSource Grades 3-4: SuperSource Grades 5-6: Tangrams Cuisenaire Rods Fraction Fill Up, p. 34 Fraction Fracas, p. 42 Fraction Spin, p. 38 Snap Cubes Geoboards Fract-Tangles, p. 26 Making Fourths, p. 62 Tangrams Pattern Blocks The More, The Better, p. 82 Wipe Out, p. 86 Pattern Blocks Colour Tiles Fraction Puzzles, p. 50 Fraction Bars, p. 46 Cuisenaire Rods Fraction Pairs, p

10 STRAND: Data Management and Probability Probability 1. Determine the theoretical probability of an outcome in a probability experiment. Represent as a fraction the probability that a specific outcome will occur in a simple probability experiment, using systematic lists and area models. Determine and represent all the possible outcomes in a simple probability experiment, using systematic lists and area models. Represent, using a common fraction, the probability that an event will occur in simple games and probability experiments. Pose and solve simple probability problems, and solve them by conducting probability experiments and selecting appropriate methods of recording the results. TERM: 3 Second Instructional Strand Chapter 13, Fair Games Chapter 13, Diagnostic Assessment: Getting Started- I Predict Lesson 1 Using Probability Language Lesson 2 Predicting Probabilities Lesson 3 Probabilities as Fractions Lesson 4 Modelling Probability Problems Ontario Supplement Lesson A: Using Organized Lists, p.75 Ontario Supplement Lesson B: Using Area Models, p.78 Teaching Student Centered Mathematics, Grades 3-5, Volume 2 by John Van de Walle Add, Then Tally, p. 341 Design a Bag, p. 342 Testing Bag Designs, p. 343 A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6: Data Management and Probability, Grades 4 to 6, 2008 Lost Socks, p. 81 SuperSource Grades 5/6: Snap Cubes Match / No Match, p. 38 What s the Chance?, p. 86 Colour Tiles What s Your Prediction?, p. 86 Tangrams Crazy Darts, p

11 STRAND: Geometry and Spatial Sense TERM: 3 Third Instructional Strand Geometric Properties of Three-Dimensional Figures 1. Three dimensional shapes have properties that allow them to be identified, sorted and classified. 2. Understanding of polyhedra and their properties helps make connections between two- and three-dimensional geometry. Geometric Relationships 1. Plane shapes and solid figures can be composed from or decomposed into other two- dimensional and three dimensional figures. 2. Relationships exist between plane and solid geometry (e.g., the faces of a polyhedron are polygons; views of a solid figure can be represented in a two- dimensional drawing). 3. Congruence is a special geometric relationship between two shapes or figures that have exactly the same size and shape. Location and Movement 1. A coordinate grid system can be used to describe the position of a plane shape or solid object. 2. Different transformations can be used to describe the movement of a shape. No Task Suggested Culminating Task for 3D figures A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6: Geometry and Spatial Sense, Grades 4-6 (2008): Complete the Nets, p Chapter 14, Ontario Supplement- Frieze Patterns, for location and movement (3D Geometry) Chapter 11, Diagnostic Assessment: Getting Started Building Shapes Compare and sort three-dimensional figures. Identify and construct nets of prisms and pyramids. Identify and describe the location of an object, using the cardinal directions, and translate two-dimensional shapes. Distinguish among prisms, right prisms, pyramids, and other three-dimensional figures. Identify prisms and pyramids from their nets. Construct nets of prisms and pyramids, using a variety of tools. Locate an object using the cardinal directions (i.e., north, south, east, west) and a coordinate system. Compare grid systems commonly used on maps (i.e., the use of numbers and letters to identify an area; the use of a coordinate system based on the cardinal directions to describe a specific location). Identify, perform, and describe translations, using a variety of tools. Create and analyse designs by translating and/or reflecting a shape, or shapes, using a variety of tools. Lesson 2 Making Nets Lesson 3 Identifying Nets (Location and Movement) Chapter 14, Diagnostic Assessment: Getting Started Extending Transformation Patterns Chapter 8 Lesson Coordinate Grids Chapter 14 Lesson 4 Translating Shapes on Grids Lesson 7 Modelling Congruence with Transformations A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6: Geometry and Spatial Sense, Grades 4-6 (2008):Package Possibilities, p A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6: Geometry and Spatial Sense, Grades 4-6 (2008): Location: City Treasure Hunt, p Movement: Drawing Designs, p

12 STRAND: Measurement TERM: 3 Fourth Instructional Strand Measurement Relationships 1. Extend their knowledge of measurement units and their relationships. 2. Investigate the relationships between, and develop formulas for, area and perimeter and surface area and volume. Chapter 8, Model a Han Dynasty Home and Chapter 11, Food Drive Estimate, measure, and record perimeter and area using a variety of strategies. Determine the relationships among units and measurable attributes, including the area of a rectangle and the volume of a rectangular prism. Estimate and measure the perimeter and area of regular and irregular polygons, using a variety of tools and strategies. Create, through investigation using a variety of tools and strategies, two-dimensional shapes with the same perimeter or the same area. Determine, through investigation using a variety of tools and strategies the relationships between the length and width of a rectangle and its area and perimeter, and generalize to develop the formulas [i.e., Area length x width; Perimeter = (2 x length) + (2 x width)]. Solve problems requiring the estimation and calculation of perimeters and areas of rectangles. Determine, through investigation, the relationship between capacity (i.e., the amount a container can hold) and volume (i.e., the amount of space taken up by an object), by comparing the volume of an object with the amount of liquid it can hold). Determine, through investigation using stacked congruent rectangular layers of concrete materials, the relationship between the height, the area of the base, and the volume of a rectangular prism, and generalize to develop the formula (i.e., Volume = area of base x height). Select and justify the most appropriate standard unit to measure mass. Chapter 8, Diagnostic Assessment: Getting Started-Measuring Area Lesson 1 Areas of Polygons Lesson 3 Relating a Perimeter and Area of Rectangles Lesson 4 Area Rule for Rectangles Lesson 5 Solve Problems by Solving Simpler Problems Chapter 11 Lesson 5 Measuring and Comparing Capacity Lesson 7 Relating Capacity Units to Volume Ontario Supplement Lesson A: Volume of Rectangular Prisms, p.67 Lesson 8 Measuring and Comparing Mass Lesson 9 Using Tonnes Ontario Supplement Lesson B: Choosing a Unit to Measure Mass, p.70 Teaching Student Centered Mathematics, Grades 3-5, Volume 2 by John Van de Walle (Area and Perimeter) Rectangle Comparison, p. 261 Tangram Areas, p. 262 Fill and Compare, p. 263 Rectangle Comparison, p. 264 Fixed Perimeters, p. 265 Fixed Areas, p. 365 (Volume and Capacity) Capacity Lineup, p. 266 Box Comparison Cubic Units, p. 267 SuperSource: Grades 5/6 Tangrams Cuisenaire Rods How Does Your Garden Grow, p. 34 Planning Playgrounds, p. 66 Lisa s Dog Pen, p. 42 Snap Cubes Grades 3/4 Making Shapes, p. 50 A Tower of Squares, p. 18 What Happens to the Area, p