Grade 5 Math Program. ARITHMETIC FACTS (memory or quick strategy) - Addition and Subtraction - Multiplication (up 100) - Division

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1 Grade 5 Math Program MAJOR STRANDS: The strands and sub-strands, including the general learning outcome for each, follow. Number Concepts and Operations n Develop number sense. Patterns and Relations n Patterns n Use patterns to describe the world and solve problems. n Variables and Equations n Represent algebraic expressions in multiple ways. Shape and Space n Measurement n Use direct and indirect measure to solve problems. n 3-D Objects and 2-D Shapes n Describe the characteristics of 3-D objects and 2-D shapes, and analyze the relationships among them. n Transformations n Describe and analyze position and motion of objects and shapes. Statistics and Probability n Data Analysis n Collect, display, and analyze data to solve problems. n Chance and Uncertainty n Use experimental or theoretical probabilities to represent and solve problems o involving uncertainty. also includes: MENTAL MATH STRATEGIES - Regular Rounding - Front End Loading - Double and Half - Compensation - Compatible Numbers - Annex the Zero PROBLEM SOLVING STRATEGIES (FOR NON-ROUTINE PROBLEMS) - Guess and Check - Draw a Picture - Logical Reasoning - Working Backwards - Use Manipulatives - Act it out - Make a Chart or Graph - and others ARITHMETIC FACTS (memory or quick strategy) - Addition and Subtraction - Multiplication (up 100) - Division

2 NUMBER CONCEPTS AND OPERATIONS (September November) Whole Numbers E-4 place value to to 0.01 [ ] E-8 rounding [ ] E-64 estimation strategies [ ] E-4 works with numerals/numbers [ ] E-22 multiples and factors [ ] E-22 composites and primes [ ] E-64 addition [ ] E-64 subtraction [ ] E-76 multiplication (2 X 3 digits) [ ] E-76 division (3 by 1 digit, with remainder) [ ] Decimals E-4 place value [ ] E-4 compare and order [ ] E-64 addition [ ] E-64 subtraction [ ] E-76 multiply [ ] E-76 divide (to the hundredth place value) [ ] Fractions E-36 relates decimals to proper fractions [ ] E-46 understands equivalent fractions [ ] E-52 compares/orders proper fractions [ ] Integers E-60 introduce meaning of integers [ ] Order of Operations E-98 introduce order of operations (BEDMAS) [ ] E-176 convert mixed to/from improper [ ] E-176 convert fraction to/from decimal [ ] E-176 convert fraction to/from percent [ ] E-176 understands rate, ratio and proportion [ ]

3 SHAPE AND SPACE (December February) Measurement D-4 knows length, width, height [ ] D-4 knows depth and thickness [ ] D-4 knows perimeter and circumference [ ] D-10 area of irregular shapes [ ] D-16 area + perimeter of rectangles [ ] D-18 volume using cubic centimetres [ ] D-20 constructs objects of specific voume [ ] D-20 relates cubic centimetres to millilitres [ ] D-24 mass using gram, kilogram and tonne [ ] D-24 time with the analog clock [ ] D-26 understands sizing of angles [ ] D-26 uses terms: acute, obtuse, right [ ] D-26 uses terms: straight and reflex [ ] D-26 estimates/measures angles with protractor [ ] 2-D Objects and 3-D Shapes D-32 knows geometric shapes and objects [ ] D-32 draws 3-D shape (given front face) [ ] D-34 builds 2-D shapes with tangram pieces [ ] D-38 identifies, knows polygons [ ] D-38 understands sides, angles and vertices [ ] D-40 understands the following: [ ] D-40 point [ ] D-40 line [ ] D-40 angle [ ] D-40 parallel lines [ ] D-40 intersecting lines [ ] D-40 perpendicular lines [ ] D-40 vertical lines [ ] D-40 horizontal lines [ ] D-46 constructs triangles based on measure of sides [ ] Transformations D-46 plots points on 1st quadrant graph [ ] D-50 understands translations (slides) [ ] D-50 understands rotations (turns) [ ] D-50 understands reflections (flips) [ ] D-60 understands tesselations [ ] D-62 understands planes of symmetry [ ]

4 PATTERNS AND RELATIONS Patterns (March April) B-4 constructs and extend patterns [ ] B-4 describes how pattern grow [ ] B-4 develops chart to record pattern growth [ ] B-4 predict and justifies pattern extensions [ ] B-4 translates to a problem solving context [ ] Variables and Equations B-40 understands concepts of balancing objects [ ] B-40 uses pre-algebra equations to solve problems [ ] UNIVERSAL BACKWARD DESIGNING Stage 1 Identify Desired Results Grade 5 Patterns and Relations (5.PR.1 5.PR.2) Enduring Understanding Students will understand that Mathematics is the study of patterns and relationships, and by recognizing and exploring the inherent patterns in mathematics, they will see relationships, make predictions, and understand concepts. Real world situations can be represented by algebraic expressions and equations in order to simplify and solve problems. Essential Questions How can we determine pattern rules? How can we solve single variable, one-step equations? Key Knowledge and Skills Skills & Processes VERBS Students will be able to Determine pattern rules to continue subsequent patterns. Solve single-variable, one-step equations using the guess-and-check method and the isolatethe-variable method. Use problem solving to solve real world problems involving patterns. Concepts & Content - NOUNS Students will know -a pattern shows a predictable arrangement of things. There are different kinds of patterns. -A repeated pattern, (ABCABCABC ) -A core pattern is the basic root of a repeating pattern, (ABCABCABC) - patterns can be increasing or decreasing, (2,4,6,8 ) -A variable is a letter representing an unknown number, (N) -a co-efficient is the number in an expression, (2N) -An operation is the ways that numbers can be manipulated, (+, -, x.) -there is an order of operations that must be followed when there is more than one operation in an expression. (3 + 4 x 2). -BEDMAS is the acronym used to remember the order of operations. -an expression is a mixture of numbers and operations, (2 + 3) -an equation is a balanced math sentence,

5 (2 + 3 = 5) -a solution is the answer when solving for an unknown variable, (if 2 + N = 5, N = 3) -extrapolation is the pictorial continuation of a linear pattern (on a graph) Key Vocabulary pattern, increasing pattern, decreasing pattern, operation, term, unknown, variable, co-efficient, expression, equation, solution, extrapolate, order of operations, BEDMAS, balance Stage 2 Determine Acceptable Evidence What evidence will show that students understand? Performance Tasks and Projects Summative Assessment: A. Banquet table project Students will complete the project which will include: 1. Given a diagram of an increasing pattern (tables and chairs), draw the next two terms in the pattern, 2. Create a t-chart that includes x (tables) and y(chairs) numbers, 3. Determine the x pattern rule and y pattern rule, 4. Determine the pattern rule that changes x into y. 5. On a 1 st quadrant graph, graph the ordered pairs to create a line, 6. Extrapolate the lines to determine subsequent numbers in the pattern, 7. Use the pattern rule to find higher subsequent numbers in the pattern. B. Unit Test Part A: Continuing Patterns Part B: Translating Words and Numbers Part C: Isolating the Variable Part D: Working with Input/Output Charts Part E: Graphing the Data Part F: Problem Solving Other Evidence (quizzes, tests, prompts, observations, dialogues, work samples): Formative Assessment: Work samples, observations, interviews Given a repeated/increasing pattern, determine the pattern rule, (concretely, pictorially, symbolically) Given a pattern rule, continue the pattern, (concretely, pictorially, symbolically) Set up one step equations, solve with substitution using a t-chart (concretely, pictorially, symbolically) Given a question with multiple operations, solve using BEDMAS. Given a one-step equation, solve for the unknown variable, using the following strategies: o Guess and check, o Isolating the variable, Chart patterns on a 1 st quadrant graph, Extrapolate data using the graph, Use problem solving to solving pattern problems. Student Self-Assessment & Reflection Math journaling, reflecting on quizzes, tests

6 Stage 3 Learning Activities Text and Resources MathFocus 5 textbook, Mathletics program, teacher-made materials, alge-tiles, learning videos Comprehension Explicit Lessons (Whole Group/Shared Reading/Mini-Lesson) 1. Activate/acquire new vocabulary. (pattern, increasing pattern, decreasing pattern, operation, term, unknown, variable, co-efficient, expression, equation, solution, extrapolate) Activate: Ask students to list patterns we have in the classroom? Patterns in the real world? Acquire: Individually, students highlight known terms on a word-splash page of unit vocabulary. Secondly, students continue in a share/pair situation. Apply: Together, as a group, discuss prior knowledge of terms using Smartboard. Assess through observation/participation. 2. Using manipulatives and pictures, determine pattern rules for concrete and pictorial patterns. Attempt to continue patterns, both repeating and increasing/decreasing patterns. Activate: Ask students if they remember what patterns looked like in kindergarten? Show Smartboard page on simple pictorial pictures... Acquire: Work through patterns of repeating patterns on Smartboard, Apply: Students work on worksheet of continuing patterns. Assess through observation and correcting of worksheet. 3. Using numbers in a pattern, determine pattern rules (symbolically). Teach the bridging strategy. Activate: Show sample increasing/decreasing number patterns (2, 4, 6, 8...) and ask them to continue pattern. Acquire: Introduce the bridging strategy. Apply: Students work on sample questions in their notes. Assess through observation and coming up to Smartboard to answer questions. 4. Teach that there is an order of operations that must be followed in math. Activate: Invite students to solve x 2. Discuss why the answer is 11, not 14. Acquire: Teach students the order of operations using BEDMAS. Apply: Students demonstrate learning through practice in notes and sticky-note quiz. 5. Translate number expressions/equations into word sentences. (eg. 4N +1 means one more than four times an unknown number ) Activate: Invite students to list all words and symbols that mean adding, subtracting, multiplying and dividing. Compare results. Distribute pre-made hand-outs. Acquire: Model to students how to translate word sentences into math equations/expressions. Apply: Students demonstrate learning through practice in notes. 6. Teach the isolate the variable method. Activate: Invite students to solve for N in 3N + 2 = 17 and other algebraic equations. Acquire: Explain how their answers were done using guess and check. Teach the isolate the variable method. Apply: Students demonstrate learning through practice in notes and sticky-note quiz. 7. Create input-output charts for patterns. Teach substitution of variables. Activate: Using the Smartboard, show students the number factory (input/output) Acquire: Teach how input/output charts are used. Teach about substitution of variables. Apply: Students work on input/output chart assignments. Students demonstrate learning through practice in notes.

7 8. Graph ordered pairs from t-charts onto a coordinate plane (quadrant one). Activate: Using Smartboard, show a sample graph of a pattern. Acquire: Explain how any number pattern can be graphed, using x as input and y as output. Apply: Students work on graphing chart assignments. Students demonstrate learning through practice in notes. 9. Use problem solving to practice applying patterning. (eg. Banquet tables, toothpick patterns ) Activate: Invite students to solve the toothpick problem. Acquire: Teach how to use these algebraic solutions to solve problems. Apply: Students will complete complex problems. Assess a completed project. STATISTICS AND PROBABILITY (GRADE 5) (April May) Data Analysis C-4 develops questions to generate data [ ] C-4 distinguish between total and sample population [ ] C-4 predicts results of data [ ] C-4 uses variety of methods for data collections [ ] C-4 appreciates reasonableness of data [ ] C-4 creates classifications and ranges for data [ ] displays data using: C-4 frequency tables [ ] C-4 line plots [ ] C-4 broken-line graphs [ ] C-4 ensure clear representation of data (ie. titles...) [ ] C-4 makes conclusion about charted data [ ] Chance and Uncertainty C-16 describes events using terms of probability [ ] C-16 conducts probability experiments [ ] C-24 lists all possible outcomes of an experiment [ ]

Math 6 Long Range Plans Bill Willis. Strand: NUMBER Develop number sense. Textbook: Math Makes Sense 6

Math 6 Long Range Plans Bill Willis. Strand: NUMBER Develop number sense. Textbook: Math Makes Sense 6 Math 6 Long Range Plans 2012-2013 Bill Willis Rationale: Based upon the mathematics program of studies, our learning environment will value and respect the diversity of students experiences and ways of