GRADE 5-8 SPIRAL YEAR PLANS FOR MATH
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1 2008 Frontier School Division Gr of 24 Strand: Number GRADE 5-8 SPIRAL YEAR PLANS FOR MATH General Outcomes Term 1 Term 2 Term 3 General Outcome: Develop number sense. Place Value Represents and describes numbers in a variety of ways: concretely, pictorially, as a numeral, number word, expanded form. 5.N.1 Represent and describe whole numbers to to to to N.8 Describe and represent decimals concretely, pictorially, and symbolically. tenths hundredths thousandths 6.N.1 Demonstrate an understanding of place value for numbers greater than one million and less than one-thousandth. 0 to tenth, hundredth, thousandth and beyond less than thousandths Multiples, Factors, Composites, and Primes 6.N.3 Demonstrate an understanding of factors and multiples by determining multiples and factors of numbers less than 100, identifying prime and composite numbers, and solving problems involving factors or multiples. LCM/GCF to 50 identify prime and composite numbers LCM/GCF to 75 LCM/GCF to 100
2 2008 Frontier School Division Gr of 24 General Outcomes Term 1 Term 2 Term 3 Divisibility Rules 7.N.1 Determine and explain why a number is divisible by 2, 3, 4, 5, 6, 8, 9, or 10, and why a number cannot be divided by 0. rules for 2 s, 5 s, and 10 s rules for 3 s and 4 s. rules for 6 s, 8 s, and 9 s. Ratio 6.N.5 Demonstrates an understanding of ratio. concretely pictorially symbolically (not a specific outcome, but required for Grade 8) Grade 8 8.N.4 Demonstrate an understanding of ratio and rate. continue with above 2-part ratios 2 and 3-part ratios rates 8.N.5 Problem solving using rates, ratios and proportional reasoning. Square roots Grade 8 8.N.1 Demonstrate an understanding of perfect squares and square roots (limited to whole numbers). concretely, pictorially, symbolically perfect square roots non-perfect square roots
3 2008 Frontier School Division Gr of 24 General Outcomes Term 1 Term 2 Term 3 8.N.2 Determine the approximate square root of numbers that are not perfect squares (limited to whole numbers). Use benchmarks for determining approximate square roots. (when using technology, review rounding skills) Percent 6.N.6 Demonstrates an understanding of percent (limited to whole numbers). concretely, pictorially, symbolically percent to fractions and decimals 7.N.3 Solve problems involving percents from 1% to 100%. review percent as a decimal and fraction. problem solving involving finding a percent. Grade 8 8.N.3 Demonstrate and understanding of percents greater than or equal to 0%. percents greater than 100% percents between 0% and 1%
4 2008 Frontier School Division Gr of 24 General Outcome Term 1 Term 2 Term 3 Fractions TEACHER S NOTE: The three key ideas in developing fraction concepts are: 1. naming (represent and describe) 2. equivalence 3. comparing and ordering Use friendly fractions (i.e., 1/2, 1/3, 1/4, 1/5, 1/6, 1/8, 1/10, 1/12. No need to use 1/11 or 1/17). Use fraction pieces to count forwards and backwards and go past 1 whole. 5.N.7 Demonstrate an understanding of fractions by: creating sets of equivalent fractions comparing fractions concretely and pictorially with like denominators with unlike denominators 6.N.4 Relate improper fractions to mixed numbers. compare and order combinations of improper fractions and mixed numbers. Decimals TEACHER S NOTE: Use Base 10 blocks to show decimals. Relating decimals to fractions 5.N.9 Relate decimals to fractions. tenths, hundredths, thousandths 7.N.4 Demonstrate an understanding of the relationship between decimals and fractions. terminating decimals terminating and repeating decimals.
5 2008 Frontier School Division Gr of 24 General Outcome Term 1 Term 2 Term 3 Comparing and ordering 5.N.10 Compare and order decimals by using benchmarks, place value, and equivalent decimals. tenths hundredths thousandths Integers 6.N.7 Demonstrate an understanding of integers, concretely, pictorially, and symbolically. extends counting numbers to less than 0 identifies practical applications compares and orders integers 7.N.7 Compare and order fractions, decimals, and integers by using benchmarks, place value, and equivalent fraction and/or decimals, Compare and order fractions, decimals, and integers to thousandths.
6 2008 Frontier School Division Gr of 24 General Outcomes Term 1 Term 2 Term 3 TEACHER S NOTE: Math facts: Quick recall of math facts is critical for middle years students. The timed tests are ineffective if thinking strategies have not been taught. They only test, not teach, basic facts. Thinking strategies such as doubles, doubles +1, etc., need to be taught. Mastery of math facts is a prerequisite to doing mental computation of larger numbers. Operations: If students are struggling with doing the operations for whole numbers, decimals, fractions, or integers, it is important for them to use hands-on materials and then draw out what they did. Using manipulatives gives students a picture in their mind and makes it more meaningful. Once students understand how to do paper-and-pencil computation, move on to using a calculator. The only place where tedious calculations with paper and pencil are done today is in schools. Connections need to be made between: Using estimation to determine if the answer on a calculator is correct is also an essential - + and facts skill. - x and facts. Students should know how to use inverse operation to check answers, concretely, Twice as much time needs to be spent on subtraction and division pictorially, and symbolically. facts. The list of math fact strategies is in the spiral planning guide on page 27. Addition and Subtraction 5.N.11 Demonstrate an understanding of addition and subtraction of decimals. tenths hundredths thousandths 7.N.2 Demonstrate an understanding of the addition and subtraction of decimals to solve problems. 7.N.5 Demonstrate an understanding of adding and subtracting positive fractions and mixed numbers, with like and unlike denominators, concretely, pictorially, and symbolically. Adding and subtracting fractions with like denominators.. Adding and subtracting fractions with un-like denominators. Adding and subtracting mixed numbers Adding and subtracting fractions with un-like and like denominators.
7 2008 Frontier School Division Gr of 24 General Outcomes Term 1 Term 2 Term 3 7.N.6 Demonstrate an understanding of addition and subtraction of integers, concretely, pictorially and symbolically. Multiplication and Division For more than 1-digit divisors and 2-digit multipliers, use of technology is expected. 5.N.3 Determine multiplication facts and related division facts. Multiplication and Division facts to 81 5.N.5 Demonstrate an understanding of multiplication to solve problems. Review 2 digit x 1 digit and 3 digit x 1 digit 2 digit x 2 digit 5.N.6 Demonstrate an understanding of division with and without concrete materials, and interpret remainders to solve problems. Review 2 digit 1 digit 3 digit 1 digit with/without concrete materials
8 2008 Frontier School Division Gr of 24 General Outcome Term 1 Term 2 Term 3 6.N.8 Demonstrate an understanding of multiplication and division of decimals. Review whole number multiplication and division Multiply tenths, using single digit whole number multipliers. (4.5 x 3) Tenths and hundredths Thousandths Divide tenths, using single digit natural number divisors. (4.5 5) Tenths and hundredths Thousandths 6.N.9 Explain and apply the order of operations, excluding exponents (limited to whole numbers). Explain and apply order of operations. 7.N.2 Demonstrate an understanding of the multiplication and division of decimals to solve problems. Multiplication and division of decimals
9 2008 Frontier School Division Gr of 24 General Outcome Term 1 Term 2 Term 3 Grade 8 8.N.6 Demonstrate an understanding of: (concretely, pictorially and symbolically) multiplying and dividing positive fractions and mixed numbers. 8.N.7 Demonstrate an understanding of (concretely, pictorially and symbolically) multiply and divide integers. multiply and divide positive fractions, mixed numbers and integers. 8.N.8 Solve problems involving positive rational numbers. Estimation and Mental Math 5.N.2 Apply estimation strategies in problemsolving contexts. use strategy of front-end rounding use compensation strategy use compatible numbers strategy 5.N.4 Apply mental math strategies for multiplication. use a variety of strategies
10 2008 Frontier School Division Gr of 24 Strand: Patterns and Relations General Outcomes Term 1 Term 2 Term 3 General Outcome: Use patterns to describe the world and solve patterns. TEACHER S NOTE: - The purpose of the patterns strand is: 1. to develop an understanding that all mathematics is based on patterns 2. to develop a foundation for algebra. Patterns 5.PR.1 Determine the pattern rule to make predictions about subsequent elements. using concrete and pictorial patterns using symbolic (tables, charts) patterns write a mathematical expression to represent a pattern 6.PR.1 Demonstrate an understanding of the relationships within tables of values to solve problems. generates a table and mathematical expression for a given pattern find a missing term within, and predict the nth value from a given table of values 6.PR.2 Represent and describe patterns and relationships using graphs and tables. create a graph using information from a table of values create a table of values using information from a pattern, graph, or rule
11 2008 Frontier School Division Gr of 24 General Outcomes Term 1 Term 2 Term 3 7.PR1 Demonstrate an understanding of oral and written patterns and their corresponding relations. write the relation from a given oral or written pattern interprets a given graph/pattern and gives a context for the situation 7.PR2 Construct a table of values from a relation, graph the table of values, and analyze the graph to draw conclusions and solve problems. Using symbolic relations (ie. 2x +3), create a table of values and graph. Write a symbolic relationship for a given graph. Grade 8 8.PR.1 Graph and analyze two-variable linear relations. Create and graph, tables of values for a linear relations. Analyze the relationship between the variables. TEACHER S NOTE: Interpolate means to find an unknown value between points of data. Extrapolate means to make a prediction by extending a graph that shows a trend beyond the range of the data shown. No. of cubes Model No. How may cubes would you need for the 6 th model?
12 2008 Frontier School Division Gr of 24 General Outcomes Term 1 Term 2 Term 3 General Outcome: Represent algebraic expressions in multiple ways. Variables and Equations TEACHER S NOTE: A first-degree equation is an expression with no exponents. E.g., 4x PR.2 Solve problems involving single-variable (expressed as symbols or letters), one-step equations with whole-number coefficients, and whole-number solutions. Solve one-step equations Write an equation to solve a word problem. Create a problem to represent an equation 6.PR.4 (This outcome should be taught before 6.PR.3) Demonstrate and explain the meaning of preservation of equality, concretely, pictorially, and symbolically. Model concretely and pictorially. Symbolically (support with models if needed) 6.PR.3 Represent generalizations arising from number relationships using equations with letter variables. Teach in conjunction with 6.SS.3
13 2008 Frontier School Division Gr of 24 General Outcome Term 1 Term 2 Term 3 7.PR.3 Demonstrate an understanding of preservation of equality. Model concretely, pictorially, and symbolically. Apply in problem solving situations. 7.PR.4 Explain the difference between an expression and an equation. Similarities and differences between expressions and equations. 7.PR. 5 Evaluate an expression given the value of the variable(s). Substitute values into, and evaluate the expression. 7.PR.6 Model and solve problems that can be represented by one-step linear equations of the form x + a = b, concretely, pictorially, and symbolically, where a and b are integers. Solve one-step equations Write an equation to solve a word problem. Create a problem to represent an equation 7.PR.7 Model and solve problems that can be represented by linear equations of the form: ax + b + c ax = b x/a = b, a does not equal 0 concretely, pictorially, and symbolically, where a, b, and c are whole numbers. Solve equations involving addition, subtraction, and multiplication. Solve equations involving division.
14 2008 Frontier School Division Gr of 24 General Outcome Term 1 Term 2 Term 3 Grade 8 8.PR.2 Model and solve problems using linear equations of the form: ax = b x/a = b, a does not = 0 ax + b = c x/a + b = c, a does not equal 0 a(x + b) = c concretely, pictorially, and symbolically, where a, b, and c are integers. Solve two-step equations involving addition, subtraction, multiplication and division. Solve equations involving division and involving the distributive property. Write and solve problems using multi-step equations.
15 2008 Frontier School Division Gr of 24 Strand: Statistics and Probability General Outcome Term 1 Term 2 Term 3 TEACHER'S NOTE: Clarify for students that a line graph is used to show change over time. Eg., weather, daily attendance, number of people using the winter road each week. You cannot put birthday months on it because they do not change over time. (You get older but the month your birthday is in remains the same.) For each graph, students should: - know where the x- and y-axes are - label axes - create a descriptive title - use a legend (if applicable) Students should be able to interpret each graph and write several statements about what the graph shows. First-hand sources mean when you ask someone directly (e.g., What s your favorite flavor of ice cream? ) or conduct an observation or experiment yourself (e.g., How often does the spinner land on a 6? ). Second-hand sources mean not getting the data directly such as asking people what their mother s favorite flavor of ice cream is or collecting data from a book (e.g., life span of different animals). A sample is a number of people, objects, or events chosen from a given population to represent the entire group. (e.g., The Gr. 1s and 6s will be the sample we survey to find out whether we sell fruit or juice to all the students at recess.) The total population is a group of people (or objects, or events) about whom you are gathering information. (e.g., When the graph is about the favorite sport of Gr. 7s in Berens River, then they are the total population.) Data Analysis General Outcome: Collect, display, and analyze data to solve problems. 5.SP.1 Differentiate between first-hand and second-hand data. Distinguish between, and produce examples of, first-hand and second-hand data.
16 2008 Frontier School Division Gr of 24 General Outcome Term 1 Term 2 Term 3 5.SP.2 Construct and interpret double bar graphs to draw conclusions. Distinguish between a single bar graph and a double bar graph. Interpret a given double bar graph from real world examples. Constructs and interprets a double bar graph. 6.SP.1 Create, label, and interpret line graphs to draw conclusions. 6.SP.2 Select, justify, and use appropriate methods of collecting data, including questionnaires experiments databases electronic media Collect data using questionnaires and experiments. Collect data using databases and media. 6.SP.3 Graph collected data and analyze the graph to solve problems. Graph and interpret the information collected through the above activities. 7.SP.1 Demonstrate an understanding of central tendency and range by determining the measures of central tendency (mean, median, mode) and range. Determining the most appropriate measures of central tendency to report findings.
17 2008 Frontier School Division Gr of 24 General Outcome Term 1 Term 2 Term 3 7.SP.2 Determine the effect on the mean, median, and mode when an outlier is included in a data set. 7.SP.3 Construct, label, and interpret circle graphs to solve problems. Grade 8 8.SP.1 Critique ways in which data are presented.
18 2008 Frontier School Division Gr of 24 Chance and Uncertainty General Outcome: use experimental or theoretical probabilities to represent and solve problems involving uncertainty. 5.SP.3 Describe the likelihood of a single outcome occurring, using words such as Impossible Possible Certain Provide examples of and conducts single outcome experiments. 5.SP.4 Compare the likelihood of two possible outcomes occurring, using words such as Less likely Equally likely More likely Provide example of, and conducts experiments with two possible outcomes. 6.SP.4 Demonstrate an understanding of theoretical and experimental probability. Conducts probability experiments.
19 2008 Frontier School Division Gr of 24 General Outcomes Term 1 Term 2 Term 3 7.SP.4 Express probabilities as ratios, fractions, and percents. 7.SP.5 Identify the sample space (where the combined sample space has 36 or fewer elements) for a probability experiment involving two independent events. 7.SP.6 Conduct a probability experiment to compare the theoretical probability (determined using a tree diagram, table, or another graphic organizer) and experimental probability of two independent events. Grade 8 8.SP.2 Solve problems involving the probability of independent events.
20 2008 Frontier School Division Gr of 24 STRAND: Shape and Space General Outcome Term 1 Term 2 Term 3 Measurement General Outcome: Use direct or indirect measurement to solve problems. 5.SS.1 Design and construct different rectangles given either perimeter or area, or both (whole numbers), and draw conclusions. Construct different rectangles for a given perimeter. Construct different rectangles for a given area. Explore the relationship between greatest area and smallest area for a given perimeter. 5.SS.2 Demonstrate an understanding of measuring length (mm, cm,m). Explain the relationship between mm, cm, and m. Select and justify which unit to use for a given situation. 5.SS.3 Demonstrate an understanding of volume of rectangular prism. Explain the relationship between cm3 and m3. Select and justify which unit to use for a given situation. 5.SS.4 Demonstrate an understanding of capacity. Explain the relationship between ml and L. Select and justify which unit to use for a given situation.
21 2008 Frontier School Division Gr of 24 General Outcome Term 1 Term 2 Term 3 6.SS.1 Demonstrate an understanding of angles. Identify, classify, estimate, measure and create angles. 6.SS.2 Demonstrate that the sum of interior angles is 180 o in a triangle 360 o in a quadrilateral 6.SS.3 Develop and apply a formula for determining the perimeter of polygons area of rectangles volume of right rectangular prisms 7.SS.1 Demonstrate an understanding of circles. Demonstrate understanding of relationship between circumference, radius, diameter, and pi. Construct circles with and without a compass. Solve problems involving circles. 7.SS.2 Develop and apply a formula for determining area. Triangles, parallelograms, and circles.
22 2008 Frontier School Division Gr of 24 Grade 8 8.SS.1 Develop and apply the Pythagorean theorem to solve problems. Model and explain, concretely and pictorially. Solve for missing sides. Use Pythagorean theorem to determine if a triangle is a right triangle. 8.SS.3 Determine surface area to solve problems. Right rectangular prisms, right triangular prisms, and right cylinders. 8.SS.4 Develop and apply formulas for determining volume. Volume of right prisms and right cylinders. 3-D Objects and 2-D Shapes General Outcome: Describe the characteristics of 3-D objects and 2-D shapes, and analyze the relationships among them. 5.SS.5 Describe and provide examples of edges and faces of 3-D objects, and sides of 2-D shapes. Demonstrate an understanding of the terms parallel, intersecting, perpendicular, vertical and horizontal using 3-D objects and 2-D shapes. 5.SS.6 Identify and sort quadrilaterals according to their attributes. 6.SS.4 Construct and compare triangles in different orientations. Classify and compare triangles according to length of sides and measures of angles. Construct triangles based on their specific attributes and discuss congruency. 6.SS.5 Describe and compare the sides and angles of regular and irregular polygons.
23 2008 Frontier School Division Gr of 24 7.SS.3 Perform geometric constructions. Construct perpendicular lines and bisectors, parallel lines, and angle bisectors. Grade 8 8.SS.2 Draw and construct nets for 3-D objects. 8.SS.5 Draw and interpret top, front, and side views of 3-D objects composed of right rectangular prisms. Transformations General outcome: Describe and analyze position and motion of objects and shapes. 5.SS.7 Perform a single transformation (translation, rotation, or reflection) of a 2-D shape, and draw and describe the image. 5.SS.8 Identify a single transformation of 2-D shapes.
24 2008 Frontier School Division Gr of 24 6.SS.6 Perform a combination of transformations on a single 2-D shape, and draw and describe the image. 6.SS.7 Perform a combination of successive transformations of 2-D shapes to create a design, and identify and describe the transformations. 6.SS.8 Identify and plot points in the first quadrant of a Cartesian plane using whole-number ordered pairs. 6.SS.9 Perform and describe single transformations of a 2-D shape in the first quadrant of a Cartesian plane (limited to whole-number vertices). 7.SS.4 Identify and plot points in the four quadrants of a Cartesian plane using ordered pairs. 7.SS.5 Perform and describe transformations of a 2- D shape in all four quadrants of a Cartesian plane (limited to integral vertices). Grade 8 8.SS.6 Demonstrate an understanding of tessellations. (this would be ideal as an art project)
25 2008 Frontier School Division Gr of 24
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