Curriculum Overview
In Pre-Algebra, math instructional time should focus on four critical areas and five standards:
STANDARD 1 – THE NUMBER SYSTEM
Students develop a unified understanding of numbers, recognizing fractions, decimals (that have a finite or a repeating decimal representation) and percents as representations of rational numbers. Students extend addition, subtraction, multiplication and division to all rational numbers, maintaining the properties of operations and the relationships between addition and subtraction, multiplication and division. By applying these properties and by viewing negative numbers in terms of everyday contexts (i.e. amounts owed, temperatures below zero, etc.), students explain and interpret the rules for adding subtracting, multiplying and dividing with negative numbers. The arithmetic of rational numbers is used as students formulate expressions and equations to solve problems. Students continue to explore numbers and learn there are numbers that are not rational, and evaluate their approximate value using rational number properties.
STANDARD 2 – RATIOS AND PROPORTIONAL RELATIONSHIP
Students extend their understanding of ratios and develop an understanding of proportionality to solve a wide variety of percent problems (i.e. discounts, interest, taxes, tips and percent of increase or decrease). Students solve problems about scale drawings by relating corresponding lengths between the objects or by using the fact that relationships of lengths within an object are preserved in similar objects. Students graph proportional relationships and understand the unit rate informally as a measure of the steepness of the related line called slope. They distinguish proportional relationships.
STANDARD 3 – EXPRESSION AND EQUATIONS
Students continue their understanding of the use of variables in mathematical expressions that were introduced in Grade 6. They continue to write expressions and equations and continue to use properties of operations to generate equivalent expressions. Students work with radicals and integer exponents and understand the connections between proportional relationships, lines, and linear equations. They continue their study to analyze and solve linear equations and pairs of simultaneous linear equations. Students learn to solve multi-step, real-life and mathematical problems with positive and negative rational numbers in any form (whole numbers, fractions, decimals etc.) becoming strategic problem solvers. Students also learn to use variables to represent quantities in a real-world or mathematical problem and construct simple equations and inequalities to solve problems by reasoning about the quantities.
STANDARD 4 – GEOMETRY
Students expand their knowledge from Grade 6, solving problems involving the area and circumference of a circle and the surface area of three-dimensional objects. They reason about relationships among two-dimensional figures using scale drawings and informal geometric constructions and gain familiarity with the relationships between angles formed by intersecting lines. They continue to study two-dimensional figures understanding congruence and similarity using physical models, transparencies, or geometry software. Students work with three-dimensional figures, relating them to two-dimensional figures by examining cross-sections. They solve real-world and mathematical problems involving area, surface areas and volume of two- and three-dimensional objects (composed of triangles, quadrilaterals, polygons, cubes, right prisms, cylinders, cones, and spheres).
STANDARD 5 – STATISTICS AND PROBABILITY
Students build on their previous work with single data distributions to compare two data distributions and address questions about differences between populations. Students understand statistics can be used to gain information about a population by examining a sample population. Students also understand they may use data from a random sample to draw inferences about a population with an unknown characteristic of interest. They realize and understand how to draw informal comparative inferences about a population with an unknown characteristic of interest. They realize and understand how to draw informal comparative inferences about two populations. Students investigate chance processes while developing, using and evaluating probability models.
- Developing an understanding of and applying proportional relationships.
- Developing an understanding of operations with rational numbers and working with expressions and linear equations;
- Solving problems involving scale drawings and informal geometric constructions as well as working with two- and three-dimensional shapes to solve problems involving area, surface area and volume;
- Drawing inferences about populations based on samples.
STANDARD 1 – THE NUMBER SYSTEM
Students develop a unified understanding of numbers, recognizing fractions, decimals (that have a finite or a repeating decimal representation) and percents as representations of rational numbers. Students extend addition, subtraction, multiplication and division to all rational numbers, maintaining the properties of operations and the relationships between addition and subtraction, multiplication and division. By applying these properties and by viewing negative numbers in terms of everyday contexts (i.e. amounts owed, temperatures below zero, etc.), students explain and interpret the rules for adding subtracting, multiplying and dividing with negative numbers. The arithmetic of rational numbers is used as students formulate expressions and equations to solve problems. Students continue to explore numbers and learn there are numbers that are not rational, and evaluate their approximate value using rational number properties.
STANDARD 2 – RATIOS AND PROPORTIONAL RELATIONSHIP
Students extend their understanding of ratios and develop an understanding of proportionality to solve a wide variety of percent problems (i.e. discounts, interest, taxes, tips and percent of increase or decrease). Students solve problems about scale drawings by relating corresponding lengths between the objects or by using the fact that relationships of lengths within an object are preserved in similar objects. Students graph proportional relationships and understand the unit rate informally as a measure of the steepness of the related line called slope. They distinguish proportional relationships.
STANDARD 3 – EXPRESSION AND EQUATIONS
Students continue their understanding of the use of variables in mathematical expressions that were introduced in Grade 6. They continue to write expressions and equations and continue to use properties of operations to generate equivalent expressions. Students work with radicals and integer exponents and understand the connections between proportional relationships, lines, and linear equations. They continue their study to analyze and solve linear equations and pairs of simultaneous linear equations. Students learn to solve multi-step, real-life and mathematical problems with positive and negative rational numbers in any form (whole numbers, fractions, decimals etc.) becoming strategic problem solvers. Students also learn to use variables to represent quantities in a real-world or mathematical problem and construct simple equations and inequalities to solve problems by reasoning about the quantities.
STANDARD 4 – GEOMETRY
Students expand their knowledge from Grade 6, solving problems involving the area and circumference of a circle and the surface area of three-dimensional objects. They reason about relationships among two-dimensional figures using scale drawings and informal geometric constructions and gain familiarity with the relationships between angles formed by intersecting lines. They continue to study two-dimensional figures understanding congruence and similarity using physical models, transparencies, or geometry software. Students work with three-dimensional figures, relating them to two-dimensional figures by examining cross-sections. They solve real-world and mathematical problems involving area, surface areas and volume of two- and three-dimensional objects (composed of triangles, quadrilaterals, polygons, cubes, right prisms, cylinders, cones, and spheres).
STANDARD 5 – STATISTICS AND PROBABILITY
Students build on their previous work with single data distributions to compare two data distributions and address questions about differences between populations. Students understand statistics can be used to gain information about a population by examining a sample population. Students also understand they may use data from a random sample to draw inferences about a population with an unknown characteristic of interest. They realize and understand how to draw informal comparative inferences about a population with an unknown characteristic of interest. They realize and understand how to draw informal comparative inferences about two populations. Students investigate chance processes while developing, using and evaluating probability models.
Long Term Plans
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Notes Pertaining to Current Unit of Study
l10-1_squares_and_square_roots.pdf | |
File Size: | 270 kb |
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l10-1_squares_and_square_roots.pdf | |
File Size: | 291 kb |
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Blank Coordinate Grids
4_blank_coordinate_grids.pdf | |
File Size: | 38 kb |
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Fraction, Decimal, Percent Equivalents Chart
fraction_decimal_percent_chart.pdf | |
File Size: | 355 kb |
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