Distinctive Math Sixth Grade

Transcription

1 Distinctive Math Sixth Grade Block 1 Aug/Sept *Solve word problems involving the division of fractions by fractions using models *Solve word problems involving the division of fractions by fractions using equations *Divide multiple- digit whole numbers by multi- digit whole numbers, with remainders expressed as fractions * Add decimals and decimals * Subtract decimals from decimals * Multiply decimals by decimals * Divide decimals by decimals * Find the GCF of two whole numbers, each less than 100 * Find the LCM of two whole numbers, each less than 12 * Express the sum of two whole numbers, each with a common factor and each less than 100, as the product of that common factor and a sum of two whole numbers Block 2 October * Demonstrate understanding of the nature integers positive numbers and their opposites, or additive inverses * Use horizontal and vertical number lines to express and identify integers Apply integers to real- world situations * Demonstrate understanding of the nature integers positive numbers and their opposites, or additive inverses * Use horizontal and vertical number lines to express and identify integers * Plot and analyze coordinates in which either the x- coordinate or y- coordinate or the companion ordered pair is the opposite, or additive inverse * Plot and identify integers and other rational numbers (whole numbers, fractions, mixed numbers, and decimals) on horizontal and vertical number lines * Plot coordinates in all quadrants of the Cartesian plane * Name coordinates that are plotted in all quadrant of the Cartesian plane * Plot integers and other rational numbers on a number line * Use symbols to compare and order the position and size of rational numbers * Create real- world scenarios for comparisons of rational numbers * Demonstrate understanding of the absolute value as a number s distance from zero * Compute the absolute value of a positive or negative rational number * Create real- world scenarios for absolute value problems * Know that absolute values do not change how negative a rational number is in real world situations Block 3 November/December * Know the symbols (: or / or ) for ratio * Write number comparisons as ratios * Create and interpret real- world scenarios for ratios * Know the meaning of unit rates * Compute unit rates for any ratio of rational numbers (a:b, b 0) * Create and interpret real- world scenarios for unit rates * Compute and create equivalent ratios by multiplying all terms in the ratio by the same factor * Display equivalent factors in a table * Solve for miss values in an equivalent ratio table

2 * Plot pairs of ratios within the Cartesian plane * Use the concept of unit rates to solve for the price of one unit * Use the concept of unit rates to find a rate, or constant speed * Use the concept of unit rates to solve world problems * Know that percents represent a quantity out of 100, or a numerator of a fraction with a denominator of 100 Solve for the whole given the percent and the part, given the proportion * Use ratios and proportional reasoning to convert measurements, such as 1ft : 12in = 4ft : Xin Block 4 January * Write expressions that involve all operations, parenthesis, and exponents * Evaluate expressions that involve all operations, parenthesis, and exponents * Write expressions that involve all operations, parenthesis, and exponents, and that include variables * Translate expressions into words, mathematical vocabulary * Evaluate expressions that involve all operations, parenthesis, and exponents, and that include variables, substituting values for variables * Evaluate expressions using order of operations, even when parentheses are absent * Evaluate expressions that represent real world problems * Evaluate expressions that represent mathematical formulas Block 5 February * Simplify expressions properties of mathematics * Identify when expressions are equivalent, with one expression representing a simplified version on another expression Block 6 March * Solve equations using guess- and- check to identify which value or values make the number sentence true * Write equations with variables that represent real world problems * Write equations with variables that represent mathematical problems * Write one- step addition equations with non- negative rational terms * Solve one- step addition equations with non- negative rational terms * Write one- step multiplication equations with non- negative rational terms * Solve one- step multiplication equations with non- negative rational terms * Write simple inequalities (e.g., x<9 or x>9) that represent real world problems * Plot solutions to inequalities on number lines, recognizing that inequalities have an infinite number of solutions * Write linear equations using two variables that represent real world problems * Represent linear equations in two variables, one independent and one dependent, in tables and as graphs in the Cartesian plane * Analyze linear equations in two variables, one independent and one dependent, in tables and as graphs in the Cartesian plane Block 7 April * Calculate the area of polygons, including triangles and quadrilaterals, by combining separate shapes in real world problems * Calculate the area of polygons, including triangles and quadrilaterals, by separating composite shapes in real world problems * Represent and compute the volume rectangular prism with fractional lengths by counting the number of unit cubes that fit within * Calculate the volume of a rectangular prism with fractional lengths by multiplying the three edge lengths

3 * Calculate the volume of a rectangular prism with fractional lengths by multiplying the area of the prism s base by the prism s height * Compare the three methods of finding volumes to confirm equivalence * Plot polygons in the Cartesian place given the coordinates of vertices * Use absolute values to find the distance between coordinates * Solve real world and mathematics problems by plotting polygons in the Cartesian plane * Draw nets that consist of rectangles and triangles to represent solids * Find the area of nets to represent the surfaces areas of solids * Solve real world and mathematics problems involving the surface area of solids Block 8 May/June * Write appropriate statistical questions * Distinguish appropriate from inappropriate statistical questions * Represent and interpret the center of shape of sets of data * Distinguish measures of center (mean, median) from measures of variation (range, interquartile range) * Plot data on a number line * Plot data on a line plot * Plot data on a histogram * Plot data within a box- and- whisker plot * Record and report the number of data points or observations in a set * Describe the variable or question under study * Describe how the variable or question was measured * Describe the units used to measure the variable or question * Compute and record measures of center * Compute and record measures of variability * Describe the meaning of measures of center and variability * Describe why certain measures of center and variability were chosen to represent a set of data Resources: Khan Academy provides teaching videos on a huge range of mathematical skills This is a website of skills that are based on common core. This is an interactive website that has all sorts of games, helps, drills, etc All students have a login and password for this website. It is an interactive website that allows students to practice various skills. Students will receive assignments that require them to successfully complete a certain number of exercises. This website has various worksheets that are focused on leveled skills. This website has many printable drills for varied levels of skills. Please work with your students on their multiplication/division facts! Please check Powerschool on a regular basis! Parent/Teacher conferences will be held on Wednesday, Nov. 6 (2-4pm) and Thursday, Nov. 7 (1-7pm) addresses: Jeff Hirz jhirz@distinctiveschools.org Jamie Funkhouser jfunkhouser@distinctiveschools.org Carey Holst cholst@distinctiveschools.org Kate Larsen klarsen@distinctiveschools.org

4 Distinctive Math Seventh Grade Block 1 August/September * Create scenarios that include positives numbers and their opposites or additive inverses * Add integers * Add rational numbers, including sums in which addends are negative * Use number lines to visualize the addition of integers and negative rational numbers * Create real world scenarios involving the addition of integers and negative rational numbers * Subtract integers * Subtract rational numbers, including sums in which subtrahends and minuends are negative * Use number lines to visualize the subtraction of integers and negative rational numbers * Create real world scenarios involving the subtraction of integers and negative rational numbers * Add rational numbers * Subtract rational numbers Block 2 October * Know and apply the rules for multiplying signed rational numbers * Multiply signed rational numbers * Create real world scenarios involving the multiplication of signed rational numbers * Know and apply the rules for dividing signed rational numbers * Divide signed rational numbers * Create real world scenarios involving the division of signed rational numbers * Multiply rational numbers * Divide rational numbers * Divide to convert rational numbers (fractions) to decimals * Know that decimals will terminate or repeat * Convert from mixed numbers to improper fractions * Add rational numbers * Subtract rational numbers * Multiply rational numbers * Divide rational numbers Block 3 November/December * Compute unit rates given fractional terms, based on real world scenarios * Prove that two terms are proportional by cross- multiplying (a short- cut for finding a common denominator) * Prove that that two terms are proportional by creating a table of terms * Prove that that two terms are proportional by plotting in the Cartesian plane * Calculate and explain the factor by which term are multiplied (called the constant of proportionality or unit rate) in proportional relationships through: Tables Graphs (the slope) Equations (m) Diagrams Written descriptions * Write equations that represent proportional relationships Interpret the meaning of coordinates in graphs that represent proportional relationships * Use proportional reasoning to solve problems involving:

5 Simple interest - I=p r t Taxes, markups, tips, gratuities, commissions, and fees Discounts Percent increase or decrease Percent error Please see attached map for formulas * Simplify expressions by combining like terms * Expand expressions by factoring * Simplify and expand expressions to clarify the meaning of real world problems * Convert between decimals, fractions, and percents to efficiently solve real world problems * Compare estimates with exact calculations Block 4 - January * Write and solve equations representing real world problems in the form px + q = r, both arithmetically and algebraically * Analyze both arithmetic and algebraic solutions and compare the required steps * Write and solve equations representing real world problems in the form p(x + q) = r, both arithmetically and algebraically * Analyze both arithmetic and algebraic solutions and compare the required steps * Write, solve, and graph (on a number line) inequalities representing real world problems in the form px + q > r Block 5 - February * Calculate actual lengths and areas from a scale drawing given the scale factor * Produce a scale drawing from a separate scale drawing, given a different scale factor * Construct shapes with given attributes by hand * Construct shapes with given attributes using a ruler and protractor * Construct shapes with given attributes using technology * Draw and describe 2D shapes that result when a 3D shape is sliced * Solve for the area of a circle using the proper formula * Solve for the circumference of a circle using the proper formula * Compare and analyze the formulas for finding the area and circumference of a circle Block 6 March * Write and solve equations for missing angles given the attributes of supplementary angles * Write and solve equations for missing angles given the attributes of complementary angles * Write and solve equations for missing angles given the attributes of vertical angles * Write and solve equations for missing angles given the attributes of adjacent angles * Find the area of polygons that may include triangles and quadrilaterals * Find the area of composite polygons that may include triangles and quadrilaterals * Find the volume of right prisms * Find the volume of composites of right prisms * Find the surface area of right prisms * Find the surface area of composites of right prisms Block 7 April * Distinguish valid from invalid samples of a population * Conduct multiple random samples to estimate a given event * Compare the measures of center and variability between samples * Infer about a broader population based on samples

6 * Compare the means and distributions between two samples that measure the same variable * Compare the means and distributions between two samples that measure the same variable to infer about the broader populations Block 8 May/June * Represent the chance (or probability) of an event occurring using a number between 0 and 1 * Know that probabilities near 0 indicate that an event is unlikely to occur * Know that probabilities near ½ indicate that an even is neither unlikely nor likely to occur * Know that probabilities near 1 indicate that an event is likely to occur * Calculate the probabilities of a simple event by conducting numerous experiments * Predict experimental outcomes based on theoretical probabilities * Compare theoretical and experimental probabilities * Calculate the theoretical probability of a simple event occurring * Calculate the probabilities of a simple event by conducting numerous experiments * Predict experimental outcomes based on theoretical probabilities * Compare theoretical and experimental probabilities * Know that the probabilities of compound events are also represented using numbers between 0 and 1 * Use lists, tables, and tree diagrams to represent all the outcomes of compound events * Use lists, tables, and tree diagrams to calculate the probabilities of compound events * Create scenarios that test the theoretical probabilities of compound events * Simulate the actual scenarios that calculate the experimental probabilities of compound events * Compare theoretical and experimental probabilities Resources: Khan Academy provides teaching videos on a huge range of mathematical skills This is a website of skills that are based on common core. This is an interactive website that has all sorts of games, helps, drills, etc All students have a login and password for this website. It is an interactive website that allows students to practice various skills. Students will receive assignments that require them to successfully complete a certain number of exercises. This website has various worksheets that are focused on leveled skills. This website has many printable drills for varied levels of skills. Please work with your students on their multiplication/division facts! Please check Powerschool on a regular basis! Parent/Teacher conferences will be held on Wednesday, Nov. 6 (2-4pm) and Thursday, Nov. 7 (1-7pm) addresses: Jeff Hirz jhirz@distinctiveschools.org Jamie Funkhouser jfunkhouser@distinctiveschools.org Carey Holst cholst@distinctiveschools.org Kate Larsen klarsen@distinctiveschools.org

7 Distinctive Math Eighth Grade Block 1 August/September * Evaluate expressions involving integer exponents * Apply rules for combining exponents when terms with common bases are multiplied or divided * Solve equations in which a number is squared or cubed * Find the square roots of perfect squares * Find the cube roots of perfect cubes * Identify irrational numbers as the roots of numbers that are not perfect * Convert from the standard form of very large numbers to scientific notation * Convert from the standard form of very small numbers to scientific notation * Determine how many times one number expressed in scientific notation is than another * Perform operations with number written in scientific notation *Determine when the use of scientific notation is appropriate *Convert from scientific notation to standard form Block 2 - October * Plot proportional relationships in the Cartesian plane * Recognize the line s slope as the unit rate * Compare and interpret graphs of proportional relationships with equations of proportional relationships * Prove that the slope of a line is constant between any two points using similar triangles * Derive the equation for a line through the origin, y = mx * Derive the equation for any line, y = mx + b Block 3 November/December * Write and solve linear equations with one solution * Write and solve linear equations with no solutions * Write and solve linear equations with an infinite number of solutions * Solve linear equations in one variable with rational number coefficients, when solutions require expanding terms using the distributive property and the combining of like terms * Know that solutions to systems of linear equations is represented graphically by the point of intersection of two lines * Know that the intersection of two lines is the only coordinate that represents a solution to both equations * Solve systems of linear equations algebraically, by substitution or elimination * Identify upon inspection the solution to a simple system of linear equations * Solve systems of linear equations that represent mathematical problems graphically * Solve systems of linear equations that represent real- world problems graphically Block 4 - January * Identify functions by examining input- output charts in which each input has only one output. * Identify functions by examining graphs horizontal lines are functions; vertical lines are not functions * Compared the properties of functions, such as slope or x- intercept or y- intercept, that are represented differently. Functions may be represented algebraically, graphically, in table or input- output charts, through verbal descriptions * Recognize the equation, y = mx + b, as the formula for a straight line * Identify equations that will not result in straight lines

8 * Write the equations for lines given the rate of change (or slope), m and a coordinate: where * Write the equations for lines given two coordinates: where * Identify the rate of change (or slope, m) and initial value (y- intercept or given coordinate) when given the written description, graph, or input- output chart * Verbally, or in writing, describe the attributes of a function * Sketch the graph of a function given a verbal or written description Block 5 - February * Demonstrate that every fraction (or rational number) will result in a terminating or repeating decimal * Contrast this attribute of rational numbers with the lack of this attribute in irrational numbers * Approximate the values of irrational numbers * Plot irrational numbers on a number line, locating irrational numbers between two whole numbers * Demonstrate instances when the Pythagorean Theorem applies to triangles * Demonstrate instances when the Pythagorean Theorem DOES NOT applies to triangles * Find the unknown sides of right triangles using the Pythagorean Theorem in 2D and 3D real world and mathematical problems * Use the Pythagorean Theorem to find the distance between two points in the Cartesian plane Block 6 - March * Solve for the volume of cones in real world and mathematical problems * Solve for the volume of cylinders in real world and mathematical problems * Solve for the volume of spheres in real world and mathematical problems * Informally prove that sum of the angles of triangles in 180 * Informally prove that the sum of the interior and exterior angles of triangles is 180 * Informally prove that the equivalent and supplementary natures of angles created when parallel lines are cut by a transversal * Informally prove the angle- angle criterion for the similarity of triangles Block 7 - April * Rotate lines and line segments * Reflect lines and line segments * Translate lines and line segments * Rotate angles * Reflect angles * Translate angles * Rotate parallel lines * Reflect parallel lines * Translate parallel lines * Prove the two 2D figures are congruent by describing how the first figure can be rotated, reflected, and/or translated to match the second figure * Demonstrate and plot the rotation of figures in the Cartesian plane * Demonstrate and plot the translation of figures in the Cartesian plane * Demonstrate and plot the reflection of figures in the Cartesian plane * Demonstrate and plot the dilation of figures in the Cartesian plane * Prove the two 2D figures are similar by describing how the first figure can be rotated, reflected, and/or translated AND dilated to match the second figure

9 Block 8 May/June * Make scatter plots based on data provided in two numerical variables * Analyze scatter plots, identifying whether clustering or outliers exist, whether plots are linear or nonlinear, and whether relationships are positive or negative * Draw a line- of- best- fit through a scatter plot and communicate whether the line- of- best- fit is strong or weak * Identify and analyze the slope and y- intercept of a line- of- best- fit * Analyze relationships between bivariate (binary or yes- no ) data in a table Resources: Khan Academy provides teaching videos on a huge range of mathematical skills This is a website of skills that are based on common core. This is an interactive website that has all sorts of games, helps, drills, etc All students have a login and password for this website. It is an interactive website that allows students to practice various skills. Students will receive assignments that require them to successfully complete a certain number of exercises. This website has various worksheets that are focused on leveled skills. This website has many printable drills for varied levels of skills. Please work with your students on their multiplication/division facts! Please check Powerschool on a regular basis! Parent/Teacher conferences will be held on Wednesday, Nov. 6 (2-4pm) and Thursday, Nov. 7 (1-7pm) addresses: Jeff Hirz jhirz@distinctiveschools.org Jamie Funkhouser jfunkhouser@distinctiveschools.org Carey Holst cholst@distinctiveschools.org Kate Larsen klarsen@distinctiveschools.org