AK-DLM ESSENTIAL ELEMENTS AND COMPLEXITY EXAMPLES FOR EIGHTH Eighth Grade Mathematics Standards: The Number System AK Clusters AK-DLM Essential Elements Instructional Examples Know that are numbers that are not rational, and approximate them by rational numbers. EE8.NS.1. Subtract fractions with like denominators (halves, thirds, fourths, and tenths) with minuends less than or Students will: EE8.NS.1. Subtract fractions with like denominators (halves, thirds, fourths, and tenths) with minuends that may be greater than one. Ex. Subtract two fractions with like denominators with models or numbers. Ex. If I have 1 3/4 and I take 1/4 away, how many wholes and fourths are 8.NS.1. Know that numbers equal to one. that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers, show that the decimal expansion repeats eventually, and convert a decimal expansion repeats eventually into a rational number. left? Students will: EE8.NS.1. Subtract fractions with like denominators (halves, thirds, fourths, and tenths) with minuends less than or to one. Ex. Use fraction bars or fraction circles to add and match a numerical representation to the model so the answer is less than or equal to one. Ex. Given 3/4, take 1/4 away and tell or show how many fourths are left. Ex. 7/10, recognize that 3/10 are needed to make a whole. (Connect to money – 10 dimes = one whole dollar.) Students will: EE8.NS.1. Use models to subtract halves, thirds, and fourths. Ex. a whole divided into thirds, tell how many times they can take a third out of the whole. Ex. Presented a rectangle with 1/3 of the shaded, tell how many thirds are left. Students will: EE8.NS.1. Use models to identify the whole and find the missing pieces of a whole using halves. Ex. Presented an object with a piece missing and a whole object, identify
AK Grade-Level Clusters AK-DLM Essential Elements the whole. Instructional Examples Ex. Given 1/2 of a pizza, identify the missing part (concrete model or touch board). Ex. Given a whole with 1/2 shaded, identify the missing part. 8.NS.2. Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of ĞǆƉƌĞƐƐŝŽŶƐ ;Ğ͘Ő͕͘ ʋ2). For example, by truncating the ĚĞĐŝŵĂů ĞǆƉĂŶƐŝŽŶ ŽĨ яϮ͕ show ƚŚĂƚ яϮ ŝƐ ďĞƚǁĞĞŶ ϭ and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations. EE8.NS.2.a. Express a fraction with a denominator of 100 as a decimal. EE8.NS.2.b. Compare quantities represented as decimals in real-world examples to hundredths. Students will: EE8.NS.2. Represent different forms and values of decimal numbers to the hundreds place (decimal, fraction, hundreds grid, and money representation). Ex. Given a hundreds grid, shade in an approximation to a given decimal or fraction. Ex. Given a picture of a shaded hundreds grid, determine the decimal or fractional part. Ex. When coins representing 60 cents, write the decimal amount as $0.60. Students will: EE8.NS.2. Represent different forms and values of decimal numbers using fractions with numerators that are multiples of five and a denominator of 100. Ex. Given a hundreds grid with one fourth shaded-in, identify the correct decimal representation from choices 25/100, 10/100, or 100/100. Ex. When coins representing 50 cents, write the decimal value as $0.50. Students will: EE8.NS.2. Distinguish between a part represented by a decimal and a whole number without decimals.
AK Clusters AK-DLM Essential Elements Instructional Examples For example, estimate the population of the United States as 3 times 108 and the population of the world as 7 109, and determine that the world population is more than 20 larger. 8.EE.4. Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. Understand the connections between proportional relationships, EE8.EE.5-6. Graph a simple ratio by connecting the origin to a point Students will: EE8.EE.5-6. Graph a simple ratio using the x and y axis points when given the ratio in standard form (2:1) and expand on the ratio by two or more lines, and linear equations. representing the ratio in the y/x. 8.EE.5. Graph proportional points. Ex. Given a ratio 2:1 (there are two balloons for every child), graph the
Eighth Grade Mathematics Standards: Functions AK Grade-Level Clusters AK-DLM Essential Elements Instructional Examples Define, evaluate, and compare functions. 8.F.1. Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.19 8.F.2. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change. EE8.F.1-3. Given a function table containing at least 2 complete ordered pairs, identify a missing number that completes another ordered pair (limited to linear functions). Students will: EE8.F.1-3. Given a function table, identify the rule and express the rule for the missing variable (e.g., n times 2). Ex. Given a function table, identify the rule to find the missing number. 1 2 3 4 n 2 4 6 8 X Ex. Given a function table, identify the rule to find the missing number. 1 2 3 4 n 5 10 15 20 X Students will: EE8.F.1-3. Given a function table, identify the missing number. Ex. 1 2 3 4 2 4 X 8 Students will: EE8.F.1-3. Identify the relationship between two numbers. Ex. Given choices, tell the relationship between two numbers (e.g., How much more is five than three? Five is two more than three). Ex. Identify the relationship between two given numbers (e.g., If you double four, you have eight). Students will: EE8.F.1-3. Given a sequence, match the element of a sequence. 19 Function notation is not required in Grade 8.
graph or a table of values. 2 2+ = 5 3 3 + = 6 Ex. Given a table, determine increase or decrease. x y 1 4 2 5 3 6 Students will: EE8.F.4. Navigate, read, use, or apply a graph or table. Ex. Given a set of coordinates, locate on a graph. Ex. Given a location, identify coordinates. Ex. a basic map of town, identify two streets over. 8.F.5. Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or EE8.F.5. Describe how a graph represents a relationship between two quantities. Students will: EE8.F.4. Identify the different parts of a graph or a table. Ex. Recognize more or less. Ex. Recognize a graph. Ex. Recognize a table. Ex. Identify rows/columns. Students will: EE8.F.5. Describe how a represents a relationship between two quantities and use the graph to answer questions using that relationship. Ex. Given a chart showing the numbers of each colored disk in a bag, show how the graph relates color to number (e.g., point to the axis that tells you the number and to the axis that tells you the color and point to the bar
AK Grade-Level Clusters AK-DLM Essential Elements Instructional Examples them. 8.G.4. Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. EE8.G.4. Identify similar shapes with and without rotation. Students will: EE8.G.4. Determine if geometric shapes are similar with rotations or reflections. Ex. Sort shapes into groups of similar shapes with rotation and similar shapes with reflections. Ex. Matches combinations of similar shapes to each other (e.g., match similar shapes with rotations to each other and match similar shapes with reflections to each other). Students will: EE8.G.4. Identify similar shapes with and without rotation. Ex. Given a shape find its similar rotation. Ex. Compare shapes in the environment to find a similar shape that is rotated. Ex. When given a group of triangles, select two that are similar when one is rotated. Ex. Select the shape that is not similar from a group of three shapes. Students will: EE8.G.4. Identify similar geometric shapes. Ex. Sort regular polygons into groups of similar shapes. Ex. When given a shape, select a similar shape. Ex. Match the shape of one small square to the shape of a large square. Students will: EE8.G.4. Recognize geometric shapes. Ex. Same comparer – compare to shapes to see if they are the same.