Grade 8 math

Units

1. 1

   Rational and irrational numbers

   2 lessons

   1. Rational and irrational numbersClassify rational and irrational numbers, and convert repeating decimals to fractions.
   2. Approximating irrational numbers on the number lineBracket square roots, plot their locations, round them to tenths, and compare them with other numbers.
2. 2

   Exponents and roots

   3 lessons

   1. Properties of integer exponentsSimplify numerical expressions with integer exponent properties, then evaluate them.
   2. Square roots and cube rootsFind square and cube roots, solve equations involving them, and use roots to find dimensions.
   3. Scientific notationWrite, compare, and calculate with very large and very small quantities.
3. 3

   Transformations, congruence and similarity

   6 lessons

   1. Translations, reflections and rotationsMove a figure by a slide, flip or turn; describe each move and follow two moves in order.
   2. Congruence through rigid motionsShow that two figures are congruent by describing moves that map every vertex onto its match.
   3. Dilations and similarityDilate figures on a grid and show when rigid motions and a dilation map one figure onto another.
   4. Parallel lines cut by a transversalFind every angle where a transversal crosses two parallel lines, name the angle pairs, and use equal and supplementary pairs to solve for unknown angles.
   5. Triangle angle sum and exterior anglesExplain why the angles of a triangle add to 180°, use it to find missing angles, and use the exterior angle fact.
   6. Angle-angle similarityShow that two pairs of equal angles make triangles similar, and use the matching sides to find an unknown length.
4. 4

   Proportional relationships and slope

   3 lessons

   1. Graphing proportional relationships and comparing themFind and compare unit rates from proportional graphs, tables, equations, and words.
   2. Slope from similar triangles; y = mx and y = mx + bExplain why a line’s slope stays constant and write its equation from a graph or two points.
   3. Linear equations in two variables: intercepts, standard form, horizontal and vertical linesShow that the solutions of ax + by = c form a line, graph it from its intercepts, rewrite it as y = mx + b, and recognise horizontal and vertical lines.
5. 5

   Linear equations and systems

   5 lessons

   1. Solving linear equations with variables on both sidesSolve an equation with the variable on both sides by doing the same thing to both sides, and check the answer in the original equation.
   2. Equations with brackets, fractions and decimalsSolve equations that need distributing, a minus before a bracket, or clearing fractions and decimals, and check each answer.
   3. One, none or infinitely many solutionsSimplify a linear equation, read its ending as one, none or infinitely many solutions, and say why using lines.
   4. Systems of two linear equations: solutions as intersectionsFind a system’s solution on a graph, check it in both equations, and recognize all three line cases.
   5. Solving systems algebraically and by inspection; systems in contextModel a ticket sale, solve its system by substitution or elimination, and recognize when equations have no shared solution.
6. 6

   Functions

   3 lessons

   1. What a function isDecide whether arrows, tables, graphs, and descriptions show a function, and explain why.
   2. Comparing functions in different representationsCompare linear functions’ rates of change and initial values across tables, graphs, equations, and words.
   3. Linear and nonlinear functionsClassify functions from tables, graphs, and equations, and justify each choice using rate of change.
7. 7

   Linear functions and models

   2 lessons

   1. Constructing linear functions: rate of change and initial valueConstruct a linear model from a situation or two points; interpret its rate and initial value with units.
   2. Describing and sketching graphs qualitativelyDescribe a graph’s direction and rate, then sketch a graph from a story.
8. 8

   The Pythagorean theorem

   3 lessons

   1. The Pythagorean theorem and its converseUse square areas to explain the theorem and test whether a triangle has a right angle.
   2. Finding unknown sides in two and three dimensionsSketch right triangles and find unknown lengths in rectangles and boxes.
   3. Distance between points on the coordinate planeFind straight-line distances between points and use them to compare triangle sides.
9. 9

   Volume

   2 lessons

   1. Volume of cylinders and conesCalculate cylinder and cone volumes, then find a missing height or radius.
   2. Volume of spheresCalculate sphere, hemisphere, and joined-solid volumes; explain why doubling a sphere’s radius multiplies its volume by eight.
10. 10

    Patterns in data

    3 lessons

    1. Scatter plots and patterns of associationPlot paired measurements, describe their pattern and outliers, and distinguish association from proof of cause.
    2. Lines of fit and interpreting slope and interceptDraw and judge a line of fit, find its equation, interpret its numbers, and make a cautious prediction.
    3. Two-way tables and relative frequencyBuild a two-way table, compare group percentages, and identify an association without claiming cause.