Grade 7 math

Units

1. 1

   Proportional relationships

   6 lessons

   1. Unit rates with fractionsFind a unit rate from two fractional quantities and name what the rate is per 1 of.
   2. Deciding whether a relationship is proportionalDecide whether a table or graph is proportional and explain why.
   3. The constant of proportionality and y = kxFind the unit rate in a table or graph, write a proportional equation, and predict an output.
   4. What points on a proportional graph meanExplain what an ordinary point, the origin, and a one-unit point mean using both quantities and their units.
   5. Percent increase, decrease and percent errorFind percent change, a new amount after a percent change, and percent error using the correct base.
   6. Tax, tips, markups, discounts, commission and simple interestIdentify each percent’s base and calculate bills, sale prices, commission and simple interest.
2. 2

   Operations with negative numbers

   6 lessons

   1. Adding positive and negative numbersAdd positive and negative rational numbers and explain the result’s sign.
   2. Subtracting rational numbers and distanceCalculate signed changes and distances by adding opposites and regrouping additions.
   3. Multiplying positive and negative numbersMultiply signed rational numbers and explain the sign of each product.
   4. Dividing positive and negative numbersDivide signed numbers, read negative fractions, and explain why division by zero is undefined.
   5. Fractions as terminating or repeating decimalsConvert fractions to exact decimals, decide whether they end or repeat, and bar only the repeating digits.
   6. Solving problems with rational numbersWrite and solve signed-number expressions for real situations, then estimate to check the answer.
3. 3

   Expressions

   3 lessons

   1. Adding and subtracting linear expressionsSimplify sums and differences of linear expressions, then check a result.
   2. Expanding and factoring linear expressionsExpand products, fully factor linear sums, and check each result by reversing the process.
   3. Rewriting expressions to reveal meaningRewrite equivalent expressions and explain what each form shows about a situation.
4. 4

   Equations and inequalities

   4 lessons

   1. Multistep problems with rational numbers in any formSolve multistep problems by choosing useful number forms, planning operations, and checking with an estimate.
   2. Solving px + q = rSolve two-step equations by keeping both sides equal, then check answers in the original equation.
   3. Solving p(x + q) = rSolve grouped equations by dividing first or distributing, choose a convenient path, and check the answer.
   4. Solving and graphing px + q > r inequalitiesSolve two-step inequalities, graph their solution sets, and interpret answers in context.
5. 5

   Geometry

   6 lessons

   1. Scale drawingsFind real lengths and area from a scale drawing, then redraw the same room at a new scale.
   2. Drawing shapes and triangles from conditionsDraw triangles from given conditions and decide whether those conditions make one, many, or no triangles.
   3. Cross sections of prisms and pyramidsDraw and name the flat shape made by slicing a prism or pyramid.
   4. Circumference and area of circlesFind a circle’s circumference and area from its diameter or radius, and choose the right measurement for a context.
   5. Supplementary, complementary, vertical and adjacent anglesUse angle relationships to write equations and find unknown angle measures.
   6. Area, surface area and volume of composite figures and prismsFind composite area, right-prism volume and surface area from a net.
6. 6

   Statistics and probability

   6 lessons

   1. Random samples and inferences about populationsChoose a fair sample, estimate a population total, and explain why estimates vary.
   2. Comparing two populationsUse overlap, centres and spread to make cautious comparisons between populations.
   3. Probability on a 0-1 scale and sample spacesPlace chances on a 0 to 1 scale, list a sample space, and find the probability of an event as favourable outcomes over all equally likely outcomes, including the chance that it does not happen.
   4. Experimental vs theoretical probabilityFind a relative frequency from trials, explain why many trials get closer to the model, build a model from data when outcomes are not equally likely, and predict a count without calling it exact.
   5. Sample spaces for compound events: lists, tables and tree diagramsList the sample space of a two-stage or three-stage chance event with an organised list, a table or a tree, count it by multiplying the stages, and find the probability of a described event by marking the outcomes that match.
   6. Designing and running simulationsChoose a random device whose chances match a real process, say what one trial is and when it stops, run enough trials, and estimate a probability as successes over trials, comparing it with the exact value when we can list it.