Ontario Grade 8 Math

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B Number3 / 12 with a lesson

Scientific notationComing soonB1.1 · E2.13 × 10⁶ doesn't make you count zeros: the exponent just says how many places the digits slide.
Multiplying by 10, 100 and 1000Why isn't ×10 just "add a 0"?B2.3Multiplying by 10 moves every digit one place to the left; 'add a zero' is only a shortcut, and it breaks for decimals.
Square rootsRadicals Unpacked — The Radical LabB1.3 · B2.2√49 asks one question: what side length makes a square with area 49?
Irrational numbersComing soonB1.2 · C1.4√2 is a real length you can draw, yet no fraction lands exactly on it, so its decimals never stop or repeat.
PercentComing soonB1.4Percent means 'out of 100', so 150% is one and a half wholes and 0.5% is half of one hundredth.
Adding and subtracting integersComing soonB2.4A positive and a negative cancel to zero, so subtracting a negative is like taking away a debt: you end up higher.
Multiplying and dividing integersComing soonB2.7Multiplying by −1 turns you around on the number line; turn around twice and you face forward again, so negative × negative is positive.
Adding and subtracting fractionsComing soonB2.5You can only add pieces of the same size, so first cut both fractions into matching pieces.
Multiplying fractionsComing soonB2.61/2 of 2/3 is a rectangle inside a rectangle: the overlap is the answer.
Dividing fractionsComing soonB2.63 ÷ 1/4 asks how many quarters fit in 3; each whole holds 4, so the answer is 3 × 4.
Properties of multiplicationWhy does 7 × 13 equal 70 + 21?B2.1Turning, regrouping or splitting an array never changes how many squares it holds; that is why order, grouping and splitting don't change a product.
Proportional reasoningComing soonB2.1 · B2.8 · E1.3Equal ratios scale together: double one side and the other doubles too.

C Algebra5 / 8 with a lesson

Repeating and growing patternsDoes a pattern repeat or grow?C1.1A repeating pattern cycles through the same core; a growing pattern changes by a rule at every step.
One pattern, many representationsShapes, table, graph: one pattern?C1.2The same growing pattern can be drawn as shapes, written as a table of values, or plotted as points on a graph.
Linear patternsComing soonC1.1 · C1.2 · C1.3A linear pattern is a starting value plus the same step every time; the step is the rate of change.
VariablesWhat does the letter stand for?C2.2A letter or symbol holds the place of a number we don't know yet.
Combining like termsComing soonC2.13x + 2x = 5x for the same reason 3 apples + 2 apples = 5 apples, and x + 3 can't merge any more than apples and oranges.
Equations as balanceWhat does the = sign really mean?C2.3An equation is a balance: do the same thing to both sides and it stays level.
InequalitiesHow many answers can □ + 3 < 10 have?C2.4An inequality's answer is not one number but a whole stretch of the number line.
Code that analyses dataComing soonC3.1 · C3.2A loop lets code do to a thousand rows what you would do to one, so changing one line changes every result.

D Data1 / 6 with a lesson

Kinds of data and choosing a graphCan a graph lie about pets?D1.3Data is either measured and counted (quantitative) or sorted into categories (qualitative), and the graph has to fit the kind of data.
Two-variable dataComing soonD1.1 · D1.3Each dot on a scatter plot is one thing measured two ways; together the dots show whether the two measures move together.
CorrelationComing soonD1.5 · D1.6Two measures can rise together without one causing the other; a third thing may be pushing both.
Misleading graphsComing soonD1.6The same numbers can look huge or tiny depending on where the axis starts, so a graph can mislead without a single false number.
Compound eventsComing soonD2.1 · D2.2Each branch of a tree diagram splits every outcome before it, so probabilities along a path multiply.
Experimental vs theoretical probabilityComing soonD2.2Ten flips can look wild, but a thousand settle close to the theory: more trials, less surprise.

E Spatial Sense5 / 13 with a lesson

TessellationsComing soonE1.1Shapes tile a floor with no gaps exactly when the angles meeting at each corner add to 360°.
Views of 3D objectsComing soonE1.2A top view, a front view and a side view together pin down a 3D object; one view alone can hide things.
Scale factor and areaComing soonE1.3Stretch every length by k and the area grows by k × k, so doubling a map makes it four times bigger.
Translations and reflectionsFlip and slide: fit the shadowE1.4Sliding or flipping a shape changes where it is, never its size or shape.
DilationsComing soonE1.4Dilating from the origin multiplies every coordinate by the same number, so the shape keeps its angles but changes size.
Angles and parallel linesComing soonE2.2A line crossing two parallel lines makes the same set of angles twice, which is why alternate and corresponding angles match.
Angle sum of polygonsComing soonE2.2Any polygon with n sides cuts into n − 2 triangles, so its angles add to (n − 2) × 180°.
Metric units and prefixesZoom from a kilometre to a millimetreE2.1Kilo means a thousand and milli means a thousandth: the same base-ten trade as place value.
Circumference and πτ — one full turnE2.3π is how many diameters it takes to wrap around any circle, big or small: always a little more than 3.
Area of a circleWhy is a circle's area πr²?E2.3Cut a circle into thin wedges and line them up: they make a rectangle πr long and r tall, so the area is πr².
Volume of prisms and cylindersComing soonE2.3A prism is the same slice stacked up, so its volume is the area of the base times the height.
Surface areaComing soonE2.3Unfold a box flat and its surface area is just the area of that net.
Pythagorean theoremWhy does 3-4-5 work?E2.4Rearrange four copies of a right triangle inside one big square and the hole changes from c² into a² + b².

F Financial Literacy0 / 1 with a lesson

Compound interestComing soonF1.4Interest earns its own interest, so the money doesn't grow in a straight line: it curves upward.

Practised inside lessons, not separate pages

These expectations are about speed and fluency with an idea above. They show up as practice in that idea's lesson.

B2.1 Use properties, order of operations and links between operations to solve multi-step problems with rational numbers, ratios, rates and percents.
B2.2 Know common square numbers and their square roots.
C1.3 Use pattern rules to extend patterns, predict, find missing terms, and solve for unknowns in linear patterns.
C2.2 Evaluate algebraic expressions with rational numbers.
C3.2 Read and change existing data-analysis code, and describe how the changes affect results and efficiency.

Not covered here

These are projects, process skills or everyday money knowledge. They don't have a single "why" to take apart, so we leave them to the classroom.

C4.1 Apply the mathematical modelling process to real-life situations.
D1.2 Collect continuous two-variable data and organize it in tables of values.
D1.4 Create an infographic that tells a data-driven story.
F1.1 Weigh payment methods when dealing with several currencies and exchange rates.
F1.2 Make a financial plan for a long-term goal, including income, expenses and taxes.
F1.3 Keep a budget balanced and track income and spending.
F1.5 Compare ways to get more value for money, such as sales and loyalty programs.
F1.6 Compare credit card interest rates, fees and rewards to find the best option.