How to learn Grade 7: Mathematics

Wyoming academic standards: Mathematics, Grade 7

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1. Statistics and Probability · Solve real-world and mathematical problems involving:

The Probability Scale: Understand probability as a measure on a scale from 0 (impossible) to 1 (certain); use the language of probability including likely, unlikely, certain, and impossible
Experimental probability: Record, describe, and analyse the frequency of outcomes from probability experiments to develop an understanding of relative frequency as an estimate of probability

Solving Linear Equations: Use algebraic methods to solve linear equations in one variable, including equations that require rearrangement, expanding brackets, and collecting terms on both sides; solve equations with rational number coefficients

Numbers on a number line: Understand inequalities as statements comparing expressions, represent solutions on a number line, and solve simple linear inequalities using the same inverse-operation methods as equations

Number Sets & Infinity: Appreciate the infinite nature of the sets of integers, real numbers, and rational numbers; position integers on a number line and distinguish between rational and irrational numbers
Sign Rules for Multiplication: Multiply and divide with positive and negative integers and rational numbers, understanding the rules for the sign of the product or quotient

Proportion Graphs: Represent proportional relationships using double number lines (two parallel number lines aligned at 0) and ratio tables; recognise that equivalent ratios generate straight lines through the origin when graphed
Ratio Notation and Relationships: Understand that a multiplicative relationship between two quantities can be expressed as a ratio; use ratio notation; simplify ratios
Proportion: Recognise and solve problems involving direct proportion (as one quantity increases, the other increases at a constant rate) and inverse proportion (as one increases, the other decreases), including graphical and algebraic representations

Proportional Reasoning Vocabulary: Know and use advanced vocabulary of multiplicative reasoning — direct proportion, inverse proportion, ratio, rate, unit rate, compound unit, scale factor — accurately in problem-solving contexts
Ratio Notation: Use ratio notation to describe the relationship between two or more quantities, simplify ratios to their simplest form, and convert between ratio and fraction representations

3-D shapes (age 11+): Use the properties of faces, surfaces, edges, and vertices of 3-D shapes (cubes, cuboids, prisms, cylinders, pyramids, cones, and spheres) to solve problems, including visualising cross-sections
Area of Triangles & Parallelograms: Calculate the area of parallelograms and triangles using formulae (A = b × h for parallelograms, A = ½ × b × h for triangles)

Properties of triangles and quadrilaterals: Derive and illustrate properties of triangles, quadrilaterals, and circles using appropriate language, including interior angles, diagonals, symmetry, and relationships between side lengths

Volume as additive: Recognise volume as additive; find volumes of composite solid figures made of two or more non-overlapping right rectangular prisms

Parts of a circle: Illustrate and name parts of circles, including radius, diameter, and circumference; know that the diameter is twice the radius
Circles: Circumference & Area: Calculate the circumference and area of circles using the formulae C = πd (or 2πr) and A = πr², and solve problems involving perimeters and areas of composite shapes that include circular parts