How to learn Grade 7: Mathematics

Missouri academic standards: Mathematics, Grade 7

0 of 16 concepts ready to learn · Markdown, for your AI

1. Data, Statistics and Probability · Develop, use and evaluate probability models.

1. 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
2. The 0-to-1 Probability Scale: Understand probability as a measure expressed as a number between 0 (impossible) and 1 (certain); place events on the probability scale; express probabilities as fractions, decimals, and percentages
3. 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

2. Geometry and Measurement · Apply and extend previous understanding of angle measure, area and volume.

1. Angles in triangles (age 11+): Derive and apply formulae for the area of triangles, parallelograms, and trapezia, and for the volume of cuboids and other prisms (including cylinders), connecting each formula to its geometric reasoning
2. 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

3. Geometry and Measurement · Draw and describe geometric figures and describe the relationships between them.

1. Parts of a circle: Illustrate and name parts of circles, including radius, diameter, and circumference; know that the diameter is twice the radius
2. 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
3. Real-World Mathematical Modelling: Model real-world problems involving ratio, scale, volume, unit conversion, and proportional reasoning with appropriate tools, diagrams, or equations

4. Expressions, Equations and Inequalities · Solve problems using numerical and algebraic expressions and equations.

1. 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
2. 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
3. Expressions & Equations Vocabulary: Understand and use the concepts and vocabulary of expressions, equations, inequalities, terms, and factors; distinguish between an expression (no equals sign), an equation (equals sign), and an inequality (inequality sign)

5. Number Sense and Operations · Apply and extend previous understandings of operations to add, subtract, multiply and divide rational numbers.

1. Using inverse operations: Recognise and use relationships between operations including inverse operations; use these relationships to check answers and simplify calculations
2. Positive and Negative Numbers: Understand positive and negative numbers as describing quantities with opposite directions or values; use them in context such as temperature, floors in a building, and bank balances

6. Ratios and Proportional Relationships · Analyze proportional relationships and use them to solve problems.

1. 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
2. Ratio Notation and Relationships: Understand that a multiplicative relationship between two quantities can be expressed as a ratio; use ratio notation; simplify ratios
3. 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