How to learn Grade 7: Mathematics

Alabama academic standards: Mathematics, Grade 7

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1. Grade 7 Accelerated Standards · Verify experimentally the properties of rigid motions (rotations, reflections, and translations): lines are taken to lines, and line segments are taken to line segments

1. Coordinate Transformations: Identify properties of translations, rotations, and reflections; describe and perform these transformations on given figures, and understand that the image is congruent to the original

2. Grade 7 Accelerated Standards · Analyze and apply properties of parallel lines cut by a transversal to determine missing angle measures.

1. Angles with parallel lines: Understand and use the relationship between parallel lines cut by a transversal: corresponding angles, alternate interior angles, and co-interior (same-side interior) angles; use these to find unknown angles

3. Grade 7 Accelerated Standards · Explain the relationships among circumference, diameter, area, and radius of a circle to demonstrate understanding of formulas for the area and circumference of a circl

1. 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

4. Grade 7 Accelerated Standards · Find probabilities of simple and compound events through experimentation or simulation and by analyzing the sample space, representing the probabilities as percents, de

1. Tree diagrams: Generate theoretical sample spaces for single and combined events using listing, tables, and tree diagrams, and calculate theoretical probabilities as the number of favourable outcomes divided by the total number of equally likely outcomes

5. Grade 7 Accelerated Standards · Approximate the probability of an event by using data generated by a simulation (experimental probability) and compare it to theoretical probability.

1. 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

6. Grade 7 Accelerated Standards · Construct a function to model the linear relationship between two variables.

1. Linear Function Graphs: Recognise that a linear function produces a straight-line graph, understand the relationship between an equation of the form y = mx + c and its graphical representation, and interpret gradient and y-intercept in context

7. Grade 7 Accelerated Standards · Solve multi-step linear equations in one variable, including rational number coefficients, and equations that require using the distributive property and combining like

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

8. Grade 7 Accelerated Standards · Express and compare very large or very small numbers in scientific notation.

1. Compound Units: Use compound units such as speed (distance ÷ time), unit pricing (cost ÷ quantity), and density (mass ÷ volume); solve problems involving compound units
2. Powers of Ten Notation: Interpret and compare numbers in standard form A × 10ⁿ where 1 ≤ A < 10 and n is an integer; convert between ordinary numbers and standard form

9. Grade 7 Accelerated Standards · Use square root and cube root symbols to represent solutions to equations.

1. Square and cube numbers: Use integer powers and associated real roots (square, cube, and higher); recognise powers of 2, 3, 4, and 5; distinguish between exact representations of roots and their decimal approximations

10. Grade 7 Accelerated Standards · Define the real number system as composed of rational and irrational numbers.

1. 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

11. Grade 7 Accelerated Standards · Apply and extend knowledge of operations of whole numbers, fractions, and decimals to add, subtract, multiply, and divide rational numbers including integers, signed fr

1. Decimals and fractions (age 11+): Work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 and 3/8); convert fluently between the two forms
2. Mixed & Improper Fractions: Use the four operations with formal written methods applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative
3. Numbers on a number line: Understand the absolute value of a rational number as its distance from zero on the number line; interpret absolute value as magnitude in real-world contexts; distinguish absolute value comparisons from ordering statements

12. Grade 7 Accelerated Standards · Graph proportional relationships.

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

13. Grade 7 Accelerated Standards · Represent a relationship between two quantities and determine whether the two quantities are related proportionally.

1. 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