8th grade Math
19 units matched to the New York State Learning Standards.
Focus areas
- Number and operations: exponents and scientific notation, linear equations and systems, and functions
- Measurement, data and geometry: transformations, congruence and similarity, the Pythagorean Theorem, volume, and scatter plots
- Mathematical practices: making sense of problems and explaining reasoning
Units
Unit 1
Squares, Cubes & Roots
Knowing perfect squares and cubes, finding square roots and cube roots, estimating where a square root falls between whole numbers, and linking squares to the area of a square.
Learning standard: NY-8.EE.2 · square roots of perfect squares and cube roots of perfect cubes
Unit 2
Patterns & Two-Step Equations
Writing and evaluating expressions like 3n + 2, solving two-step equations, and finding the rule for a growing pattern or a cost made of whole items such as tickets.
Learning standard: NY-8.EE.7 · solving linear equations in one variable
Unit 3
Pythagorean Theorem
Finding a missing side of a right triangle, checking whether a triangle is a right triangle, and using the theorem for ladders and diagonals.
Learning standard: NY-8.G.6; NY-8.G.7 · the Pythagorean Theorem and its converse in problems in context
Unit 4
Surface Area & Volume
Finding surface area and volume of boxes, cubes, triangular prisms and cylinders, working backwards to a missing dimension, linking cm³ to milliliters, and recognizing nets and views of 3D objects.
Learning standard: NY-8.G.9 · the volume of cylinders
Unit 5
Big, Small & Real Numbers
Writing very large and very small numbers in scientific notation, telling rational from irrational numbers, ordering numbers such as √2 and π, and mentally multiplying and dividing by powers of ten.
Learning standard: NY-8.NS.1; NY-8.NS.2; NY-8.EE.3; NY-8.EE.4 · irrational numbers and scientific notation
Unit 6
Scatter Plots & Stories
Deciding when two-variable data is needed, picking the best graph, describing scatter plots as strong, weak, positive, negative or none, spotting outliers, and noticing graphs that mislead.
Learning standard: NY-8.SP.1; NY-8.SP.2 · scatter plots and patterns of association
Unit 7
Tessellations & Transformations
Why some shapes tessellate, naming the transformations in a tiling, and finding the image of a point after a translation, reflection, rotation or dilation on a coordinate grid.
Learning standard: NY-8.G.1; NY-8.G.3 · translations, reflections, rotations and dilations on the coordinate plane
Unit 8
Angle Detective
Using equal and supplementary angles when a transversal crosses parallel lines, and the angle sums of triangles, quadrilaterals and polygons, including exterior angles.
Learning standard: NY-8.G.5 · angle sums of triangles and angles formed by parallel lines
Unit 9
Similarity & Scale
Using scale factors to find missing sides, solving shadow and scale-drawing problems, and seeing how enlarging a shape changes its area and volume.
Learning standard: NY-8.G.4 · similar figures, scale factors and finding missing side lengths
Unit 10
Tables, Graphs & Linear Relations
Using an equation like y = 3x + 2 to build a table of values, find a missing x or y, and describe how the variables change together.
Learning standard: NY-8.F.3; NY-8.F.4 · linear functions of the form y = mx + b, their tables and graphs
Unit 11
Equations with Brackets
Solving one-variable equations, including ones with brackets and negative numbers, checking by substitution, and spotting a common mistake with the distributive property.
Learning standard: NY-8.EE.7 · solving linear equations that need the distributive property
Unit 12
Congruent Shapes
Recognizing congruent shapes, matching corresponding sides and angles, and finding the coordinates of a point after a slide, flip or turn.
Learning standard: NY-8.G.2 · congruence through rotations, reflections and translations
Unit 13
Exponent Rules
Properties of integer exponents: multiplying and dividing powers with the same base, a power of a power, zero exponents and negative exponents.
Learning standard: NY-8.EE.1 · applying the properties of integer exponents to write equivalent expressions
Unit 14
Systems of Equations
Solving pairs of linear equations, checking a solution, telling when a system has no solution or infinitely many, and simple word problems.
Learning standard: NY-8.EE.8 · finding and interpreting solutions to pairs of linear equations
Unit 15
Functions
Deciding whether a relation is a function, comparing two functions shown in different ways, spotting linear functions, and matching a graph to a story.
Learning standard: NY-8.F.1; NY-8.F.2; NY-8.F.3; NY-8.F.5 · functions as one output for each input, comparing functions, linear functions, and describing graphs in words
Unit 16
Cones, Cylinders & Spheres
Using the volume formulas for cylinders, cones and spheres, in terms of π and with 3.14.
Learning standard: NY-8.G.9 · using the formulas for the volumes of cones, cylinders and spheres
Unit 17
Slope & Rate of Change
Finding slope from two points or a table, reading slope as a unit rate, writing y = mx + b, and saying what the intercept means.
Learning standard: NY-8.EE.5; NY-8.EE.6; NY-8.F.4 · slope as the unit rate and writing lines as y = mx + b
Unit 18
Distance on a Grid
Finding the straight-line distance between two points on a coordinate grid by drawing a right triangle and using the Pythagorean Theorem, a² + b² = c².
Learning standard: NY-8.G.8 · applying the Pythagorean Theorem to find the distance between two points in a coordinate system
Unit 19
Lines of Best Fit
Using the equation of a line of best fit to make predictions from data, and explaining what the slope and the y-intercept mean in the situation.
Learning standard: NY-8.SP.3 · using the equation of a linear model of two-variable data to solve problems, and interpreting its slope and intercept
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