7th grade Math
20 units matched to the New York State Learning Standards.
Focus areas
- Number and operations: proportional relationships, operations with rational numbers, and equations and inequalities
- Measurement, data and geometry: scale drawings, circles and angles, box plots, and the probability of compound events
- Mathematical practices: making sense of problems and explaining reasoning
Units
Unit 1
Add & Subtract Integers
Adding and subtracting positive and negative numbers with number lines, temperatures and elevations, including the idea that subtracting a number is the same as adding its opposite.
Learning standard: NY-7.NS.1 · adding and subtracting rational numbers, including negative numbers
Unit 2
Decimal Operations
All four operations with decimals, estimating to check answers, ordering decimals, and money problems such as unit prices.
Learning standard: NY-7.NS.3; NY-7.EE.3 · computing with decimals and solving multi-step problems with rational numbers
Unit 3
Fractions, Decimals & Percents
Moving between fractions, decimals (including repeating decimals) and percents, finding a percent of a number, and simplifying and scaling ratios.
Learning standard: NY-7.NS.2; NY-7.RP.3 · writing numbers as fractions, decimals and percents and using them in percent problems
Unit 4
Two-Step Equations
Solving equations like 3x + 5 = 26 by undoing each step on both sides, writing equations from word problems and checking solutions.
Learning standard: NY-7.EE.4 · writing and solving two-step equations from problems in context
Unit 5
Circles
Using radius, diameter and π (about 3.14) to find the distance around a circle and the area inside it, including real objects like wheels and pizzas.
Learning standard: NY-7.G.4 · the circumference and area of circles
Unit 6
Probability
Listing outcomes of two independent events (like a coin and a die), finding theoretical probabilities by multiplying, and comparing them with experimental results.
Learning standard: NY-7.SP.8 · probabilities of compound events with organized lists, tables and simulation
Unit 7
Fractions
Adding and subtracting fractions with different denominators, and multiplying and dividing a fraction by a fraction.
Learning standard: NY-7.NS.1; NY-7.NS.2 · adding, subtracting, multiplying and dividing fractions
Unit 8
Percents & Proportions
Knowing common fraction, decimal and percent equivalents, increasing and decreasing numbers by 1%, 5%, 10%, 25%, 50% and 100%, and deciding whether a relationship is proportional.
Learning standard: NY-7.RP.2; NY-7.RP.3 · proportional relationships and percent increase and decrease
Unit 9
Algebra Moves
Combining like terms, evaluating expressions with decimals, solving two-step equations, and finding and graphing solutions to inequalities.
Learning standard: NY-7.EE.1; NY-7.EE.4 · writing equivalent expressions and solving equations and inequalities
Unit 10
Dependent Events
Telling independent from dependent events and finding the probability of two events, with and without putting the first item back.
Learning standard: NY-7.SP.8 · probabilities of compound events with organized lists and tree diagrams
Unit 11
Mean, Median & Mode
Mean, median, mode and range, and how an outlier changes them.
Learning standard: NY-7.SP.3; NY-7.SP.4 · comparing two data sets with measures of center and variability
Unit 12
Center & Spread
Telling a statistical question from a regular question, and describing data with the mean, median, range and interquartile range.
Learning standard: NY-7.SP.1; NY-7.SP.4 · finding the interquartile range, spotting outliers, and describing data with measures of center and variability
Unit 13
Multiply & Divide Signed Numbers
Multiplying and dividing positive and negative numbers (including fractions), using the sign rules, and real-world changes such as falling temperatures.
Learning standard: NY-7.NS.2 · multiplying and dividing rational numbers, including negative numbers
Unit 14
Proportional Relationships
Deciding whether a table shows a proportional relationship, finding the constant of proportionality, writing y = kx, and unit rates with fractions.
Learning standard: NY-7.RP.1; NY-7.RP.2 · unit rates with fractions, recognizing proportional relationships and finding the constant of proportionality
Unit 15
Angle Relationships
Using complementary, supplementary, vertical and adjacent angles to find a missing angle, sometimes with a simple equation.
Learning standard: NY-7.G.5 · using supplementary, complementary, vertical and adjacent angles to find unknown angles
Unit 16
Scale Drawings
Finding real lengths and areas from a scale drawing or map, and redrawing at a different scale.
Learning standard: NY-7.G.1 · solving problems with scale drawings, including actual lengths and areas
Unit 17
Rewriting Expressions
Writing the same expression in a different form to see what it means: a 6% increase as 1.06p, 20% off as 0.8p, and 4t + 4s as 4(t + s), what each friend spends times 4.
Learning standard: NY-7.EE.2 · rewriting expressions in different forms to show how the quantities in a problem are related
Unit 18
One Triangle, Many or None?
Deciding whether given sides and angles make exactly one triangle, more than one, or none: the two shorter sides must add to more than the longest, the angles must add to 180°, and three angles fix the shape but not the size.
Learning standard: NY-7.G.2 · drawing triangles from given angles and sides, and noticing when the conditions make one triangle, more than one, or none
Unit 19
Slicing Solids
Picturing the flat shape you get when you slice a prism, pyramid, cylinder, cone or sphere parallel or perpendicular to its base, like slicing a loaf of bread or a block of cheese.
Learning standard: NY-7.G.3 · describing the two-dimensional shapes made by slicing three-dimensional solids parallel or perpendicular to the base
Unit 20
Area of Composite Shapes
Finding the area of floors, walls, signs and gardens made of rectangles, triangles and trapezoids by splitting them into parts, adding the areas, or subtracting a cut-out part.
Learning standard: NY-7.G.6 · solving real-world problems with the area of shapes made of rectangles, triangles and trapezoids
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