6th grade Math
21 units matched to the New York State Learning Standards.
Focus areas
- Number and operations: ratios and rates, dividing fractions, negative numbers, and expressions and equations
- Measurement, data and geometry: area, surface area and volume, statistics with the range and measures of centre, and simple probability
- Mathematical practices: making sense of problems and explaining reasoning
Units
Unit 1
Facts & Factors
Quick recall of multiplication and division facts, plus factors, multiples and prime numbers, the greatest common factor (GCF) and least common multiple (LCM), and word problems that use them.
Learning standard: NY-6.NS.4 · greatest common factor and least common multiple
Unit 2
Mixed Numbers & Ratios
Switching between improper fractions (like 13/5) and mixed numbers (2 3/5), placing them on a number line, and writing and using ratios such as 3:4 in tables and word problems.
Learning standard: NY-6.RP.1 · ratio language and ratio relationships
Unit 3
Decimal × and ÷
Multiplying and dividing decimals, estimating to check where the decimal point goes, and solving shopping and measurement problems.
Learning standard: NY-6.NS.3 · adding, subtracting, multiplying and dividing multi-digit decimals
Unit 4
Percents & Budgets
Finding percents of amounts, working out sale prices and savings, comparing unit prices to find the better buy, and planning a simple budget and savings goal.
Learning standard: NY-6.RP.3 · solving percent and rate problems with ratio reasoning
Unit 5
Patterns & Graphs
Describing growing and shrinking patterns with rules like 3n + 2, using tables and graphs to predict values, and reading change over time from line graphs.
Learning standard: NY-6.EE.9 · relating two changing quantities with tables, graphs and equations
Unit 6
Equations
Using the order of operations (brackets, then × and ÷, then + and −) and solving one-step equations like 6n = 42 with inverse operations, including writing equations for word problems.
Learning standard: NY-6.EE.5; NY-6.EE.6; NY-6.EE.7 · using a letter for an unknown number in a real-world problem, and solving one-step equations of the form x + p = q and px = q
Unit 7
Perimeter & Area
Finding the perimeter of L-shapes and other polygons, and the area of triangles (b × h ÷ 2), parallelograms (b × h) and trapezoids ((a + b) × h ÷ 2), including working backwards to a missing measurement.
Learning standard: NY-6.G.1 · area of triangles, trapezoids and other polygons
Unit 8
Volume & Capacity
Finding the volume of rectangular prisms, converting between liters and milliliters, and connecting volume to capacity (1 cm³ holds 1 mL).
Learning standard: NY-6.G.2 · volume of right rectangular prisms
Unit 9
Probability
Writing probabilities as fractions for spinners, dice and marbles, comparing theoretical probability with experimental results, and making predictions from data.
Learning standard: NY-6.SP.6; NY-6.SP.7; NY-6.SP.8 · probability as a number from 0 to 1, comparing experimental and theoretical probability, and simple probability models
Unit 10
Integers & Decimals
Meeting negative numbers on a number line, comparing and ordering integers, decimals and fractions, working with thousandths, and rounding decimals.
Learning standard: NY-6.NS.5; NY-6.NS.6; NY-6.NS.7 · positive and negative numbers on the number line, ordering and absolute value
Unit 11
Algebra Moves
Combining like terms such as 3x + 5x, evaluating expressions, and finding values that make an inequality true and showing them on a number line.
Learning standard: NY-6.EE.2; NY-6.EE.3; NY-6.EE.4; NY-6.EE.8 · evaluating expressions with letters for numbers, combining like terms to write equivalent expressions such as y + y + y = 3y, and writing inequalities of the form x > c or x < c
Unit 12
Data & Graphs
Telling discrete data (counted) from continuous data (measured), reading histograms and line graphs, finding the range, and spotting misleading graphs.
Learning standard: NY-6.SP.4; NY-6.SP.5 · showing numerical data in dot plots and histograms, and summarizing it with the range and measures of center
Unit 13
Powers and Common Factors
Reading and writing powers such as 3⁴, evaluating them, order of operations with powers, writing prime factorizations with exponents, and finding common factors and the greatest common factor.
Learning standard: NY-6.EE.1; NY-6.NS.4 · writing and evaluating expressions with whole-number exponents, and common factors
Unit 14
Dividing Fractions
Dividing a fraction by a fraction by multiplying by the reciprocal, and solving “how many servings” and “how many pieces” problems.
Learning standard: NY-6.NS.1 · dividing fractions by fractions and solving word problems with fraction division
Unit 15
Four Quadrants
Plotting and naming points in all four quadrants, reflecting points across an axis, and finding distances and areas on the coordinate plane.
Learning standard: NY-6.NS.8; NY-6.G.3; NY-6.NS.6 · graphing points in all four quadrants and finding the distance between points with a shared coordinate
Unit 16
Unit Rates
Finding unit rates and unit prices, choosing the better buy, completing rate tables, and converting measurement units with ratios.
Learning standard: NY-6.RP.2; NY-6.RP.3 · finding unit rates, using rate tables, and converting measurement units with ratio reasoning
Unit 17
Nets & Surface Area
Using nets made of rectangles and triangles to find the surface area of prisms and pyramids.
Learning standard: NY-6.G.4 · showing three-dimensional figures with nets and using them to find surface area
Unit 18
Samples & Populations
Telling a sample from a population, choosing a fair random sample, and using sample results to estimate for a whole population.
Learning standard: NY-6.SP.1b; NY-6.SP.1c · telling a sample from a population and choosing a sample that represents the population
Unit 19
Long Division
Dividing multi-digit numbers with the standard algorithm (divide, multiply, subtract, bring down), including two-digit divisors and word problems where the remainder matters.
Learning standard: NY-6.NS.2 · fluently dividing multi-digit numbers with the standard algorithm
Unit 20
Perfect Squares & Cubes
Using unit squares and unit cubes to see why 36 is a perfect square (a 6 by 6 square) and 27 is a perfect cube (a 3 by 3 by 3 cube), and what the exponents 2 and 3 mean.
Learning standard: NY-6.G.5 · using area and volume models to explain perfect squares and perfect cubes
Unit 21
Center, Spread & Shape
Telling statistical questions (answers that vary) from questions with one answer, and describing data by its center (mean, median), its spread (range, IQR) and its shape (clusters, outliers, symmetric or skewed), and knowing that each measure sums up the data in one number.
Learning standard: NY-6.SP.1a; NY-6.SP.2; NY-6.SP.3 · recognizing statistical questions, describing a data distribution by its center, spread and overall shape, and telling measures of center from measures of variation
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