Math Ladder · Middle school · Grade 6

Grade 6

Ratios and rates, dividing fractions, negative numbers, expressions and one-step equations, area, volume and data.

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52 topics in 7 units. Builds on Grade 5. Leads to Grade 7. It also opens the way to Earth Science on the Earth & Space Ladder. Not sure this is the right course? Find your rung.

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Unit 1 Ratios and Rates

9 topics

Compare quantities with ratios, find unit rates and percents, and convert units.

  1. Ratios
  2. Equivalent Ratios and Ratio Tables
  3. Graphing Ratios
  4. Unit Rates
  5. Unit Price and Constant Speed
  6. Percent Means per 100
  7. Finding a Percent of a Number
  8. Finding the Whole from a Part
  9. Converting Units with Ratios

Unit 2 Fractions, Decimals and Factors

7 topics

Divide fractions, compute fluently with multi-digit numbers, and use GCF and LCM.

  1. What Dividing by a Fraction Means
  2. Dividing Fractions
  3. Fraction Division Word Problems
  4. Long Division Fluency
  5. Decimal Operations Fluency
  6. Greatest Common Factor and Least Common Multiple
  7. Factoring a Sum with the GCF

Unit 3 Negative Numbers

7 topics

Place positive and negative numbers on lines and grids, compare them, and find absolute value.

  1. Positive and Negative Numbers
  2. Opposites
  3. Rational Numbers on the Number Line
  4. Ordering Rational Numbers
  5. Absolute Value
  6. The Four-Quadrant Coordinate Plane
  7. Distance on the Coordinate Plane

Unit 4 Expressions

8 topics

Use exponents and variables, write and evaluate expressions, and make equivalent expressions.

  1. Whole-Number Exponents
  2. Order of Operations with Exponents
  3. What a Variable Stands For
  4. Writing Expressions with Variables
  5. Terms, Coefficients and Factors
  6. Evaluating Expressions and Formulas
  7. Equivalent Expressions with Properties
  8. Are These Expressions Equal?

Unit 5 Equations and Inequalities

6 topics

Check solutions, solve one-step equations, and write inequalities.

  1. Is It a Solution?
  2. One-Step Equations with Adding and Subtracting
  3. One-Step Equations with Multiplying and Dividing
  4. Writing Equations for Word Problems
  5. Inequalities and Their Graphs
  6. Dependent and Independent Variables

Unit 6 Area, Surface Area and Volume

7 topics

Find areas of triangles and polygons, surface area from nets, and volume with fractional edges.

  1. Area of a Parallelogram
  2. Area of a Triangle
  3. Area of a Trapezoid
  4. Area of Composite Polygons
  5. Polygons on the Coordinate Plane
  6. Nets and Surface Area
  7. Volume with Fractional Edge Lengths

Unit 7 Statistics

8 topics

Ask statistical questions and describe data by its center, spread and shape.

  1. Statistical Questions
  2. Dot Plots and Histograms
  3. The Mean as a Fair Share
  4. Median and Mode
  5. Range and Interquartile Range
  6. Box Plots
  7. Mean Absolute Deviation
  8. Describing a Distribution
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