Grade 6 Math Curriculum Guide

In grade 6, instructional time will focus on five areas: (1) connecting ratio and rate to whole number multiplication and division, and using concepts of ratio and rate to solve problems; (2) completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers; (3) writing, interpreting, and using expressions and equations; (4) solving real-world and mathematical problems involving area, surface area, and volume; (5) describing the variability and center of data distributions.

Unit

Timeframe

Big Ideas 

Major Learning Experiences  

Unit 1

Number Theory

September

Every number can be built using its prime factors.  The prime factorization of a number can help us find common factors and multiples.  We can use the greatest common factor and least common multiple to solve many real world problems related to creating groupings.  



Students will:

  • Discover how to write numbers as the product of prime numbers.

  • Solve a variety of real world problems using the greatest common factor and the least common multiple.

  • Create a project about their favorite number and describe the number's attributes.  



Unit 2

Decimal Operations

October



 



The operations for fractions, decimals, and whole numbers are connected.  We can use decimal operations to solve everyday problems. 





Students will:

  • Solve real world multi-step decimal problems using all four operations.

  • Develop conceptual understanding of long division using base ten blocks and connect that understanding to the standard algorithm. 

  • Develop a conceptual understanding of dividing decimals by decimals by connecting to their understanding of equivalent fractions. 

Unit 3

Ratios, Rates and Percents 

November/December


A ratio is a multiplicative comparison of quantities; there are different types of comparisons that can be represented as ratios.  We can solve ratio problems using a variety of representations.  

Percentages are used worldwide to communicate information about sports, shopping, stocks, weather conditions, survey results, and many more ratio relationships.

Students will:

  • Compare quantities by writing ratios and using ratio language.

  • Create tables of equivalent ratios and fill in missing values.

  • Learn about how artists use ratio concepts to create mosaics, and create their own math mosaic.

  • Solve real world problems about speed and pricing by finding unit rates.

  • Use multiple representations such as tape diagrams, double number line diagrams, equations, and tables to solve real world problems involving percents.

Unit 4

Fraction Division

December/January




Fraction division can be represented with visual models. To make sense of real world fraction division problems, we need to interpret the meaning of the quotient.





Students will:

  • Use fraction tiles to conceptually understand how to divide fractions by fractions.

  • Understand why we multiply by the reciprocal when dividing fractions through explorations of concrete and visual models. 

  • Create their own real world story problem that involves division of fractions and show how to solve the problem using an equation and a visual model. 

  • Solve problems about area, cooking, pricing and speed.


    Unit 5

The Number Line and Coordinate Plane

January/February






Number lines can be used to represent, order and compare rational numbers. Absolute value can be used to find the horizontal or vertical distance between points on a number line or coordinate grid.




Students will:

  • Use positive and negative numbers to represent real world quantities and explain the meaning of zero in each situation.

  • Represent, compare, and order positive & negative rational numbers on a number line.

  • Write statements of inequality to compare rational numbers from real world contexts, and order rational numbers. 

  • Understand that absolute value is the distance from zero and I can interpret absolute value in real world situations.

  • Plot points on the coordinate plane in all four quadrants and find the distance between points. 

    Unit 6

Expressions, Equations and Inequalities



February/March


We can use expressions, equations, and inequalities to model mathematical and real world situations.  Expressions, equations and inequalities can be rewritten into many equivalent forms using mathematical properties.


 

Students will:

  • Evaluate numerical and algebraic expressions involving exponents using the order of operations.

  • Write algebraic expressions from words and real life situations, and identify parts of the expression. 

  • Expand/factor and simplify algebraic expressions using the distributive property and combining like terms. I can use these skills to recognize equivalent expressions.

  • Write and solve one-step algebraic equations and inequalities that represent real world contexts.  

  • Represent the solutions of an inequality on a numberline.  

    Unit 7

Geometry - Area and Volume





April







2-D and 3-D shapes can be composed and decomposed to find their area, surface area, and volume.

Student will:

  • Discover the formulas for finding the areas of polygons composed of triangles and rectangles.  

  • Draw polygons in the coordinate plane given coordinates, and find the area or missing dimensions of these polygons.

  • Solve real world problems involving area and distance on the coordinate plane. 

  • Find the volume of rectangular prisms with fractional edge lengths.

  • Find the surface area of 3-D shapes using nets, and apply this in the context of real-world problems.

    Unit 8

Statistics

May







Data can answer statistical questions and can be visually displayed and described using center, spread and overall shape.

Students will:

  • Write and recognize a statistical question.  

  • Collect data to answer statistical questions.

  • Create and interpret dot plots, histograms, and box plots.  

  • Calculate measures of center (mean, median, mode) from a set of data and a graph.

  • Calculate measures of variability (range and interquartile range) from a set of data and a graph. 

  • Describe and interpret numerical data displays, including symmetry, outliers and skew.  

  • Create a culminating project in which students survey their classmates, analyze their results, conduct research on their topic, and make recommendations on how to improve the lives of 6th graders.