In this course, instructional time should focus on four main areas: (1) connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems; (2) completing the 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; and (4) developing understanding of statistical thinking.
Grade Level(s): Sixth Grade
Related Priority Standards (State &/or National): K-12 Mathematics Missouri Learning Standards
- How does decomposing and composing help us find the area of polygons?
- How does understanding the area of polygons connect to finding the surface area of prisms?
- What does a ratio say about the relationship between quantities?
- How can graphs and tables help us see the relationship between values?
- How can the distributive property help me with computation?
- How do I know which mathematical operations to use?
- How do mathematical operations relate to each other?
- What conclusions can be drawn from data?
- What strategies can I use to understand and represent real situations using algebraic expressions and equations?
Enduring Understandings/Big Ideas
- Area, surface area and volume have applications in real world situations.
- Relations between two quantities can often be expressed as ratios and can be explained using ratio language.
- Numbers in our world will appear as fractions and decimals and can be positive or negative.
- The equal sign is more than a prompt, it’s also a way to indicate balance.
- There are two kinds of expressions - numerical and algebraic.
- Statistics are a powerful tool to seek answers to statistical questions and to understand data distributions and what inferences can be drawn about the data.
- Graphical representations of data, including dot plots, histograms, and frequency tables are useful to organize data.
Course-Level Scope & Sequence (Units &/or Skills)
Unit 1: Geometry
- Students will calculate the area and perimeter of triangles and parallelograms.
- Students will calculate the area of polygons and irregular figures by decomposing them into rectangles and triangles. This includes trapezoids and special polygons (e.g. L or U-shaped polygons).
- Students will connect polyhedra with nets that represent them.
- Students will calculate the surface area of polyhedra made up of rectangles and triangles.
- Students will use repeated reasoning to develop a formula for the area of a parallelogram and triangle.
Unit 2: Ratios
- Students will use ratio language to describe a relationship between two quantities and identify equivalent ratios.
- Students develop and use strategies to compare ratios.
- Students will use tables, double number line diagrams and unit prices to solve problems with equivalent ratios.
- Students will develop and use strategies to compare ratios in context.
- Students will use unit rates, double number lines and tables of equivalent ratios to solve real-world problems.
- Students develop and use strategies to compare ratios in context.
Unit 3: Rates and Percentages
- Students will use ratio reasoning to convert between units of measurement.
- Students will recognize and calculate two unit rates for the same ratio relationship.
- Students will use unit rates to solve problems involving tables of equivalent ratios.
- Students will make connections between percentages, ratios, and rates.
- Students will use ratio reasoning to determine unknown parts, wholes, and percentages.
Unit 4: Fractions
- Students will use any of the four operations to solve problems in context.
- Students will multiply fractions and mixed numbers using a variety of strategies.
- Students will interpret and create diagrams that represent dividing whole numbers by fractions.
- Students will use a variety of strategies to calculate quotients of fractions.
- Students will solve problems that involve dividing fractions and mixed numbers.
- Students will determine the LCM and GCF of two numbers.
Unit 5: Decimals
- Students will add and subtract multi-digit decimals using a variety of strategies.
- Students will multiply and divide multi-digit decimals using a variety of strategies.
- Students will divide multi-digit numbers with and without remainders using long division.
- Students will use decimal operations to solve problems in context.
- Students will determine the LCM and GCF of two numbers.
Unit 6: Expressions and Equations
- Students will write expressions and equations given a mathematical sentence.
- Students will be able to describe a variable expression or equation as a mathematical sentence.
- Students will identify parts of an expression and equation.
- Students will identify like terms.
- Students will be able to combine like terms to simplify an expression, including using the distributive property.
- Students will use inverse operations to solve one-step equations algebraically.
- Students will identify various inequality statements, including less than or equal to and greater than or equal to.
- Students will graph the solution set of an inequality on a number line.
- Students will be able to solve one-step inequalities using inverse operations.
- Students will be able to graph the solution of one-step inequalities.
- Students will evaluate numerical and variable expressions with whole number exponents.
- Students will write equivalent expressions by adding, subtracting, expanding, and factoring.
- Students will use tape diagrams to represent equations and situations in context to determine unknown values.
- Students will solve equations in the form px + q = r and p(x + q) = r.
- Students will use the distributive property to write equivalent expressions with variables.
- Students will write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable.
- Students will analyze the relationship between independent and dependent variables using graphs, tables, and equations.
Unit 7: Rational Numbers
- Students will describe locations on the number line using positive and negative numbers.
- Students will compare and order positive and negative numbers and absolute values.
- Students will represent inequalities using symbols, words, and graphs.
- Students will identify solutions to inequalities.
- Students will solve problems by graphing points with positive and negative coordinates.
- Students will draw polygons given coordinates for the vertices.
Unit 8: Statistics and Graphing
- Students will be able to determine a statistical question.
- Students will understand that a sample is a subset of a population.
- Students will find the mean, median, mode, and range of a set of data.
- Students will be able to determine how outliers help select the best measure of center for the given data.
- Students will describe the data distribution from a graph (skew).
- Students will explain how the shape of the data set affects its mean and median.
- Students will read and create dot plots.
- Students will read and create histograms.
- Students will read and create box plots.
- Students will informally describe and compare data sets.
- Students will calculate the mean absolute deviation.
- Students will compare and contrast the mean and median as measures of center.
- Students will calculate the quartiles, interquartile range (IQR), and range of a data set.
- Students will create box plots to visualize data.
- Students will use median and IQR to describe and compare data sets.
Course Resources & Materials: DESMOS
Date Last Revised/Approved: 2022