COOPERATIVE MIDDLE SCHOOL
Grade 6 Mathematics Course Summary
th
Course Title 6 Grade Mathematics, 6th Grade Supported Mathematics, 6th Grade Extension
6th Grade Mathematics will focus on four critical 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; and (4) developing understanding of statistical thinking.
Course
Description
Entering middle school, students have been placed into either 6th grade Math, 6th
grade Math Supported, or 6th grade Math Extension. All classes focus on the
same mathematical topics while offering students opportunities to apply and
extend their thinking throughout the school year. Students in 6th grade Math and
6th grade Math Supported class progress in a way that provides appropriate
opportunities for repeated practice and reinforcement of skills and concepts,
while students in a 6th grade Math Extension have a range of higher-challenge
opportunities in addition to the same core skills and concepts taught in the 6th
grade Math class.
Completion of 5th Grade Math Competencies
New Hampshire College and Career Ready Standards (NH CCRS) for
Standards
Mathematics
The following NH CCRS for Mathematics define what students should understand and be able to
do in their study of 6th grade mathematics:
Prerequisite
Ratios and Proportional Relationships
●
Understand ratios and use ratio language to describe a ratio relationship between two
quantities.
●
Understand the concept of a unit rate and use rate language in the context of a ratio
relationship.
●
Use ratio and rate reasoning to solve real-world and mathematical problems.
●
Make tables of equivalent ratios with whole-number measurements. Find missing values in
the tables, and plot the pairs of values on a coordinate plane.
●
Solve unit rate problems including those involving unit pricing and constant speed.
●
Solve problems finding the percent of a quantity and determining the whole, given a part
and the percent.
●
Use ratio reasoning to convert measurement units; manipulate and transform units
appropriately when multiplying or dividing quantities.
The Number System
●
Divide fractions by fractions and interpret quotients in word problems.
●
Fluently divide multi-digit numbers using the standard algorithm.
●
Fluently add, subtract, multiply, and divide multi-digit decimals using the standard
algorithm for each operation.
●
Find the greatest common factor of two whole numbers less than or equal to 100 and the
COOPERATIVE MIDDLE SCHOOL
Grade 6 Mathematics Course Summary
least common multiple of two whole numbers less than or equal to 12. Use the distributive property
to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two
whole numbers with no common factor.
●
Understand that positive and negative numbers are used together to describe quantities
having opposite directions or values.
●
Use positive and negative numbers to represent quantities in real-world contexts,
explaining the meaning of 0 in each situation.
●
Understand a rational number as a point on the number line.
●
Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the
number line.
●
Understand signs of numbers in ordered pairs as indicating
locations in quadrants of the
coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the
points are related by reflections across one or both axes.
●
Understand ordering and absolute value of rational numbers.
●
Write, interpret, and explain statements about ordering for rational numbers in real-world
contexts.
●
Understand the absolute value of a rational number as its distance from 0 on the number
line. Interpret absolute value as magnitude for a positive or negative quantity in a real-world
situation.
Expressions and Equations
●
Write and evaluate numerical expressions involving whole-number exponents.
●
Write, read, and evaluate expressions in which letters stand for numbers.
●
Identify parts of an expression (sum, term, product, factor, quotient, coefficient).
●
Solve real world problems using substitution of number for variable in formulas and
following the Order of Operations.
●
Apply the properties of operations to generate equivalent expressions.
●
Determine which value(s) from a specified set make an equation or inequality true.
●
Solve real world mathematical problems by writing and solving equations in the forms x +
p = q and px = q for nonnegative rational numbers.
●
Write inequalities in the form x > c and x < c to represent real world and mathematical
problems and graph the solutions of the inequalities on a number line.
●
Represent and analyze the relationship between dependent and independent variables in a
real world problem using graphs, tables, and equations.
Geometry
●
Find the area of right triangles, other triangles, special quadrilaterals, and polygons in real
world and mathematical problems.
●
Find the volume of a right rectangular prism with fractional edge lengths by packing it with
unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as
would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V =
bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving
real-world and mathematical problems.
●
Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates
to find the length of a side joining points with the same first coordinate or the same second
coordinate.
●
Represent three-dimensional figures using nets made up of rectangles and triangles, and use
COOPERATIVE MIDDLE SCHOOL
Grade 6 Mathematics Course Summary
the nets to find the surface area of these figures
Statistics and Probability
●
Recognize that a statistical question anticipates variability in the data.
●
Understand that a set of data collected to answer a statistical question has a distribution,
which can be described by its center, spread, and overall shape.
●
Recognize that a measure of center for a numerical data set summarizes all of its values
with a single number, while a measure of variation describes how its values vary with a single
number.
●
Display numerical data in plots on a number line, including dot plots, histograms, and box
plots.
●
Summarize data by reporting the number of observations and describing the attribute being
measured.
●
Find measures of center (median and/or mean) and variability (interquartile range and/or
mean absolute deviation) of a set of data.