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Goals and domain icons were developed by Angie Seltzer. Highlighted parts are from Grade 6 CCSS, Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
Grade 6
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CCSS ID MathPaths Grade 6 Goals
CCSS
THE NUMBER SYSTEM
A
1
Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
6.NS.1
1-1
Relate division and multiplication of fractions.
6.NS.1
1-2
Divide fractions by fractions using models. Students will be expected to understand the algorithm in Grade 7.
6.NS.1
1-3
Divide fractions by fractions to solve problems.
B
2
Compute fluently with multi-digit numbers and find common factors and multiples.
6.NS.2
2-1
Divide multi-digit numbers using the standard algorithm.
6.NS.3
2-2
Add and subtract multi-digit decimals.
6.NS.3
2-3*
Multiply multi-digit decimals.
6.NS.3
2-4
Divide multi-digit decimals.
6.NS.4
2-5
Find greatest common factors. Factors and multiples were introduced in Grade 4, but GCF is a new concept.
6.NS.4
2-6
Find least common multiples. LCM is a new concept.
6.NS.4
2-7
Use the distributive property to isolate a common factor. For example, express 28 + 40 as 4(7 + 10).
C
3
Apply and extend previous understandings of numbers to the system of rational numbers.
6.NS.5
3-1
Relate positive and negative numbers to real situations. Note that at this level students should not be given rules for abstract integer operations. Students should learn meanings of integers and use number lines to solve problems. Introducing rules too early detracts from focus on concepts.
6.NS.6a
3-2
Write and identify opposites of integers.
6.NS.6b
3-3
Relate opposite numbers in ordered pairs to reflections.
6.NS.6c
3-4
Graph or identify points in four quadrants. This goal also includes locations on vertical or horizontal number lines. First-quadrant graphs were introduced in the Geometry domain in Grade 5.
6.NS.7a
3-5
Compare rational numbers using a number line.
6.NS.7bcd
3-6
Write comparisons for ordering rational numbers in real situations. This goal also includes understanding absolute value, including vertical bar symbols. For example, |–7| = 7.
6.NS.8
3-7
Solve problems involving coordinate graphs in four quadrants.
6.NS.8
3-8
Find distance between two points with the same first or second coordinate.
CCSS
EXPRESSIONS & EQUATIONS
A
1
Apply and extend previous understandings of arithmetic to algebraic expressions.
6.EE.1
1-1*
Evaluate numerical expressions that include exponents.
6.EE.2a
1-2
Write or interpret simple expressions with variables. Variables are new at this level.
6.EE.2b
1-3
Identify parts of an expression using mathematical terms.
6.EE.2c
1-4
Evaluate expressions for specific values of the variables.
6.EE.2c
1-5
Evaluate formulas for specific values.
6.EE.3
1-6
Write equivalent expressions using the distributive property.
6.EE.4
1-7
Identify when two expressions are equivalent.
B
2
Reason about and solve one-variable equations and inequalities.
6.EE.5
2-1
Use substitution to decide if a number is a solution to an equation.
6.EE.6
2-2
Use variables and expressions to represent situations.
6.EE.7
2-3
Write equations of the form x + p = q to solve problems.
6.EE.7
2-4
Write equations of the form px = q to solve problems.
6.EE.8
2-5
Write or interpret inequalities x > c or x < c.
6.EE.8
2-6*
Represent inequalities on number line diagrams.
C
3
Represent and analyze quantitative relationships between dependent and independent variables.
6.EE.9
3-1
Use two variables to represent two related quantities.
6.EE.9
3-2
Graph ordered pairs of related quantities.
6.EE.9
3-3
Write equations to describe related variables.
CCSS
RATIOS & PROPORTIONAL RELATIONSHIPS
A
1
Understand ratio concepts and use ratio reasoning [and percents] to solve problems.
6.RP.1
1-1
Write and interpret ratios. This goal is understanding ratios such as "A to B" and A:B.
6.RP.2
1-2
Find unit rates related to ratios. The ratio A:B can also be expressed as a unit rate A/B.
6.RP.3a
1-3
Write equivalent ratios, including ratio tables.
6.RP.3d
1-4
Use ratios to convert measurements.
6.RP.3a
1-5
Plot pairs of ratios on the coordinate plane.
6.RP.3b
1-6
Solve unit rate problems such as unit pricing. This goal also includes problems about constant speed.
6.RP.3c
1-7*
Write a fraction or ratio as a percent. These should be solved by writing the fraction as hundredths. At this level, the percent problems should be solved by writing equal ratios. In Grade 7, students will use proportions and solve more advanced percent problems.
6.RP.3c
1-8
Find a number given the part and the percent. In this case, the whole or total is unknown. For example, if 30% of a number is 6, the number is found by writing a ratio equal to 30/100 with a numerator of 6.
6.RP.3c
1-9
Find a percent of a number. For example, 20% of 40 can be found by simplifying 20/100 and then finding 1/5 x 40.
CCSS
GEOMETRY
A
1
Solve real-world and mathematical problems involving area, surface area, and volume.
6.G.1
1-1*
Find areas of triangles. Starting in Grade 3, students found areas of rectangles and shapes made from rectangles.
6.G.1
1-2
Decompose and compose shapes into triangles and rectangles.
6.G.1
1-3
Find areas of polygons.
6.G.2
1-4
Use cubes to find volumes of prisms with fractional edge lengths. For example, how many1/2-inch cubes make a prism 1-1/2 by 2-1/2 by 4? (This requires 3 x 5 x 8 or 120 cubes. Each cube's volume is 1/2 x 1/2 x 1/2, or 1/8 cubic inch. The volume of the prism is 120/8 or 15 cubic inches.)
6.G.2
1-5
Multiply to find volumes of prisms with fractional edge lengths. For example, 1-1/2 x 2-1/2 x 4 = 3/2 x 5/2 x 4 = 60/4 = 15.
6.G.3
1-6
Draw polygons given coordinates for the vertices.
6.G.3
1-7*
Use coordinates to calculate the length of vertical or horizontal segments.
6.G.4
1-8*
Represent 3-dimensional figures as nets.
6.G.4
1-9*
Calculate surface areas.
CCSS
STATISTICS & PROBABILITY
A
1
Develop understanding of statistical variability.
6.SP.1
1-1
Recognize statistical questions. Statistical questions have variability in the answers.
6.SP.2
1-2
Describe the center, spread (range), and shape of data on a dot plot. Dot plots (also called line plots) were introduced and developed in Grades 2 through 5. The important new terms are clusters, peaks, gaps, and symmetry. (See the Common Core Grade 6 Introduction.)
6.SP.2
1-3*
Find the median of a data set. Common Core standards at lower grades do not include median or mean. Both of these are important measures of center.
6.SP.2
1-4
Find the mean of a data set.
6.SP.3
1-5
Recognize measures of center and variation of data. Students should identify mean and median and informally compare spreads. Calculations of spread are included in the next cluster.
B
2
Summarize and describe distributions.
6.SP.5c
2-1
Find quartiles and interquartile range. For a large set of data, identify the median of the lower half and the median of the upper half of the data. The difference, or range of the middle half of the data, is called the interquartile range.
6.SP.4
2-2
Display and describe data on box plots. Before making a box plot, students need to find the minimum, maximum, and quartiles.
6.SP.4
2-3
Display and describe data on histograms. To make a histogram, the RANGE must be divided into equal intervals. This is unlike a box plot, where the DATA SET was divided into equal groups.
6.SP.5c
2-4
Find the mean absolute deviation of a data set. After finding the mean, calculate the positive difference (deviation) between each data element and the mean. The mean of these deviations is called the mean absolute deviation. The use of technology is recommended for this topic.
6.SP.5
2-5
Summarize data sets in relation to their context. Discuss whether median or mean is a better measure of center, and which measures are best to describe the spread.
*See Grades 6-8 Games for goals marked with asterisks.