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6th Grade Common Core Math
Sixth Grade Number System
What Your Child Will Learn
Divide by fractions by fractions (6.NS.1)
Fluently divide multi-digit numbers using the standard algorithm (6.NS.2)
Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation (6.NS.3)
Find the greatest common factor and multiples of numbers (6.NS.4)
Understand the meaning of positive and negative numbers (6.NS.5)
Order rational numbers (6.NS.6)
Understand ordering and absolute value of rational numbers (6.NS.7)
Graph points on a coordinate plane to solve real-world and mathematical problems. (6.NS.8)
StandardWhat Does It Mean?
What Does It Look Like?
Vocabulary
Standard Algorithm: A way of setting out a step a step-by-step mathematical procedure
Multiples: The product of a given whole number and another number. For example, the multiples of 10 are 0, 10, 20, 30, 40, 50, ...
Operations: Addition, Subtraction, Multiplication, Division
Rational Numbers: A real number that can be written as: a ratio of two integers (fraction), excluding zero as a denominator; a repeating or terminating decimal; or an integer
Factors: The numbers being multiplied together to form a product.
Absolute Value: The value of the number, ignoring the sign. The distance the number is from zero on the number line written | x | = x or | -x | = x
Great Common Factor (GCF): The greatest factor that two or more numbers have in common
Coordinate Plane: A plane containing two perpendicular axes (x and y) intersecting at a point called the origin (0, 0)
Integers: A set of whole numbers and their opposites.
Negative Integer: Any integer less than zero.
Positive Integer: Any integer greater than zero.
Fraction: A way of representing part of a whole number or part of a group by telling the number of equal parts in the whole and the number of those parts you are describing.
Activities At Home
Pick or create numbers to make fractions with. Add, subtract, multiply, divide, or simplify using the fractions
you created.With a partner, pick numbers. Race to find the common factors of those numbers.
With a partner, choose fractions. Race to put the fractions in order from least to greatest or greatest to least.
Find examples of integers in the newspaper, on the internet, or in magazines.
Create or pick numbers to make decimals. Add, subtract, multiply, or divide the decimals.
Create a treasure map on a coordinate plane. Write clues, using coordinates, to find the treasure.
Learning Links
Ordering Rational Numbers
Sixth Grade Expressions and Equations
What Your Child Will Learn
*Write and evaluate numerical expressions involving whole-number exponents (6.EE.1)
Write, read, and evaluate expressions in which letters stand for numbers (6.EE.2)
Simplify algebraic expressions using the distributive, associative, and communicative properties when appropriate.
For example, 3 (2 + x) can be expressed as 6 + 3x (6.EE.3)
Identify equivalent expressions. For example, the expressions y + y + y and 3y are equivalent because they name
the same number regardless of which number y stands for (6.EE.4)
Understand equations and inequalities (6.EE.5)
Use variables and expressions to solve real-world problems (6.EE.6)
Use variables and equations to solve real-world problems (6.EE.7)
Write inequalities for real-world or mathematical problems (6.EE.8)
Use variables to represent two quantities in a real-world problem (6.EE.9)
StandardWhat Does It Look Like?
What Does It Mean?
Vocabulary
Expression: A mathematical combination of numbers, variables, and operations.
Exponent: Shows the number of times the base number is multiplied by itself.
Variables: A quantity that can change or vary, taking on different values.
Distributive Property: Multiplying a number is the same as multiplying its addends by the number, then adding the products.
6 x 9 = 6 x (4 + 5) = (6 x 4) + (6 x 5) = 24 + 30 = 54
Associative Property: In addition or multiplication, no matter how the numbers are grouped, the answer will always be the same (a + b) + c = a + (b + c)
Communicative Property: In addition and multiplication, numbers may be added or multiplied together in any order.
a + b = b + a
Equivalent: Having the same value
Inequalities: Not equal in size, amount or value
Activities At Home
Write expressions to describe real life things (siblings age, number of pets, etc.)
Write expressions and use order of operations to solve.
Write a story incorporating variables. Have a friend try to solve for the variables.
Make flashcards using algebraic expressions and properties.
Learning Links
Sixth Grade Ratio and Proportion
What Your Child Will Learn
Understand the concept of a ratio (6.RP.1)
Understand the concept of unit rate (6.RP.2)
Use ratio and rate reasoning to solve real world problems (6.RP.3)
StandardWhat Does It Look Like?
What Does It Mean?
Vocabulary
Ratio: A comparison of two numbers. Example: 3 : 4, 3/4, or 3 to 4.
Equivalent Ratios: Ratios that name the same comparisons.
Proportion: A statement that two ratios are equal - two fractions that are equal, (e.g. 3/4 = 6/8)
Unit Rate: A comparison of two measurements in which one of the terms has a value of 1.
Rate: A ratio that compares quantities measured in different units.
Activities At Home
Practice finding ratios and equal ratios by finding equivalent fractions.
Create ratios for objects around the house. For example, the ratio of male shoes to female shoes.
Create fractions. Find fractions that are equivalent to the original fraction.
Go to the grocery store and find the unit rates for different items at the store.
Learning Links
Sixth Grade Geometry
What Your Child Will Learn
Find the area of regular and irregular polygons (6.G.1)
Find the volume of rectangular prisms (6.G.2)
Represent three-dimensional figures using nets (6.G.4)
Draw polygons in the coordinate plane to solve real-world and mathematical problems (6.G.3)
StandardWhat Does It Look Like?
What Does It Mean?
Vocabulary
Area: Measured in square units, the size a surface takes up
Volume: The amount of space that a three-dimensional figure contains. Volume is expressed in cubic units, (how many small cubes would fit inside a solid figure)
Regular Polygons: A plane shape that has equal sides or equal angles
Coordinate Plane: A plane containing two perpendicular axes (x and y) intersecting at a point called the origin (0, 0)
Irregular Polygons: A plane shape that does not have all side equal or all angles equal
Three-Dimensional Figure: A measure in three directions, such as length and width
Rectangular Prism: A solid figure in which all six faces are rectangles
Net: A two-dimensional object that can be folded to make a three-dimensional objectActivities At Home
Write clues to describe polygons. Try to guess your partners polygon.
Use a compass or computer to draw geometric figures.
Take the measurements of your bedroom. Determine the amount of carpet needed to cover the floor. Determine the amount of wallpaper to cover your walls.
Estimate the size of your classroom. Determine the area and volume of your classroom. Think about different ways you could figure out the volume without measuring with a yard stick or measuring tape.
Using weighted paper, draw a net of a three-dimensional figure. Using color pencils, decorate and cut.
Learning Links
Nets
Area
Sixth Grade Statistics and Probability
What Your Child Will Learn
Standard
Understand center measures (mean, median, mode) and measures of variation (range) (6.SP.3)
Recognize a statistical question as one that accounts for changes in data based on the question. "How old am I?" is not a statistical question, but "How old are the students in my school?" is a statistical question because one accounts for changes in students' ages (6.SP.1)
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 (6.SP.2)
Display numerical data in plots on a number line, including dot plots, histograms, and box plots (6.SP.4)
Explain data sets in relation to their context, such as by:
Reporting the number of observations
Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.
Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.
Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. (6.SP.5)
What Does It Look Like?
What Does It Mean?
Lesson Set
Lesson Set 1
Lesson Set 2
Lesson Set
Vocabulary
Data Set: A collection of data points
Median: When numbers are arranged from least to greatest, the median is the middle number or mean of two middle numbers.
Center Measures: The "middle' value or perhaps the typical value of the data, most frequently measured using mean, median and mode.
Mode: The number that appears most frequently in a set of data.
Measures of Variation: A measure that describes how spread out or "scattered" a set of data.
Range: The difference between the greatest and the least numbers in a set of data.
Mean: A number found by adding the data and dividing by the number of data. It is also referred to as the average.
Number Line: A line marked with numbers, used to show operations.
Dot Plots: A number line long enough to encompass all numbers in the sample, showing a dot over the position corresponding to each number.
Histograms: A bar graph representing frequency distribution for certain ranges or intervals.
Box Plots: A diagram or graph using a number line to show the distribution of a set of data. The box plot displays the median, upper and lower quartiles, and the maximum and minimum values of the data.
Interquartile Range: The difference between the first quartile and third quartile of a set of data. This is one way to describe the spread of a set of data.
Mean Absolute Deviation: Average distance between each data value and the mean.
Cluster: A group of data that appears bunched together on a line plot.
Activities At Home
Find the mean, median, mode and range of different data sets. The sports section in the newspaper or on the internet could offer some good data sets.
Look in newspapers, magazines, and appropriate online resources to analyze, interpret, and make predictions about different graphs and tables.
Find different data sets and have your student create an appropriate way to display the data (dot plots, histograms, box plots, etc.)
Practice multiplication and division facts.
Learning Links