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6-1: Whole Number Multiplication & Division (Lime Green)
Key Vocabulary:
• algorithm • product • difference • quotient • dividend • remainder • divisor • sum • factor of a number
• algorithm • product • difference • quotient • dividend • remainder • divisor • sum • factor of a number
1.1 Applying Properties of Arithmetic
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1.2 Division with Remainder
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1.3 Multiplication & Division: Standard AlgorithmsStudents review the standard algorithm for multiplication of whole numbers. Then students review the standard algorithm for division of whole numbers.
Standards 4.NBT.B, 5.NBT.A, 6.NS.B |
6-2: Whole Number Applications (Blue)
Key Vocabulary:
• base • least common multiple • composite number • multiple • exponential notation • order of operations • factor • prime number • greatest common factor • square number
• base • least common multiple • composite number • multiple • exponential notation • order of operations • factor • prime number • greatest common factor • square number
2.1 Factors & MultiplesStudents review factors and multiples of numbers, and prime and composite numbers.
Standards 6.NS.B |
2.2 GCF & LCMStudents learn how to find the greatest common factor (GCF) of two natural numbers and the least common multiple (LCM) of two natural numbers. Students use GCF and LCM to solve problems. Standards 6.NS.B
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2.3 Numerical ExpressionsStudents use their knowledge of greatest common factor to write equivalent expressions using the distributive property. Students learn about exponents. Students simplify expressions using the conventions for the order of operations.
Standards 6.EE.A |
6-3: Fraction Concepts (Yellow)
Key vocabulary:
• area model for fractions • benchmark fraction • denominator • equivalent fractions • fraction • inequality • linear model for fraction • multiplicative identity property • numerator • unit fraction
• area model for fractions • benchmark fraction • denominator • equivalent fractions • fraction • inequality • linear model for fraction • multiplicative identity property • numerator • unit fraction
3.1 Fraction Slips |
3.2 Ordering Fractions on a Number Line |
3.3 Renaming Fractions |
Students use a linear model to explore fraction equivalence. Students use sense-making strategies to order fractions. Students read and measure with a ruler. Students identify improper fractions and mixed numbers on a number line.
Standards 4.NF.A |
Students use sense-making strategies to order fractions on a number line.
Standards 4.NF.A |
Students represent fractions greater than one as mixed numbers and as improper fractions using an area model, a set model, and a linear model. Students explore how mixed numbers are used on a ruler that is marked off in inches.
Standards 4.NF.A |
6-4 Decimal Concepts (Magenta)
Key vocabulary:
• area model for fractions • decimal • denominator • equivalent fractions • fraction • linear model for fractions • numerator • percent • place value number system
• area model for fractions • decimal • denominator • equivalent fractions • fraction • linear model for fractions • numerator • percent • place value number system
4.1 Fractions & Decimals |
4.2 Decimal Place Value & Number Lines |
4.3 Fraction, Decimal & Percent Gardens |
Students represent fractions and decimals with pictures (area models), numbers, and words. Students write fractions whose denominators are powers of 10 in decimal form.
Standards 4.NF.C, 5.NBT.A |
Students compare and order decimals on a number line and ruler.
Standards 4.NF.C, 5.NBT.A |
Students use an area model to explore fraction, decimal, and percent concepts.
Standards 4.NF.C, 5.NBT.A, 6.RP.A |
6-5 Data & Statistics (Green)
Key vocabulary:
• box plot • mean absolute deviation (MAD) • dot plot • median • five-number summary • mode • histogram • number of observations • interquartile range (IQR) • outlier • mean • range of a data set
• box plot • mean absolute deviation (MAD) • dot plot • median • five-number summary • mode • histogram • number of observations • interquartile range (IQR) • outlier • mean • range of a data set
5.1 Name ScoresStudents find our “name scores” using the given values for each letter. Then students create a human number line to help us organize our data. Students calculate the five-number summary and observe measures of center and spread for the name score data.
Standards 6.SP.A, 6.SP.B |
5.2 Data DisplaysStudents display data by constructing dot plots, histograms, and box plots. Students describe and analyze the overall shape of the data.
Standards 6.SP.A, 6.SP.B |
Data SurveysStudents gather data through a class activity. Students display data by constructing dot plots, histograms, and box plots. Students describe and analyze the overall shape of the data.
Standards 6.SP.A, 6.SP.B |
6-6 Fraction Addition & Subtraction (Purple)
Key vocabulary:
• common denominator • difference • equivalent fractions • estimate • greatest common factor • least common denominator • least common multiple • multiplicative identity property • sum
• common denominator • difference • equivalent fractions • estimate • greatest common factor • least common denominator • least common multiple • multiplicative identity property • sum
6.1 Equivalent Fractions |
6.2 Fraction Addition |
6.3 Fraction Subtraction |
Students use diagrams to illustrate equivalent fractions. Students connect the diagrams to computations. Students compare fractions in a problem solving setting.
Standards 5.NF.A, 6.NS.B |
Students review adding fractions and learn different methods to add mixed numbers.
Standards 5.NF.A, 6.NS.B |
Students review subtracting fractions, and learn different methods to subtract fractions.
Standards 5.NF.A, 6.NS.B |
6-7 Fraction Multiplication & Division (Orange)
Key vocabulary:
• commutative property of multiplication • product • distributive property • quotient • divisor • reciprocal • factor • remainder • multiplicative identity property
• commutative property of multiplication • product • distributive property • quotient • divisor • reciprocal • factor • remainder • multiplicative identity property
7.1 Fraction Multiplication |
7.2 Fraction Division 1 |
7.3 Fraction Division 2 |
Students use whole number multiplication concepts to provide meaning for fraction multiplication. Students develop procedures to multiply fractions.
Standards 5.NF.B |
Students explore division of fractions in measuring contexts, and explore whether the multiply-across rule for multiplication can be extended to division.
Standards 5.NF.B, 6.NS.A |
Students explore division of fractions in measuring and fair-share contexts, and learn an efficient rule for dividing fractions.
Standards 5.NF.B, 6.NS.A |
6-8 Decimal Operations (Pink)
Key vocabulary:
• addend • minuend • decimal • product • difference • quotient • dividend • subtrahend • divisor • sum • factor of a number
• addend • minuend • decimal • product • difference • quotient • dividend • subtrahend • divisor • sum • factor of a number
8.1 A Checking AccountStudents add and subtract decimal numbers. Students learn to maintain a check register and write checks.
Standards 5.NBT.B |
8.2 Decimal MultiplicationStudents explore decimal multiplication using repeated addition, an area model, and decimal-fraction equivalence.
Standards 5.NBT.A, 5.NBT.B, 6.NS.B |
8.3 Decimal DivisionStudents explore concepts related to decimal division and establish an algorithm for dividing a decimal number by a decimal number. Students use decimals to solve a problem.
Standards 5.NBT.A, 5.NBT.B, 6.NS.B |
6-9 Expressions & Equations 1 (Lime Green)
Key vocabulary:
• coefficient • inequality • constant term • like terms • equation • product • expression • term • factor of a number • variable
• coefficient • inequality • constant term • like terms • equation • product • expression • term • factor of a number • variable
9.1 Introduction to Variables & ExpressionsStudents write and evaluate algebraic expressions. Students represent the costs of items on a menu algebraically. Students translate verbal statements into numerical or variable expressions.
Standards 6.NS.B, 6.EE.A |
9.2 EquationsStudents represent the costs of items on a menu algebraically. Students find values that make equations true. Students translate verbal statements into numerical or variable equations.
Standards 6.NS.B, 6.EE.A, 6.EE.B |
9.3 InequalitiesStudents write linear inequalities with one variable. Students find values that make inequalities true.
Standards 6.NS.B, 6.EE.B |
6-10 Expressions & Equations 2 (Blue)
Key vocabulary:
• area • order of operations • distributive property • perimeter • equation • solve an equation • exponential notation • variable • expression • volume • inverse operations
• area • order of operations • distributive property • perimeter • equation • solve an equation • exponential notation • variable • expression • volume • inverse operations
10.1 Numerical and Variable ExpressionsStudents apply the order of operations conventions. Students write and evaluate numerical and algebraic expressions.
Standards 6.NS.B, 6.EE.A |
10.2 Equation Solving Strategies
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10.3 Solving Equations with Fractions & DecimalsStudents solve equations that include fraction and decimal coefficients and constants. Standards 6.NS.B, 6.EE.B
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6-11 Ratios & Unit Rates (Yellow)
Key vocabulary:
• double number line diagram • unit price • equivalent ratios • unit rate • ratio • value of a ratio • tape diagram
• double number line diagram • unit price • equivalent ratios • unit rate • ratio • value of a ratio • tape diagram
11.1 RatiosStudents define ratio and explore when ratios are equivalent. Students represent ratios using tables and diagrams, and solve problems involving ratios.
Standards 6.RP.A |
11.2 Unit RatesStudents explore the relationship between ratios and rates, and unit rate is defined. Students represent ratios and rates with tables and double number line diagrams, and solve problems using rates.
Standards 6.RP.A |
11.3 Ratio & Unit Rate ProblemsStudents solve ratio and rate problems using tables, diagrams, and equations.
Standards 6.RP.A |
6-12 Measurement Conversions & Percent (Magenta)
Key vocabulary:
• conversion rate • percent of a number • customary measurement unit • ratio • metric measurement unit • unit rate • percent
• conversion rate • percent of a number • customary measurement unit • ratio • metric measurement unit • unit rate • percent
12.1 Measurement ConversionsStudents use double number lines and tables to compare and convert units of measure, both within and between measurement systems. Students use conversion rates to make conversions.
Standards 6.RP.A |
12.2 Understanding Percents of NumbersStudents use double number lines and chunking strategies to find percents of numbers.
Standards 6.RP.A |
12.3 Percent ProblemsStudents solve more percent problems using double number line diagrams and chunking. Students learn a multiplication procedure for finding percents of numbers.
Standards 6.RP.A |
6-13 Geometry (Green)
Key vocabulary:
• altitude of a parallelogram • apex • area • base • net • polygon • polyhedron • prism • pyramid • surface area • volume
• altitude of a parallelogram • apex • area • base • net • polygon • polyhedron • prism • pyramid • surface area • volume
13.1 Area of PolygonsStudents establish formulas for areas of parallelograms, triangles, and trapezoids. Students find areas of irregular polygons. Students apply area formulas to solve problems.
Standards 6.EE.A, 6.G.A |
13.2 VolumeStudents establish formulas for the volume of a right rectangular prism in three ways. Students solve real world and mathematical problems that involve volume.
Standards 6.EE.A, 6.G.A |
13.3 Surface AreaStudents construct polyhedra from nets. Students use nets to find surface areas of polyhedra.
Standards 6.EE.A, 6.G.A |
6-14 Rational Numbers on a Number Line (Purple)
Key vocabulary:
• absolute value • integer • distance • opposite of a number • inequality • rational number
• absolute value • integer • distance • opposite of a number • inequality • rational number
14.1 IntegersStudents extend the number line to include integers. Students use temperature as a context to locate numbers, write inequalities, and solve problems. Students use arrows to represent direction and distance.
Standards 6.NS.C |
14.2 Opposites & Absolute ValueStudents interpret and find the value of the opposite of a number. Students interpret and find the value of the absolute value of a number.
Standards 6.NS.C |
14.3 Rational NumbersStudents use number lines to explore the meaning of rational numbers. Students find opposites and absolute values of rational numbers. Students use arrows on a number line to represent direction and distance, and to solve problems with rational numbers. Students graph solutions to inequalities on the number line.
Standards 6.NS.C, 6.EE.B |
6-15 Graphing in the Coordinate Plane (Orange)
Key vocabulary:
• coordinate plane • vertex • line of symmetry • x-axis • ordered pair • x-coordinate • quadrant • y-axis • reflection • y-coordinate
• coordinate plane • vertex • line of symmetry • x-axis • ordered pair • x-coordinate • quadrant • y-axis • reflection • y-coordinate
15.1 Graphing Points with Integer CoordinatesStudents graph ordered pairs of integers in the coordinate plane in one quadrant and in four quadrants. Students solve graphing challenges, scale graphs appropriately, draw polygons in the plane given coordinates of vertices, and find the lengths of horizontal and vertical line segments.
Standards 6.NS.C, 6.G.A |
15.2 Graphing Points with Rational CoordinatesStudents graph ordered pairs of rational numbers in four quadrants. Students solve graphing challenges, scale graphs appropriately, draw polygons in the plane given coordinates of vertices, and find the lengths of horizontal and vertical segments.
Standards 6.NS.C, 6.G.A |
15.3 Reflections
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6-16 Applications of Proportional Reasoning (Pink)
Key vocabulary:
• coordinate plane • dependent variable • double number line diagram • equivalent ratios • independent variable • input-output rule • ordered pair • tape diagram • unit price • unit rate
• coordinate plane • dependent variable • double number line diagram • equivalent ratios • independent variable • input-output rule • ordered pair • tape diagram • unit price • unit rate
16.1 Saving for a Purchase |
16.2 Best Buy Problems |
16.3 Painting a Room |
Students use input-output rules, tables, and graphs to determine how much time is needed to save for purchases. Students use this context to recognize the relationship between independent and dependent variables.
Standards 6.EE.B, 6.EE.C |
Students use numbers, graphs, and equations to determine which choices are better buys.
Standards 6.RP.A, 6.EE.B, 6.EE.C |
Students solve problems that involve ratio reasoning and many of the mathematical concepts and skills we have learned this year.
Standards 6.RP.A, 6.EE.A, 6.EE.B, 6.EE.C, 6.G.A |