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# Virginia - Mathematics: 6th Grade

## VA--Standards of Learning | Adopted: 2016

### NS: : Number and Number Sense

NS.6.1: : The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b.

Beam to Moon (Ratios and Proportions)

Apply ratios and proportions to find the weight of a person on the moon (or on another planet). Weigh an object on Earth and on the moon and weigh the person on Earth. Then set up and solve the proportion of the Earth weights to the moon weights. 5 Minute Preview

Part-to-part and Part-to-whole Ratios

Compare a ratio represented by an area with its percent, fraction, and decimal forms. 5 Minute Preview

NS.6.2: : The student will

NS.6.2.a: : represent and determine equivalencies among fractions, mixed numbers, decimals, and percents; and

Fraction, Decimal, Percent (Area and Grid Models)

Model and compare fractions, decimals, and percents using area models. Each area model can have 10 or 100 sections and can be set to display a fraction, decimal, or percent. Click inside the area models to shade them. Compare the numbers visually or on a number line. 5 Minute Preview

Improper Fractions and Mixed Numbers

Represent a quantity given by a shaded region as an improper fraction and as a mixed number. Experiment with different shaded regions sliced differently. 5 Minute Preview

Modeling Decimals (Area and Grid Models)

Model and compare decimals using area models. Set the number of sections in each model to 1, 10, or 100, and then click in the models to shade sections. Compare decimals visually and on a number line. 5 Minute Preview

Percents, Fractions, and Decimals

Compare a quantity represented by an area with its percent, fraction, and decimal forms. 5 Minute Preview

NS.6.2.b: : compare and order positive rational numbers.

Comparing and Ordering Decimals

Use grids to model decimal numbers and compare them graphically. Then compare the numbers on a number line. 5 Minute Preview

NS.6.3: : The student will

NS.6.3.a: : identify and represent integers;

Integers, Opposites, and Absolute Values

Compare and order integers using draggable points on a number line. Also explore opposites and absolute values on the number line. 5 Minute Preview

NS.6.3.b: : compare and order integers; and

Integers, Opposites, and Absolute Values

Compare and order integers using draggable points on a number line. Also explore opposites and absolute values on the number line. 5 Minute Preview

Rational Numbers, Opposites, and Absolute Values

Use a number line to compare rational numbers. Change values by dragging points on the number line. Compare the opposites and absolute values of the numbers. 5 Minute Preview

NS.6.3.c: : identify and describe absolute value of integers.

Integers, Opposites, and Absolute Values

Compare and order integers using draggable points on a number line. Also explore opposites and absolute values on the number line. 5 Minute Preview

Rational Numbers, Opposites, and Absolute Values

Use a number line to compare rational numbers. Change values by dragging points on the number line. Compare the opposites and absolute values of the numbers. 5 Minute Preview

NS.6.4: : The student will recognize and represent patterns with whole number exponents and perfect squares.

Square Roots

Explore the meaning of square roots using an area model. Use the side length of a square to find the square root of a decimal number or a whole number. 5 Minute Preview

### CE: : Computation and Estimation

CE.6.5: : The student will

CE.6.5.a: : multiply and divide fractions and mixed numbers;

Dividing Fractions

Divide fractions using area models. Adjust the numerators and denominators of the divisor and dividend and see how the area model and calculation change. 5 Minute Preview

Dividing Mixed Numbers

Choose the correct steps to divide mixed numbers. Use step-by-step feedback to diagnose and correct incorrect steps. 5 Minute Preview

Multiplying Fractions

Multiply two fractions using an area model. Vary the vertical area to change one fraction and vary the horizontal area to change the other. Then examine the intersection of the areas to find the product. 5 Minute Preview

Multiplying Mixed Numbers

Choose the correct steps to multiply mixed numbers. Use the step-by-step feedback to diagnose incorrect steps. 5 Minute Preview

CE.6.5.b: : solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers; and

Dividing Fractions

Divide fractions using area models. Adjust the numerators and denominators of the divisor and dividend and see how the area model and calculation change. 5 Minute Preview

CE.6.5.c: : solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.

Multiplying with Decimals

Multiply two decimals using a dynamic area model. On a grid, shade the region with width equal to one of the decimals and height equal to the other decimal and find the area of the region. 5 Minute Preview

CE.6.6: : The student will

CE.6.6.a: : add, subtract, multiply, and divide integers;

Adding and Subtracting Integers

Add and subtract integers on a number line using dynamic arrows. 5 Minute Preview

Adding and Subtracting Integers with Chips

Use chips to model addition and subtraction of positives and negatives. Explore the effect of zero pairs. See how to use zero pairs to help special cases of addition and subtraction. 5 Minute Preview

Adding on the Number Line

Add real numbers using dynamic arrows on a number line. Find the sum of the numbers at the end of the final arrow. Compare the numerical calculation. 5 Minute Preview

CE.6.6.c: : simplify numerical expressions involving integers.

Adding and Subtracting Integers

Add and subtract integers on a number line using dynamic arrows. 5 Minute Preview

Adding and Subtracting Integers with Chips

Use chips to model addition and subtraction of positives and negatives. Explore the effect of zero pairs. See how to use zero pairs to help special cases of addition and subtraction. 5 Minute Preview

Order of Operations

Select and evaluate the operations in an expression following the correct order of operations. 5 Minute Preview

### MG: : Measurement and Geometry

MG.6.7: : The student will

MG.6.7.a: : derive ϖ (pi);

Circumference and Area of Circles

Resize a circle and compare its radius, circumference, and area. 5 Minute Preview

MG.6.7.b: : solve problems, including practical problems, involving circumference and area of a circle; and

Circumference and Area of Circles

Resize a circle and compare its radius, circumference, and area. 5 Minute Preview

MG.6.7.c: : solve problems, including practical problems, involving area and perimeter of triangles and rectangles.

Area of Parallelograms

Examine and manipulate a parallelogram and find its area. Explore the relationship between the area of a parallelogram and the area of a rectangle using an animation. 5 Minute Preview

Area of Triangles

Use a dynamic triangle to explore the area of a triangle. With the help of an animation, see that any triangle is always half of a parallelogram (with the same base and height). Likewise, a similar animation shows the connection between parallelograms and rectangles. 5 Minute Preview

Chocomatic (Multiplication, Arrays, and Area)

Use the Chocomatic to design candy bars made out of chocolate squares. Use multiplication to find the number of squares in each chocolate bar. Build collections of chocolate bars that all have the same number of squares. Solve multiplication problems by joining two smaller chocolate bars into a large bar. 5 Minute Preview

Fido's Flower Bed (Perimeter and Area)

Construct models of gardens on a grid using squares of sod. Fence the gardens to find and compare perimeters. Work with pre-built gardens made of 36 squares each to compare perimeters of shapes with equal areas. 5 Minute Preview

Perimeter and Area of Rectangles

Discover how to find the perimeter and area of a rectangle, and of a square (which is really just a special case of a rectangle). 5 Minute Preview

MG.6.8: : The student will

MG.6.8.a: : identify the components of the coordinate plane; and

City Tour (Coordinates)

Go sightseeing in fictional cities all over the world. Learn about coordinates on a graph by navigating around these cities on a grid-like city map. Some landmarks are shown on the map. For others, you are only given the coordinates. Can you find all of them? 5 Minute Preview

Points in the Coordinate Plane

Identify the coordinates of a point in the coordinate plane. Drag the point in the plane and investigate how the coordinates change in response. 5 Minute Preview

Points, Lines, and Equations

Compare the graph of a linear function to its rule and to a table of its values. Change the function by dragging two points on the line. Examine how the rule and table change. 5 Minute Preview

MG.6.8.b: : identify the coordinates of a point and graph ordered pairs in a coordinate plane.

City Tour (Coordinates)

Go sightseeing in fictional cities all over the world. Learn about coordinates on a graph by navigating around these cities on a grid-like city map. Some landmarks are shown on the map. For others, you are only given the coordinates. Can you find all of them? 5 Minute Preview

Function Machines 2 (Functions, Tables, and Graphs)

Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview

Points in the Coordinate Plane

Identify the coordinates of a point in the coordinate plane. Drag the point in the plane and investigate how the coordinates change in response. 5 Minute Preview

Points, Lines, and Equations

Compare the graph of a linear function to its rule and to a table of its values. Change the function by dragging two points on the line. Examine how the rule and table change. 5 Minute Preview

### PS: : Probability and Statistics

PS.6.10: : The student, given a practical situation, will

PS.6.10.a: : represent data in a circle graph;

Graphing Skills

Create a graph (bar graph, line graph, pie chart, or scatter plot) based on a given data set. Title the graph, label the axes, and choose a scale. Adjust the graph to fit the data, and then check your accuracy. The Gizmo can also be used to create a data table based on a given graph. 5 Minute Preview

PS.6.10.b: : make observations and inferences about data represented in a circle graph; and

Graphing Skills

Create a graph (bar graph, line graph, pie chart, or scatter plot) based on a given data set. Title the graph, label the axes, and choose a scale. Adjust the graph to fit the data, and then check your accuracy. The Gizmo can also be used to create a data table based on a given graph. 5 Minute Preview

PS.6.11: : The student will

PS.6.11.a: : represent the mean of a data set graphically as the balance point; and

Mean, Median, and Mode

Build a data set and find the mean, median, and mode. Explore the mean, median, and mode illustrated as frogs on a seesaw, frogs on a scale, and as frogs stacked under a bar of variable height. 5 Minute Preview

PS.6.11.b: : determine the effect on measures of center when a single value of a data set is added, removed, or changed.

Describing Data Using Statistics

Investigate the mean, median, mode, and range of a data set through its graph. Manipulate the data and watch how the mean, median, mode, and range change (or, in some cases, how they don't change). 5 Minute Preview

Mean, Median, and Mode

Build a data set and find the mean, median, and mode. Explore the mean, median, and mode illustrated as frogs on a seesaw, frogs on a scale, and as frogs stacked under a bar of variable height. 5 Minute Preview

### PFA: : Patterns, Functions, and Algebra

PFA.6.12: : The student will

PFA.6.12.a: : represent a proportional relationship between two quantities, including those arising from practical situations;

Beam to Moon (Ratios and Proportions)

Apply ratios and proportions to find the weight of a person on the moon (or on another planet). Weigh an object on Earth and on the moon and weigh the person on Earth. Then set up and solve the proportion of the Earth weights to the moon weights. 5 Minute Preview

Part-to-part and Part-to-whole Ratios

Compare a ratio represented by an area with its percent, fraction, and decimal forms. 5 Minute Preview

Percents and Proportions

Find a part from the percent and whole, a percent from the part and whole, or a whole from the part and percent using a graphic model. 5 Minute Preview

Proportions and Common Multipliers

Complete a proportion using a graphical model. Use counters to fill cells in the numerators and denominators given. Use the visual pattern to determine how many counters to put in the missing numerator or denominator. 5 Minute Preview

Slope-Intercept Form of a Line

Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview

PFA.6.12.b: : determine the unit rate of a proportional relationship and use it to find a missing value in a ratio table;

Beam to Moon (Ratios and Proportions)

Apply ratios and proportions to find the weight of a person on the moon (or on another planet). Weigh an object on Earth and on the moon and weigh the person on Earth. Then set up and solve the proportion of the Earth weights to the moon weights. 5 Minute Preview

PFA.6.12.c: : determine whether a proportional relationship exists between two quantities; and

Proportions and Common Multipliers

Complete a proportion using a graphical model. Use counters to fill cells in the numerators and denominators given. Use the visual pattern to determine how many counters to put in the missing numerator or denominator. 5 Minute Preview

PFA.6.12.d: : make connections between and among representations of a proportional relationship between two quantities using verbal descriptions, ratio tables, and graphs.

Part-to-part and Part-to-whole Ratios

Compare a ratio represented by an area with its percent, fraction, and decimal forms. 5 Minute Preview

PFA.6.13: : The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable.

Modeling One-Step Equations

Solve a linear equation using a tile model. Use feedback to diagnose incorrect steps. 5 Minute Preview

Modeling and Solving Two-Step Equations

Solve a two-step equation using a cup-and-counter model. Use step-by-step feedback to diagnose and correct incorrect steps. 5 Minute Preview

Solving Algebraic Equations I

Are there times when you wish you could escape from everyone and just be alone? Meet our variable friend, a real loner who doesn't like coefficients and neighboring terms. Learn how to use inverses to isolate a variable – a foundational skill for solving algebraic equations. 5 Minute Preview

Solving Algebraic Equations II

Is solving equations tricky? If you know how to isolate a variable, you're halfway there. The other half? Don't do anything to upset the balance of an equation. Join our plucky variable friend as he encounters algebraic equations and a (sometimes grumpy) equal sign. With a little practice, you'll find that solving equations isn't tricky at all. 5 Minute Preview

Solving Equations by Graphing Each Side

Solve an equation by graphing each side and finding the intersection of the lines. Vary the coefficients in the equation and explore how the graph changes in response. 5 Minute Preview

Solving Equations on the Number Line

Solve an equation involving decimals using dynamic arrows on a number line. 5 Minute Preview

PFA.6.14: : The student will

PFA.6.14.a: : represent a practical situation with a linear inequality in one variable; and

Solving Linear Inequalities in One Variable

Solve one-step inequalities in one variable. Graph the solution on a number line. 5 Minute Preview

PFA.6.14.b: : solve one-step linear inequalities in one variable, involving addition or subtraction, and graph the solution on a number line.

Exploring Linear Inequalities in One Variable

Solve inequalities in one variable. Examine the inequality on a number line and determine which points are solutions to the inequality. 5 Minute Preview

Solving Linear Inequalities in One Variable

Solve one-step inequalities in one variable. Graph the solution on a number line. 5 Minute Preview

Correlation last revised: 9/16/2020

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