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  • Virginia Standards
  • Mathematics: 6th Grade

Virginia - Mathematics: 6th Grade

Standards of Learning | Adopted: 2023

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.

6.NS: : Number and Number Sense


6.NS.1: : The student will reason and use multiple strategies to express equivalency, compare, and order numbers written as fractions, mixed numbers, decimals, and percents.

6.NS.1.a: : Estimate and determine the percent represented by a given model (e.g., number line, picture, verbal description), including percents greater than 100% and less than 1%.

Screenshot of Fraction, Decimal, Percent (Area and Grid Models)

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


Lesson Info
Launch Gizmo
Screenshot of Part-to-part and Part-to-whole Ratios

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


Lesson Info
Launch Gizmo
Screenshot of Percents, Fractions, and Decimals

Percents, Fractions, and Decimals

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


Lesson Info
Launch Gizmo

6.NS.1.b: : Represent and determine equivalencies among decimals (through the thousandths place) and percents incorporating the use of number lines, and concrete and pictorial models.

Screenshot of Fraction, Decimal, Percent (Area and Grid Models)

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


Lesson Info
Launch Gizmo
Screenshot of Part-to-part and Part-to-whole Ratios

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


Lesson Info
Launch Gizmo
Screenshot of Percents, Fractions, and Decimals

Percents, Fractions, and Decimals

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


Lesson Info
Launch Gizmo

6.NS.1.c: : Represent and determine equivalencies among fractions (proper or improper) and mixed numbers that have denominators that are 12 or less or factors of 100 and percents incorporating the use of number lines, and concrete and pictorial models.

Screenshot of Fraction, Decimal, Percent (Area and Grid Models)

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


Lesson Info
Launch Gizmo
Screenshot of Part-to-part and Part-to-whole Ratios

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


Lesson Info
Launch Gizmo
Screenshot of Percents, Fractions, and Decimals

Percents, Fractions, and Decimals

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


Lesson Info
Launch Gizmo

6.NS.1.d: : Represent and determine equivalencies among decimals, percents, fractions (proper or improper), and mixed numbers that have denominators that are 12 or less or factors of 100 incorporating the use of number lines, and concrete and pictorial models.

Screenshot of Fraction, Decimal, Percent (Area and Grid Models)

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


Lesson Info
Launch Gizmo
Screenshot of Part-to-part and Part-to-whole Ratios

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


Lesson Info
Launch Gizmo
Screenshot of Percents, Fractions, and Decimals

Percents, Fractions, and Decimals

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


Lesson Info
Launch Gizmo

6.NS.1.e: : Use multiple strategies (e.g., benchmarks, number line, equivalency) to compare and order no more than four positive rational numbers expressed as fractions (proper or improper), mixed numbers, decimals, and percents (decimals through thousandths, fractions with denominators of 12 or less or factors of 100) with and without models. Justify solutions orally, in writing or with a model. Ordering may be in ascending or descending order.

Screenshot of Ordering Percents, Fractions, and Decimals Greater Than 1

Ordering Percents, Fractions, and Decimals Greater Than 1

Compare and order numbers greater than 1 using area grids and a number line. Examine the numbers represented as percents, improper fractions, and decimals. 5 Minute Preview


Lesson Info
Launch Gizmo

6.NS.2: : The student will reason and use multiple strategies to represent, compare, and order integers.

6.NS.2.a: : Represent integers (e.g., number lines, concrete materials, pictorial models), including models derived from contextual situations, and identify an integer represented by a point on a number line.

Screenshot of Integers, Opposites, and Absolute Values

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


Lesson Info
Launch Gizmo

6.NS.2.b: : Compare and order integers using a number line.

Screenshot of Integers, Opposites, and Absolute Values

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


Lesson Info
Launch Gizmo

6.NS.2.c: : Compare integers, using mathematical symbols (<, >, =).

Screenshot of Integers, Opposites, and Absolute Values

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


Lesson Info
Launch Gizmo

6.NS.2.d: : Identify and describe the absolute value of an integer as the distance from zero on the number line.

Screenshot of Integers, Opposites, and Absolute Values

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


Lesson Info
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6.NS.3: : The student will recognize and represent patterns with whole number exponents and perfect squares.

6.NS.3.a: : Recognize and represent patterns with bases and exponents that are whole numbers.

Screenshot of Exponents and Power Rules

Exponents and Power Rules

Choose the correct steps to simplify expressions with exponents using the rules of exponents and powers. Use feedback to diagnose incorrect steps. 5 Minute Preview


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6.NS.3.b: : Recognize and represent patterns of perfect squares not to exceed 20², by using concrete and pictorial models.

Screenshot of Ordering and Approximating Square Roots

Ordering and Approximating Square Roots

Order square roots on a number line. Approximate the square roots using the side lengths of square regions in a grid. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Square Roots

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


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6.NS.3.c: : Justify if a number between 0 and 400 is a perfect square through modeling or mathematical reasoning.

Screenshot of Ordering and Approximating Square Roots

Ordering and Approximating Square Roots

Order square roots on a number line. Approximate the square roots using the side lengths of square regions in a grid. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Square Roots

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


Lesson Info
Launch Gizmo

6.NS.3.d: : Recognize and represent powers of 10 with whole number exponents by examining patterns in place value.

Screenshot of Number Systems

Number Systems

Explore number systems and convert numbers from one base to another using counter beads in place-value columns. 5 Minute Preview


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6.CE: : Computation and Estimation


6.CE.1: : The student will estimate, demonstrate, solve, and justify solutions to problems using operations with fractions and mixed numbers, including those in context.

6.CE.1.a: : Demonstrate/model multiplication and division of fractions (proper or improper) and mixed numbers using multiple representations.

Screenshot of Dividing Fractions

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


Lesson Info
Launch Gizmo
Screenshot of Dividing Mixed Numbers

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


Lesson Info
Launch Gizmo
Screenshot of Multiplying Fractions

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


Lesson Info
Launch Gizmo
Screenshot of Multiplying Mixed Numbers

Multiplying Mixed Numbers

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


Lesson Info
Launch Gizmo

6.CE.1.b: : Multiply and divide fractions (proper or improper) and mixed numbers that include denominators of 12 or less. Answers are expressed in simplest form.

Screenshot of Dividing Fractions

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


Lesson Info
Launch Gizmo
Screenshot of Dividing Mixed Numbers

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


Lesson Info
Launch Gizmo
Screenshot of Multiplying Fractions

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


Lesson Info
Launch Gizmo
Screenshot of Multiplying Mixed Numbers

Multiplying Mixed Numbers

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


Lesson Info
Launch Gizmo

6.CE.1.c: : Investigate and explain the effect of multiplying or dividing a fraction, whole number, or mixed number by a number between zero and one.

Screenshot of Dividing Fractions

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


Lesson Info
Launch Gizmo

6.CE.1.d: : Estimate, determine, and justify the solution to single-step and multistep problems in context that involve addition and subtraction with fractions (proper or improper) and mixed numbers, with and without regrouping, that include like and unlike denominators of 12 or less. Answers are expressed in simplest form.

Screenshot of Adding Fractions (Fraction Tiles)

Adding Fractions (Fraction Tiles)

Add fractions with the help of the Fractionator, a fraction-tile-making machine in the Gizmo. Model sums by placing the tiles on side-by-side number lines. Explore the usefulness of common denominators in adding. Express sums as improper fractions or mixed numbers. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Fractions Greater than One (Fraction Tiles)

Fractions Greater than One (Fraction Tiles)

Explore fractions greater than one with the Fractionator, a fraction-tile-making machine in the Gizmo. Create sums of fraction tiles on two number lines. Sums greater than one are shown as improper fractions on the top number line, and as mixed numbers on the bottom number line. 5 Minute Preview


Lesson Info
Launch Gizmo
Screenshot of Improper Fractions and Mixed Numbers

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


Lesson Info
Launch Gizmo

6.CE.1.e: : Estimate, determine, and justify the solution to single-step and multistep problems in context that involve multiplication and division with fractions (proper or improper) and mixed numbers that include denominators of 12 or less. Answers are expressed in simplest form.

Screenshot of Dividing Mixed Numbers

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


Lesson Info
Launch Gizmo
Screenshot of Multiplying Mixed Numbers

Multiplying Mixed Numbers

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


Lesson Info
Launch Gizmo

6.CE.2: : The student will estimate, demonstrate, solve, and justify solutions to problems using operations with integers, including those in context.

6.CE.2.a: : Demonstrate/model addition, subtraction, multiplication, and division of integers using pictorial representations or concrete manipulatives.

Screenshot of Adding and Subtracting Integers

Adding and Subtracting Integers

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


Lesson Info
Launch Gizmo
Screenshot of Adding and Subtracting Integers with Chips

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


Lesson Info
Launch Gizmo
Screenshot of Adding on the Number Line

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


Lesson Info
Launch Gizmo

6.CE.2.b: : Add, subtract, multiply, and divide two integers.

Screenshot of Adding and Subtracting Integers

Adding and Subtracting Integers

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


Lesson Info
Launch Gizmo
Screenshot of Adding and Subtracting Integers with Chips

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


Lesson Info
Launch Gizmo
Screenshot of Adding on the Number Line

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


Lesson Info
Launch Gizmo

6.CE.2.d: : Estimate, determine, and justify the solution to one and two-step contextual problems, involving addition, subtraction, multiplication, and division with integers.

Screenshot of Adding and Subtracting Integers with Chips

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


Lesson Info
Launch Gizmo
Screenshot of Adding on the Number Line

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


Lesson Info
Launch Gizmo

6.MG: : Measurement and Geometry


6.MG.1: : The student will identify the characteristics of circles and solve problems, including those in context, involving circumference and area.

6.MG.1.a: : Identify and describe chord, diameter, radius, circumference, and area of a circle.

Screenshot of Circumference and Area of Circles

Circumference and Area of Circles

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


Lesson Info
Launch Gizmo

6.MG.1.b: : Investigate and describe the relationship between:

6.MG.1.b.i: : diameter and radius;

Screenshot of Circumference and Area of Circles

Circumference and Area of Circles

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


Lesson Info
Launch Gizmo

6.MG.1.b.ii: : radius and circumference; and

Screenshot of Circumference and Area of Circles

Circumference and Area of Circles

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


Lesson Info
Launch Gizmo

6.MG.1.b.iii: : diameter and circumference.

Screenshot of Circumference and Area of Circles

Circumference and Area of Circles

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


Lesson Info
Launch Gizmo

6.MG.1.c: : Develop an approximation for pi (3.14) by gathering data and comparing the circumference to the diameter of various circles, using concrete manipulatives or technological models.

Screenshot of Circumference and Area of Circles

Circumference and Area of Circles

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


Lesson Info
Launch Gizmo

6.MG.1.d: : Develop the formula for circumference using the relationship between diameter, radius, and pi.

Screenshot of Circumference and Area of Circles

Circumference and Area of Circles

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


Lesson Info
Launch Gizmo

6.MG.1.e: : Solve problems, including those in context, involving circumference and area of a circle when given the length of the diameter or radius.

Screenshot of Circumference and Area of Circles

Circumference and Area of Circles

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


Lesson Info
Launch Gizmo

6.MG.2: : The student will reason mathematically to solve problems, including those in context, that involve the area and perimeter of triangles and parallelograms.

6.MG.2.a: : Develop the formula for determining the area of parallelograms and triangles using pictorial representations and concrete manipulatives (e.g., two-dimensional diagrams, grid paper).

Screenshot of Area of Parallelograms

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


Lesson Info
Launch Gizmo
Screenshot of Area of Triangles

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


Lesson Info
Launch Gizmo

6.MG.2.b: : Solve problems, including those in context, involving the perimeter and area of triangles and parallelograms.

Screenshot of Area of Parallelograms

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


Lesson Info
Launch Gizmo
Screenshot of Area of Triangles

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


Lesson Info
Launch Gizmo

6.MG.3: : The student will describe the characteristics of the coordinate plane and graph ordered pairs.

6.MG.3.a: : Identify and label the axes, origin, and quadrants of a coordinate plane.

Screenshot of Points in the Coordinate Plane

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


Lesson Info
Launch Gizmo

6.MG.3.b: : Identify and describe the location (quadrant or the axis) of a point given as an ordered pair. Ordered pairs will be limited to coordinates expressed as integers.

Screenshot of Points in the Coordinate Plane

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


Lesson Info
Launch Gizmo

6.MG.3.c: : Graph ordered pairs in the four quadrants and on the axes of a coordinate plane. Ordered pairs will be limited to coordinates expressed as integers.

Screenshot of Points in the Coordinate Plane

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


Lesson Info
Launch Gizmo

6.MG.3.d: : Identify ordered pairs represented by points in the four quadrants and on the axes of the coordinate plane. Ordered pairs will be limited to coordinates expressed as integers.

Screenshot of Points in the Coordinate Plane

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


Lesson Info
Launch Gizmo

6.MG.3.e: : Relate the coordinates of a point to the distance from each axis and relate the coordinates of a single point to another point on the same horizontal or vertical line. Ordered pairs will be limited to coordinates expressed as integers.

Screenshot of Points in the Coordinate Plane

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


Lesson Info
Launch Gizmo

6.MG.3.f: : Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to determine the length of a side joining points with the same first coordinate or the same second coordinate. Ordered pairs will be limited to coordinates expressed as integers. Apply these techniques in the context of solving contextual and mathematical problems.

Screenshot of Points in the Coordinate Plane

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


Lesson Info
Launch Gizmo

6.MG.4: : The student will determine congruence of segments, angles, and polygons.

6.MG.4.a: : Identify regular polygons.

Screenshot of Polygon Angle Sum

Polygon Angle Sum

Derive the sum of the angles of a polygon by dividing the polygon into triangles and summing their angles. Vary the number of sides and determine how the sum of the angles changes. Dilate the polygon to see that the sum is unchanged. 5 Minute Preview


Lesson Info
Launch Gizmo

6.MG.4.c: : Determine the congruence of segments, angles, and polygons given their properties.

Screenshot of Similar Figures

Similar Figures

Vary the scale factor and rotation of an image and compare it to the preimage. Determine how the angle measures and side lengths of the two figures are related. 5 Minute Preview


Lesson Info
Launch Gizmo

6.MG.4.d: : Determine whether polygons are congruent or noncongruent according to the measures of their sides and angles.

Screenshot of Similar Figures

Similar Figures

Vary the scale factor and rotation of an image and compare it to the preimage. Determine how the angle measures and side lengths of the two figures are related. 5 Minute Preview


Lesson Info
Launch Gizmo

6.PS: : Probability and Statistics


6.PS.1: : The student will apply the data cycle (formulate questions; collect or acquire data; organize and represent data; and analyze data and communicate results) with a focus on circle graphs.

6.PS.1.d: : Organize and represent data using circle graphs, with and without the use of technology tools. The number of data values should be limited to allow for comparisons that have denominators of 12 or less or those that are factors of 100 (e.g., in a class of 20 students, 7 choose apples as a favorite fruit, so the comparison is 7 out of 20, 7/20, or 35%).

Screenshot of Mascot Election (Pictographs and Bar Graphs)

Mascot Election (Pictographs and Bar Graphs)

A brand new school is opening and it is time to elect the school mascot! Students can choose the Eagle, Lion, Bear, or Wolf. Voting results can be displayed in a table, tally chart, pictograph, bar graph, circle graph, or dot plot. You can change student votes by selecting a group of students and clicking a mascot. 5 Minute Preview


Lesson Info
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6.PS.2: : The student will represent the mean as a balance point and determine the effect on statistical measures when a data point is added, removed, or changed.

6.PS.2.a: : Represent the mean of a set of data graphically as the balance point represented in a line plot (dot plot).

Screenshot of Mean, Median, and Mode

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


Lesson Info
Launch Gizmo

6.PS.2.b: : Determine the effect on measures of center when a single value of a data set is added, removed, or changed.

Screenshot of Mean, Median, and Mode

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


Lesson Info
Launch Gizmo

6.PS.2.c: : Observe patterns in data to identify outliers and determine their effect on mean, median, mode, or range.

Screenshot of Mean, Median, and Mode

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


Lesson Info
Launch Gizmo

6.PFA: : Patterns, Functions, and Algebra


6.PFA.1: : The student will use ratios to represent relationships between quantities, including those in context.

6.PFA.1.a: : Represent a relationship between two quantities using ratios.

Screenshot of Part-to-part and Part-to-whole Ratios

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


Lesson Info
Launch Gizmo

6.PFA.1.b: : Represent a relationship in context that makes a comparison by using the notations a/b, a:b, and a to b.

Screenshot of Part-to-part and Part-to-whole Ratios

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


Lesson Info
Launch Gizmo

6.PFA.1.c: : Represent different comparisons within the same quantity or between different quantities (e.g., part to part, part to whole, whole to whole).

Screenshot of Part-to-part and Part-to-whole Ratios

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


Lesson Info
Launch Gizmo

6.PFA.1.d: : Create a relationship in words for a given ratio expressed symbolically.

Screenshot of Part-to-part and Part-to-whole Ratios

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


Lesson Info
Launch Gizmo

6.PFA.2: : The student will identify and represent proportional relationships between two quantities, including those in context (unit rates are limited to positive values).

6.PFA.2.a: : Identify the unit rate of a proportional relationship represented by a table of values, a contextual situation, or a graph.

Screenshot of Road Trip (Problem Solving)

Road Trip (Problem Solving)

Plan a cross-country road trip through various U.S. state capitals. First choose a vehicle to drive, and then fill up the tank with gas and go! Find the range and gas mileage of each vehicle, and discover the shortest path between two cities. 5 Minute Preview


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6.PFA.2.d: : When given a contextual situation representing a proportional relationship, find the unit rate and create a table of values or a graph.

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Road Trip (Problem Solving)

Plan a cross-country road trip through various U.S. state capitals. First choose a vehicle to drive, and then fill up the tank with gas and go! Find the range and gas mileage of each vehicle, and discover the shortest path between two cities. 5 Minute Preview


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6.PFA.3: : The student will write and solve one-step linear equations in one variable, including contextual problems that require the solution of a one-step linear equation in one variable.

6.PFA.3.a: : Identify and develop examples of the following algebraic vocabulary: equation, variable, expression, term, and coefficient.

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Modeling One-Step Equations

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


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Screenshot of Solving Algebraic Equations II

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


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Screenshot of Solving Equations by Graphing Each Side

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


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Screenshot of Using Algebraic Equations

Using Algebraic Equations

Translate equations into English sentences and translate English sentences into equations. Read the equation or sentence and select word tiles or symbol tiles to form the corresponding sentence or equation. 5 Minute Preview


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Screenshot of Using Algebraic Expressions

Using Algebraic Expressions

Translate algebraic expressions into English phrases, and translate English phrases into algebraic expressions. Read the expression or phrase and select word tiles or symbol tiles to form the corresponding phrase or expression. 5 Minute Preview


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6.PFA.3.b: : Represent and solve one-step linear equations in one variable, using a variety of concrete manipulatives and pictorial representations (e.g., colored chips, algebra tiles, weights on a balance scale).

Screenshot of Modeling One-Step Equations

Modeling One-Step Equations

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


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Screenshot of Solving Algebraic Equations II

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


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Screenshot of Solving Equations on the Number Line

Solving Equations on the Number Line

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


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6.PFA.3.c: : Apply properties of real numbers and properties of equality to solve a one-step equation in one variable. Coefficients are limited to integers and unit fractions. Numeric terms are limited to integers.

Screenshot of Modeling One-Step Equations

Modeling One-Step Equations

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


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Screenshot of Solving Algebraic Equations II

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


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6.PFA.3.d: : Confirm solutions to one-step linear equations in one variable using a variety of concrete manipulatives and pictorial representations (e.g., colored chips, algebra tiles, weights on a balance scale).

Screenshot of Modeling One-Step Equations

Modeling One-Step Equations

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


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Screenshot of Solving Equations on the Number Line

Solving Equations on the Number Line

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


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6.PFA.3.e: : Write a one-step linear equation in one variable to represent a verbal situation, including those in context.

Screenshot of Modeling One-Step Equations

Modeling One-Step Equations

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


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Screenshot of Solving Equations on the Number Line

Solving Equations on the Number Line

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


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6.PFA.4: : The student will represent a contextual situation using a linear inequality in one variable with symbols and graphs on a number line.

6.PFA.4.b: : Write a linear inequality in one variable to represent a given constraint or condition in context or given a graph on a number line.

Screenshot of Exploring Linear Inequalities in One Variable

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


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Screenshot of Solving Linear Inequalities in One Variable

Solving Linear Inequalities in One Variable

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


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6.PFA.4.d: : Use substitution or a number line graph to justify whether a given number in a specified set makes a linear inequality in one variable true.

Screenshot of Exploring Linear Inequalities in One Variable

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


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Screenshot of Solving Linear Inequalities in One Variable

Solving Linear Inequalities in One Variable

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


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6.PFA.4.e: : Identify a numerical value(s) that is part of the solution set of a given inequality in one variable.

Screenshot of Exploring Linear Inequalities in One Variable

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


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Screenshot of Solving Linear Inequalities in One Variable

Solving Linear Inequalities in One Variable

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


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Correlation last revised: 4/9/2024

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