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Oregon - Mathematics: 6th Grade
Mathematics Standards | Adopted: 2021
6.AEE: : Algebraic Reasoning: Expressions and Equations
6.AEE.A: : Apply and extend previous understandings of arithmetic to algebraic expressions.
6.AEE.A.1: : Write and evaluate numerical expressions involving whole-number bases and exponents.
Order of Operations
Select and evaluate the operations in an expression following the correct order of operations. 5 Minute Preview
6.AEE.A.2: : Write, read, and evaluate expressions in which letters stand for numbers. Apply knowledge of common mathematical terms to move between the verbal and mathematical forms of an expression including expressions that arise from authentic contexts.
Circumference and Area of Circles
Resize a circle and compare its radius, circumference, and area. 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
Prisms and Cylinders
Vary the height and base-edge or radius length of a prism or cylinder and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of an oblique prism or cylinder to the volume of a right prism or cylinder. 5 Minute Preview
Pyramids and Cones
Vary the height and base-edge or radius length of a pyramid or cone and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of a skew pyramid or cone to the volume of a right pyramid or cone. 5 Minute Preview
Surface and Lateral Areas of Prisms and Cylinders
Vary the dimensions of a prism or cylinder and investigate how the surface area changes. Use the dynamic net of the solid to compute the lateral area and the surface area of the solid. 5 Minute Preview
Surface and Lateral Areas of Pyramids and Cones
Vary the dimensions of a pyramid or cone and investigate how the surface area changes. Use the dynamic net of the solid to compute the lateral area and the surface area of the solid. 5 Minute Preview
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
6.AEE.A.3: : Apply the properties of operations to generate equivalent expressions and to determine when two expressions are equivalent.
Equivalent Algebraic Expressions I
Grumpy’s Restaurant is now hiring! As a new chef at this underwater bistro, you’ll learn the basics of manipulating algebraic expressions. Learn how to make equivalent expressions using the Commutative and Associative properties, how to handle pesky subtraction and division, and how to identify equivalent and non-equivalent expressions. 5 Minute Preview
Equivalent Algebraic Expressions II
Continue your meteoric rise in the undersea culinary world in this follow-up to Equivalent Algebraic Expressions I. Make equivalent expressions by using the distributive property forwards and backwards, sort expressions by equivalence, and personally assist Chef Grumpy himself with a project that will bring him (and maybe you) fame and fortune. 5 Minute Preview
6.AEE.B: : Reason about and solve one-variable equations and inequalities.
6.AEE.B.4: : Understand solving an equation or inequality as a process of answering which values from a specified set, if any, make the equation or inequality true. Use substitution to determine which number(s) in a given set make an equation or inequality true.
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
Modeling One-Step Equations
Solve a linear equation using a tile model. Use feedback to diagnose incorrect steps. 5 Minute Preview
6.AEE.B.5: : Use variables to represent numbers and write expressions when solving problems in authentic contexts.
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
Modeling One-Step Equations
Solve a linear equation using a tile model. Use feedback to diagnose incorrect steps. 5 Minute Preview
Solving Equations on the Number Line
Solve an equation involving decimals using dynamic arrows on a number line. 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
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
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
6.AEE.B.6: : Write and solve equations of the form x + p = q and px = q in problems that arise from authentic contexts for cases in which p, q and x are all nonnegative rational numbers.
Modeling One-Step Equations
Solve a linear equation using a tile model. Use feedback to diagnose incorrect steps. 5 Minute Preview
Solving Equations on the Number Line
Solve an equation involving decimals using dynamic arrows on a number line. 5 Minute Preview
6.AEE.B.7: : Write inequalities of the form x > c and x < c to represent constraints or conditions to solve problems in authentic contexts. Describe and graph on a number line solutions of inequalities of the form x > c and x < c.
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
6.RP: : Proportional Reasoning: Ratios and Proportions
6.RP.A: : Understand ratio concepts and use ratio reasoning to solve problems.
6.RP.A.1: : Understand the concept of a ratio in authentic contexts, and use ratio language to describe a ratio relationship between two quantities.
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
Beam to Moon (Ratios and Proportions) - Metric
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
6.RP.A.2: : Understand the concept of a unit rate in authentic contexts and use rate language in the context of a ratio relationship.
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
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
6.RP.A.3: : Use ratio and rate reasoning to solve problems in authentic contexts that use equivalent ratios, unit rates, percents, and/or measurement units.
Percent of Change
Apply markups and discounts using interactive "percent rulers." Improve number sense for percents with this dynamic, visual tool. Reinforce the original cost (or original price) as the baseline for percent calculations. 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
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
Unit Conversions
Use unit conversion tiles to convert from one unit to another. Tiles can be flipped to cancel units. Convert between metric units or between metric and U.S. customary units. Solve distance, time, speed, mass, volume, and density problems. 5 Minute Preview
6.NS: : Numeric Reasoning: Number Systems
6.NS.A: : Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
6.NS.A.1: : Represent, interpret, and compute quotients of fractions to solve problems in authentic contexts involving division of fractions by 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
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
6.NS.B: : Compute fluently with multi-digit numbers and find common factors and multiples.
6.NS.B.2: : Fluently divide multi-digit numbers using accurate, efficient, and flexible strategies and algorithms based on place value and properties of operations.
No Alien Left Behind (Division with Remainders)
The alien school children from the planet Zigmo travel to distant planets on a field trip. The goal is to select a bus size so that all buses are full and no aliens are left behind. This is a nice illustration of division with remainders. 5 Minute Preview
6.NS.B.3: : Fluently add, subtract, multiply, and divide positive rational numbers using accurate, efficient, and flexible strategies and algorithms.
Adding Whole Numbers and Decimals (Base-10 Blocks)
Use base-10 blocks to model two numbers. Then combine the blocks to model the sum. Blocks of equal value can be exchanged from one area of the mat to the other to help understand carrying when adding. Four sets of blocks are available to model different place values. 5 Minute Preview
Multiplying Decimals (Area Model)
Model the product of two decimals by finding the area of a rectangle. Estimate the area of the rectangle first. Then break the rectangle into several pieces and find the area of each piece (partial product). Add these areas together to find the whole area (product). 5 Minute Preview
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
Subtracting Whole Numbers and Decimals (Base-10 Blocks)
Use base-10 blocks to model a starting number. Then subtract blocks from this number by dragging them into a subtraction bin. Blocks of equal value can be exchanged from one section of the mat to the other to help understand regrouping and borrowing. Four sets of blocks are available to model different place values. 5 Minute Preview
Sums and Differences with Decimals
Find the sum or difference of two decimal numbers using area models. Find the decimals and their sum or difference on a number line. 5 Minute Preview
6.NS.B.4: : Determine greatest common factors and least common multiples using a variety of strategies. Apply the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor.
Equivalent Algebraic Expressions II
Continue your meteoric rise in the undersea culinary world in this follow-up to Equivalent Algebraic Expressions I. Make equivalent expressions by using the distributive property forwards and backwards, sort expressions by equivalence, and personally assist Chef Grumpy himself with a project that will bring him (and maybe you) fame and fortune. 5 Minute Preview
Pattern Flip (Patterns)
In the Pattern Flip carnival game, you are shown a pattern of cards. The first cards are face-up so you can see the pattern, and the rest are face-down. Can you guess which animals are on the face-down cards? Use one of the preset patterns, or make your own custom pattern. Good luck! 5 Minute Preview
6.NS.C: : Apply and extend previous understandings of numbers to the system of rational numbers.
6.NS.C.5: : Understand that positive and negative numbers are used together to describe quantities having opposite directions or values. Use positive and negative numbers to represent quantities in authentic contexts, explaining the meaning of zero in each situation.
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
6.NS.C.6: : Represent a rational number as a point on the number line. Extend number line diagrams and coordinate axes to represent points on the line and in the coordinate plane with negative number coordinates.
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
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
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
6.NS.C.7: : Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. Write, interpret, and explain statements of order for rational numbers and absolute value in authentic applications.
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
6.NS.C.8: : Graph points in all four quadrants of the coordinate plane to solve problems in authentic contexts. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.
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
6.GM: : Geometric Reasoning and Measurement
6.GM.A: : Solve real-world and mathematical problems involving area, surface area, and volume.
6.GM.A.1: : Find the area of triangles, quadrilaterals, and other polygons by composing into rectangles or decomposing into triangles and other shapes. Apply these techniques to solve problems in authentic contexts.
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
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
6.GM.A.3: : Draw polygons in the four quadrant coordinate plane given coordinates for the vertices and find the length of a side. Apply these techniques to solve problems in authentic contexts.
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
6.GM.A.4: : Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures, including those from authentic contexts.
Surface and Lateral Areas of Prisms and Cylinders
Vary the dimensions of a prism or cylinder and investigate how the surface area changes. Use the dynamic net of the solid to compute the lateral area and the surface area of the solid. 5 Minute Preview
Surface and Lateral Areas of Pyramids and Cones
Vary the dimensions of a pyramid or cone and investigate how the surface area changes. Use the dynamic net of the solid to compute the lateral area and the surface area of the solid. 5 Minute Preview
6.DR: : Data Reasoning
6.DR.A: : Formulate Statistical Investigative Questions.
6.DR.A.1: : Formulate and recognize statistical investigative questions as those that anticipate changes in descriptive data related to the question and account for it in the answers.
Box-and-Whisker Plots
Construct a box-and-whisker plot to match a line plots, and construct a line plot to match a box-and-whisker plots. Manipulate the line plot and examine how the box-and-whisker plot changes. Then manipulate the box-and-whisker plot and examine how the line plot changes. 5 Minute Preview
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
Histograms
Change the values in a data set and examine how the dynamic histogram changes in response. Adjust the interval size of the histogram and see how the shape of the histogram is affected. 5 Minute Preview
Movie Reviewer (Mean and Median)
Movie reviewers rate movies on a scale of 0 to 10. Each movie comes with a set of reviews that can be changed by the user. The mean of a data set can be explored using a see-saw balance model. Students can also find the median, mode, and range of the data set. 5 Minute Preview
Polling: City
Poll residents in a large city to determine their response to a yes-or-no question. Estimate the actual percentage of yes votes in the whole city. Examine the results of many polls to help assess how reliable the results from a single poll are. See how the normal curve approximates a binomial distribution for large enough polls. 5 Minute Preview
Polling: Neighborhood
Conduct a phone poll of citizens in a small neighborhood to determine their response to a yes-or-no question. Use the results to estimate the sentiment of the entire population. Investigate how the error of this estimate becomes smaller as more people are polled. Compare random versus non-random sampling. 5 Minute Preview
Reaction Time 2 (Graphs and Statistics)
Test your reaction time by catching a falling ruler or clicking a target. Create a data set of experiment results, and calculate the range, mode, median, and mean of your data. Data can be displayed on a list, table, bar graph or dot plot. The Reaction Time 2 Student Exploration focuses on mean. 5 Minute Preview
6.DR.B: : Collect and Consider Data.
6.DR.B.2: : Collect and record data with technology to identify and describe the characteristics of numerical data sets using quantitative measures of center and variability.
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
Movie Reviewer (Mean and Median)
Movie reviewers rate movies on a scale of 0 to 10. Each movie comes with a set of reviews that can be changed by the user. The mean of a data set can be explored using a see-saw balance model. Students can also find the median, mode, and range of the data set. 5 Minute Preview
Reaction Time 1 (Graphs and Statistics)
Test your reaction time by catching a falling ruler or clicking a target. Create a data set of experiment results, and calculate the range, mode, median, and mean of your data. Data can be displayed on a list, table, bar graph or dot plot. The Reaction Time 1 Student Exploration focuses on range, mode, and median. 5 Minute Preview
Reaction Time 2 (Graphs and Statistics)
Test your reaction time by catching a falling ruler or clicking a target. Create a data set of experiment results, and calculate the range, mode, median, and mean of your data. Data can be displayed on a list, table, bar graph or dot plot. The Reaction Time 2 Student Exploration focuses on mean. 5 Minute Preview
6.DR.C: : Analyze, summarize, and describe data.
6.DR.C.3: : Analyze data representations and describe measures of center and variability of quantitative data using appropriate displays.
Box-and-Whisker Plots
Construct a box-and-whisker plot to match a line plots, and construct a line plot to match a box-and-whisker plots. Manipulate the line plot and examine how the box-and-whisker plot changes. Then manipulate the box-and-whisker plot and examine how the line plot changes. 5 Minute Preview
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
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
Histograms
Change the values in a data set and examine how the dynamic histogram changes in response. Adjust the interval size of the histogram and see how the shape of the histogram is affected. 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
Reaction Time 1 (Graphs and Statistics)
Test your reaction time by catching a falling ruler or clicking a target. Create a data set of experiment results, and calculate the range, mode, median, and mean of your data. Data can be displayed on a list, table, bar graph or dot plot. The Reaction Time 1 Student Exploration focuses on range, mode, and median. 5 Minute Preview
Reaction Time 2 (Graphs and Statistics)
Test your reaction time by catching a falling ruler or clicking a target. Create a data set of experiment results, and calculate the range, mode, median, and mean of your data. Data can be displayed on a list, table, bar graph or dot plot. The Reaction Time 2 Student Exploration focuses on mean. 5 Minute Preview
Stem-and-Leaf Plots
Build a data set and compare the line plot of the data set to the stem-and-leaf plot. 5 Minute Preview
6.DR.D: : Interpret data and answer investigative questions.
6.DR.D.4: : Interpret quantitative measures of center to describe differences between groups from data collected to answer investigative questions.
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
Movie Reviewer (Mean and Median)
Movie reviewers rate movies on a scale of 0 to 10. Each movie comes with a set of reviews that can be changed by the user. The mean of a data set can be explored using a see-saw balance model. Students can also find the median, mode, and range of the data set. 5 Minute Preview
Correlation last revised: 11/9/2023
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Students assume the role of a scientist trying to solve a real world problem. They use scientific practices to collect and analyze data, and form and test a hypothesis as they solve the problems.
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