Grade 6 Mathematics Sample Performance Task Worksheet Answers

Grade 6

6.RP. Grade 6 - Ratios and Proportional Relationships

6.RP.A. Understand ratio concepts and use ratio reasoning to solve problems.

• Baking Bread 1
• Climbing the steps of El Castillo
• Equivalent Ratios 1
• Equivalent Ratios 2
• Hunger Games versus Divergent
• Ratio of boys to girls
• Sweet Tea
• Voting for Two, Variation 1
• Voting for Two, Variation 2
• Voting for Two, Variation 3
• Voting for Two, Variation 4

6.RP.A.1. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, "The ratio of wings to beaks in the bird house at the zoo was $2:1$, because for every $2$ wings there was $1$ beak." "For every vote candidate A received, candidate C received nearly three votes."

• Apples to Apples
• Bag of Marbles
• Evaluating Ratio Statements
• Games at Recess
• Many Ways to Say It
• Representing a Context with a Ratio
• The Escalator, Assessment Variation

6.RP.A.2. Understand the concept of a unit rate $a/b$ associated with a ratio $a:b$ with $b \neq 0$, and use rate language in the context of a ratio relationship. For example, "This recipe has a ratio of $3$ cups of flour to $4$ cups of sugar, so there is $3/4$ cup of flour for each cup of sugar." "We paid $\$75$ for $15$ hamburgers, which is a rate of $\$5$ per hamburger." Expectations for unit rates in this grade are limited to non-complex fractions.

• Equivalent Ratios and Unit Rates
• Hippos Love Pumpkins
• Mangos for Sale
• Price per pound and pounds per dollar
• Riding at a Constant Speed, Assessment Variation
• The Escalator, Assessment Variation
• Ticket Booth

6.RP.A.3. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

• Baking Bread 2
• Constant Speed
• Converting Square Units
• Currency Exchange
• Dana's House
• Exam scores
• Fizzy Juice
• Friends Meeting on Bicycles
• Fruit Salad
• Gianna's Job
• Hunger Games versus Divergent
• Jim and Jesse's Money
• Kendall's Vase - Tax
• Mixing Concrete
• Painting a Barn
• Party Planning
• Pennies to heaven
• Perfect Purple Paint I
• Riding at a Constant Speed, Assessment Variation
• Running at a Constant Speed
• Same and Different
• Security Camera
• Voting for Three, Variation 1
• Voting for Three, Variation 2
• Voting for Three, Variation 3
• Which detergent is a better buy?

6.RP.A.3.a. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.

• Bag of Marbles
• Gianna's Job
• Perfect Purple Paint I
• Ticket Booth
• Walk-a-thon 1

6.RP.A.3.b. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?

• Data Transfer
• Friends Meeting on Bicycles
• Gianna's Job
• Running at a Constant Speed
• Walk-a-thon 1

6.RP.A.3.c. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.

• Anna in D.C.
• Exam scores
• Overlapping Squares
• Shirt Sale

6.RP.A.3.d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

• Perfect Purple Paint I
• Simple Unit Conversion Using Ratio Reasoning
• Speed Conversions
• Unit Conversions

6.NS. Grade 6 - The Number System

6.NS.A. Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

• Dividing by a Fraction is the Same as Multiplying by its Reciprocal
• How Many Batches/What Fraction of a Batch?
• How Much in One Batch?
• Reciprocity

6.NS.A.1. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for $(2/3) \div (3/4)$ and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that $(2/3) \div (3/4) = 8/9$ because $3/4$ of $8/9$ is $2/3$. (In general, $(a/b) \div (c/d) = ad/bc$.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?

• Baking Cookies
• Cup of Rice
• Dan's Division Strategy
• Drinking Juice, Variation 2
• Drinking Juice, Variation 3
• How many _______ are in. . . ?
• How Many Containers in One Cup / Cups in One Container?
• Making Hot Cocoa, Variation 1
• Making Hot Cocoa, Variation 2
• Running to School, Variation 2
• Running to School, Variation 3
• Standing in Line
• Traffic Jam
• Video Game Credits

6.NS.B. Compute fluently with multi-digit numbers and find common factors and multiples.

• Estimating Products of Decimals
• Tenths of (and So On)

6.NS.B.2. Fluently divide multi-digit numbers using the standard algorithm.

• Batting Average
• How many staples?
• Interpreting a Division Computation

6.NS.B.3. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

• 12 Rectangular Units
• 2 Units Wide and 3 Units Long
• Adding Base Ten Numbers, Part 1
• Adding Base Ten Numbers, Part 2
• Adding Base Ten Numbers, Part 3
• Buying Gas
• Changing Currency
• Gifts from Grandma, Variation 3
• Jayden's Snacks
• Movie tickets
• Pennies to heaven
• Reasoning about Multiplication and Division and Place Value, Part 1
• Reasoning about Multiplication and Division and Place Value, Part 2
• Setting Goals
• Tenths of Tenths and Hundredths of Hundredths
• What is the Best Way to Divide?

6.NS.B.4. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use 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. For example, express $36 + 8$ as $4 (9 + 2)$.

• Adding Multiples
• Bake Sale
• Factors and Common Factors
• Multiples and Common Multiples
• The Florist Shop

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 (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.

• It's Warmer in Miami
• Mile High

6.NS.C.6. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.

• Extending the Number Line
• Locations in the Coordinate Plane

6.NS.C.6.a. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., $-(-3) = 3$, and that 0 is its own opposite.

• Integers on the Number Line 2

6.NS.C.6.b. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.

• Reflecting points over coordinate axes

6.NS.C.6.c. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.

• Plotting points in the coordinate plane

6.NS.C.7. Understand ordering and absolute value of rational numbers.

• Above and below sea level
• Jumping Flea

6.NS.C.7.a. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret $-3 > -7$ as a statement that $-3$ is located to the right of $-7$ on a number line oriented from left to right.

• Fractions on the Number Line
• Integers on the Number Line 1

6.NS.C.7.b. Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write $-3^\circ C > -7^\circ C$ to express the fact that $-3^\circ C$ is warmer than $-7^\circ C$.

• Comparing Temperatures

6.NS.C.7.c. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of $-30$ dollars, write $|-30| = 30$ to describe the size of the debt in dollars.

• No tasks yet illustrate this standard.

6.NS.C.7.d. Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than $-30$ dollars represents a debt greater than 30 dollars.

• No tasks yet illustrate this standard.

6.NS.C.8. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

• Distances between Points
• Nome, Alaska

6.EE. Grade 6 - Expressions and Equations

6.EE.A. Apply and extend previous understandings of arithmetic to algebraic expressions.

• Introducing Equivalent Expressions 1
• Introducing Equivalent Expressions 2
• Reciprocity
• Rectangle Perimeter 3
• Watch out for Parentheses

6.EE.A.1. Write and evaluate numerical expressions involving whole-number exponents.

• Exponent Experimentation 1
• Exponent Experimentation 2
• Exponent Experimentation 3
• Seven to the What?!?
• Sierpinski's Carpet
• The Djinni's Offer

6.EE.A.2. Write, read, and evaluate expressions in which letters stand for numbers.

• Distance to School
• Rectangle Perimeter 1

6.EE.A.2.a. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation "Subtract $y$ from 5" as $5 - y$.

• No tasks yet illustrate this standard.

6.EE.A.2.b. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression $2 (8 + 7)$ as a product of two factors; view $(8 + 7)$ as both a single entity and a sum of two terms.

• No tasks yet illustrate this standard.

6.EE.A.2.c. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas $V = s^3$ and $A = 6 s^2$ to find the volume and surface area of a cube with sides of length $s = 1/2$.

• Families of Triangles

6.EE.A.3. Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression $3 (2 + x)$ to produce the equivalent expression $6 + 3x$; apply the distributive property to the expression $24x + 18y$ to produce the equivalent expression $6 (4x + 3y)$; apply properties of operations to $y + y + y$ to produce the equivalent expression $3y$.

• Anna in D.C.

6.EE.A.4. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions $y + y + y$ and $3y$ are equivalent because they name the same number regardless of which number $y$ stands for.

• Equivalent Expressions
• Rectangle Perimeter 2

6.EE.B. Reason about and solve one-variable equations and inequalities.

• All, Some, or None?
• Busy Day
• Triangular Tables
• Which Goes with Which?

6.EE.B.5. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.

• Exponent Experimentation 3
• Log Ride
• Make Use of Structure

6.EE.B.6. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.

• Firefighter Allocation
• Pennies to heaven

6.EE.B.7. Solve real-world and mathematical problems by writing and solving equations of the form $x + p = q$ and $px = q$ for cases in which $p$, $q$ and $x$ are all nonnegative rational numbers.

• Anna in D.C.
• Firefighter Allocation
• Fruit Salad
• Morning Walk

6.EE.B.8. Write an inequality of the form $x > c$ or $x < c$ to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form $x > c$ or $x < c$ have infinitely many solutions; represent solutions of such inequalities on number line diagrams.

• Fishing Adventures 1
• Height Requirements

6.EE.C. Represent and analyze quantitative relationships between dependent and independent variables.

6.EE.C.9. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation $d = 65t$ to represent the relationship between distance and time.

• Chocolate Bar Sales
• Families of Triangles

6.G. Grade 6 - Geometry

6.G.A. Solve real-world and mathematical problems involving area, surface area, and volume.

• Christo's Building
• Painting a Barn

6.G.A.1. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

• 24 Unit Squares
• Areas of Right Triangles
• Areas of Special Quadrilaterals
• Base and Height
• Finding Areas of Polygons
• Polygons in the Coordinate Plane
• Same Base and Height, Variation 1
• Same Base and Height, Variation 2
• Sierpinski's Carpet
• Wallpaper Decomposition

6.G.A.2. Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas $V = l w h$ and $V = b h$ to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.

• Banana Bread
• Computing Volume Progression 1
• Computing Volume Progression 2
• Computing Volume Progression 3
• Computing Volume Progression 4
• Volumes with Fractional Edge Lengths

6.G.A.3. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.

• Polygons in the Coordinate Plane
• Walking the Block

6.G.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. Apply these techniques in the context of solving real-world and mathematical problems.

• Nets for Pyramids and Prisms

6.SP. Grade 6 - Statistics and Probability

6.SP.A. Develop understanding of statistical variability.

6.SP.A.1. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, "How old am I?" is not a statistical question, but "How old are the students in my school?" is a statistical question because one anticipates variability in students' ages.

• Buttons: Statistical Questions
• Identifying Statistical Questions
• Statistical Questions

6.SP.A.2. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.

• Average Number of Siblings
• Describing Distributions
• Electoral College
• Is It Center or Is It Variability?
• Puppy Weights

6.SP.A.3. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.

• Is It Center or Is It Variability?

6.SP.B. Summarize and describe distributions.

6.SP.B.4. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

• Average Number of Siblings
• Comparing Test Scores
• Describing Distributions
• Puppy Weights
• Puzzle Times

6.SP.B.5. Summarize numerical data sets in relation to their context, such as by:

• No tasks yet illustrate this standard.

6.SP.B.5.a. Reporting the number of observations.

• No tasks yet illustrate this standard.

6.SP.B.5.b. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.

• No tasks yet illustrate this standard.

6.SP.B.5.c. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.

• Average Number of Siblings
• Comparing Test Scores
• Math Homework Problems
• Puzzle Times

6.SP.B.5.d. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.

• Electoral College
• Mean or Median?

Grade 6 Mathematics Sample Performance Task Worksheet Answers

Source: https://tasks.illustrativemathematics.org/6

Posted by: lewissithen.blogspot.com

Share this post