In plain English: MP2 is the Common Core Standard for Mathematical Practice about moving between a situation and its symbols. Students decontextualize (turn a situation into an expression or equation and work with it) and contextualize (stop to ask what each symbol and result means), keep track of units, and use properties of operations flexibly. It applies in every grade 6-12 math course.
Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.
Common Core State Standards for Mathematics · Domain: Standards for Mathematical Practice (MP) · Practice group: Reasoning and explaining Also written as CCSS.MATH.PRACTICE.MP2 · Official standard
MP2 names two complementary abilities. To decontextualize is to take a situation, represent it with symbols, and work with those symbols "as if they have a life of their own." To contextualize is to pause during the work and ask what the symbols and results mean in the situation. Students who reason quantitatively also build a coherent representation of the problem, keep track of units, attend to what a quantity means and not only how to compute it, and use properties of operations flexibly.
This lesson teaches both directions with short tasks from grades 6-12: rates and unit prices, expressions and equations, linear and exponential functions, and statistics. Each task is labeled with a typical course, so teachers can keep the tasks that fit their class.
Learning Objectives
By the end of this lesson, students will be able to:
Translate a situation into an expression, equation or inequality and solve it without the context
Interpret each number, variable and result of an expression or equation in the context, with units
Use units to set up and check a calculation
Explain what a quantity such as a mean or a rate means, not only how to compute it
Use properties of operations to rewrite expressions and explain why the forms are equivalent
Prior Knowledge Required
Students should already be comfortable with:
Writing and evaluating expressions with variables 6.EE.A.2
Unit rates and proportional relationships 7.RP.A.2
Rate of change and initial value of a linear function 8.F.B.4
For the Algebra I tasks: interpreting parts of an expression in context HSA.SSE.A.1
Write the expression on the board with no context. Students work alone for three minutes, then share with a partner.
Warm-Up Prompt
"Here is an expression: 40 - 2.5w, where w is a number of weeks. Write a short story that this expression could describe. What does the 40 mean in your story? What does the 2.5 mean? What are the units of each number?"
Share three or four stories, for example "I have $40 on a gift card and spend $2.50 a week on snacks." Ask what kind of quantity w can be in each story: whole weeks only, or any number? Ask when each story stops making sense (in the gift-card story, after 16 weeks the card is empty). Tell students that writing a story for symbols is contextualizing, and that today they will also practice the reverse.
Direct Instruction20 minutes
Use Diagram 1 to name the two directions. Then model five short examples. In each one, say aloud when you leave the context and when you come back to it.
Name the quantities: write each one with its unit, such as "h = hours of video".
Decontextualize: write the expression, equation or inequality and work with it using properties of operations.
Contextualize: stop and ask what each number and result means, and whether its units make sense.
Answer the question that was asked, in a sentence with units.
Decontextualize, then contextualize (Grade 7)
Jada has used 47 GB of her 120 GB monthly data plan. HD video uses 3 GB per hour. How many full hours of HD video can she still watch this month?
Equation: 47 + 3h ≤ 120, so 3h ≤ 73 and h ≤ 24.33... Back in context: h counts full hours, so she can watch 24 hours.
Meaning of each number (Algebra I)
The value of a car t years after purchase is V = 25,000(0.84)ᵗ dollars. What do 25,000 and 0.84 mean? What is the value after 3 years?
Equation: 25,000 is the price when new. 0.84 means the car keeps 84% of its value each year. After 3 years: 25,000(0.84)³ ≈ $14,818 (Diagram 2).
Units guide the calculation (Grade 6-7 rates)
A car travels 36 miles per gallon, and gas costs $3.60 per gallon. What does the gas cost per mile?
Equation: ($3.60 per gallon) ÷ (36 miles per gallon) = $0.10 per mile, or 10 cents per mile. The gallons cancel, leaving dollars per mile.
Meaning, not just computing (Grade 6 statistics)
A survey of 40 families finds a mean of 2.35 children per family. No family has 2.35 children. What does the mean tell us?
Equation: The families have 2.35 × 40 = 94 children in all. If those 94 children were shared out equally, each family would have 2.35.
Properties of operations (Grade 7)
A student says 3(x + 4) is the same as 3x + 4. Use a property and a test value to decide.
Equation: The distributive property gives 3(x + 4) = 3x + 12, not 3x + 4. Test x = 2: 3(6) = 18 but 3(2) + 4 = 10.
After Example 2, show Diagram 2 and ask: "Does the car lose the same number of dollars every year?" (No. It loses 16% of a smaller value each year: $4,000 in the first year, then $3,360 in the second.) After Example 3, write the units as fractions and cross out the gallons, so students see why dividing is right.
Guided Practice15 minutes
Pairs build a coherent representation of one problem in three forms before solving it.
Problem (Grade 8 systems): A water park charges $32 for an adult ticket and $19 for a child ticket. A group of 11 people pays $274. How many adults and how many children are in the group?
Name the quantities: a = number of adults, c = number of children (both whole numbers).
Table: try a = 3, 4, 5 and compute the cost with c = 11 - a. (a = 3 gives 96 + 152 = $248 and a = 4 gives $261; students continue until the cost reaches $274.)
Equations: a + c = 11 and 32a + 19c = 274. Substitute c = 11 - a: 32a + 19(11 - a) = 274, so 13a + 209 = 274 and a = 5.
Ask: "If the total had been $280, what would the equations tell you, and what would that mean about the group?" (13a = 71 has no whole-number solution, so no group of 11 pays exactly $280.)
Independent Practice15 minutes
A garden bed is a rectangle with length L meters and width W meters. Students match each expression to its meaning and its unit, then write one more expression with its own meaning.
Expressions for a rectangular garden bed
Expression
Meaning
Unit
2L + 2W
the length of fencing all the way around
meters
LW
the area to be covered with soil
square meters
L/W
how many times longer the bed is than it is wide
no unit
0.1LW
the volume of a 0.1 m deep layer of soil
cubic meters
The table above is the answer key; give students the expressions and a shuffled list of meanings and units. Then ask: "For a bed 6 m by 2.5 m, which expression tells you how much fencing to buy, and how much is it?" (2L + 2W = 17 m.) Students who finish explain why L/W has no unit.
Closure5-10 minutes
Exit ticket:
Write a situation for the expression 15 + 2.5t. Give the unit of 15, of 2.5 and of t.
In your situation, what would the solution of 15 + 2.5t = 40 mean?
Name one moment today when you stopped computing to ask what a number meant.
Differentiation Strategies
For Struggling Students
Give a "name the quantities" frame: "Let ___ = the number of ___ (unit: ___)" before any equation is written
Keep the units in every line of a calculation, written as fractions that can be crossed out
Start with whole-number situations before using decimals or exponents
For Advanced Students
Ask students to write two different situations for the same equation, one where every solution makes sense and one where only some do
Ask: the car in Diagram 2 loses 16% a year. After how many whole years is it worth less than half its price? Explain with the expression
Ask students to find and explain an error in units in a news headline or advertisement they find
Assessment Guidance
What to Look For
Listen for students naming quantities with units before writing symbols, and for them returning to the context at the end ("so 24 full hours"). Strong students explain each number in an expression, such as "0.84 is the part of the value kept each year," and reject solutions that do not fit, such as a negative width. Watch for answers given without units, for 24.33 hours reported as the answer to a whole-hours question, and for students who treat a percent decrease as the same dollar amount every year.
02
Classroom Activities
3 Activities
1
Story to Symbols to Story
20 minGroups of 3-4
Groups practice both directions of MP2. In Round 1 they decontextualize four situations, solve, and state the answer in context. In Round 2 they contextualize four expressions by writing a story for each.
Round 1: Situation Cards (with answers for the teacher)
Card A (Grade 6): A school sells 85 tickets at $6 each and pays $140 for decorations. What is the profit? (85 × 6 - 140 = $370.)
Card B (Grade 6-7): A recipe needs 2/3 cup of sugar per batch, and you have 5 cups. How many full batches can you make? (5 ÷ 2/3 = 7.5, so 7 full batches.)
Card C (Algebra I): A plant is 4 cm tall and grows 1.5 cm per week. When is it 19 cm tall? (4 + 1.5w = 19, so w = 10 weeks.)
Card D (Algebra I): A culture of 500 bacteria doubles every 3 hours. Write the number after t hours and find it after 12 hours. (500 · 2^(t/3); after 12 hours, 8,000.)
Round 2: Expression Cards
50 - 3n
1.08p
2(l + 8)
100(0.9)ᵗ
For each card, write a situation, name the unit of every number and letter, and say what values of the variable make sense.
Procedure
For each situation card, write "Let ___ = ___" first, then the symbols, then the solution, then one sentence in context
Circle the step where you left the context and the step where you came back
Groups swap Round 2 stories and check that each story really fits its expression
Discussion Questions
On Card B, why is 7.5 not the answer?
What different stories did groups write for 1.08p? What does the 0.08 mean in each?
Which expression card was hardest to contextualize, and why?
2
Units Detective
20 minPairs
Pairs inspect five finished calculations. For each one, they write the units next to every number, decide whether the calculation and its units make sense, and fix any that do not.
The Five Calculations (with answers for the teacher)
1. "A car goes 150 miles in 3 hours, so its speed is 150 × 3 = 450." (Wrong: miles × hours is not a speed. 150 ÷ 3 = 50 miles per hour.)
2. "A metal block has mass 54 g and volume 20 cm³, so its density is 54 ÷ 20 = 2.7 g/cm³." (Right; 2.7 g/cm³ is the density of aluminum.)
3. "A pool 10 m by 5 m by 2 m holds 100 m³, which is 100,000 liters." (Right: 1 m³ = 1,000 L.)
4. "3 gallons of paint cover 1,050 square feet, so 1 gallon covers 3 ÷ 1,050 = 0.003 square feet." (Wrong: 1,050 ÷ 3 = 350 square feet per gallon.)
5. "A runner covers 5 km in 25 minutes: 5 ÷ 25 = 0.2 km per minute, which is 12 km per hour." (Right: 0.2 × 60 = 12.)
Procedure
Write each quantity as a number with its unit, and units as fractions where they are rates
Decide: right, wrong, or right number with the wrong unit
For each wrong one, write the corrected calculation and one sentence on what the result means
Discussion Questions
How did the units tell you calculation 1 was wrong before you thought about the numbers?
In calculation 4, how could you tell that 0.003 square feet makes no sense?
Is 12 km per hour a realistic running speed? How do you know?
Modification for Distance Learning
Post the five calculations on a shared slide; pairs mark each one with a colored sticky note (right or wrong) and type the fix in a comment.
3
Same Equation, Different Stories
20 minGroups of 4
Every group gets the same equation, 12x + 30 = 102. Each student writes a different situation for it, the group solves it once, and then everyone decides what the solution means, and whether it makes sense, in each story.
Procedure
Each student writes a situation for 12x + 30 = 102 and names the unit of 12, 30, x and 102
The group solves the equation once, without any context: x = 6
Each student states what x = 6 means in his or her own story
The group rewrites 12x + 30 as 6(2x + 5) and asks what "6 groups of (2x + 5)" could mean in one of the stories
Sample Stories (for the teacher)
"A gym charges a $30 fee plus $12 per class. I paid $102." x = 6 classes.
"I have read 30 pages of a book and read 12 pages a day. After how many days will I have read 102 pages?" x = 6 days. A story about something that shrinks, such as a melting candle, does not fit: it would need a negative rate.
"A tank has 30 L and fills at 12 L per minute until it holds 102 L." x = 6 minutes.
Discussion Questions
Why did one solution, x = 6, answer four different questions?
In which stories could x be a fraction? In which must it be a whole number?
Which properties of operations let you rewrite 12x + 30 as 6(2x + 5)?
Challenge Variation
Groups change one number in the equation so that the solution makes sense in one of their stories but not in another, and explain why.
03
Diagrams & Visual Aids
2 diagrams
Diagram 1: Two Directions of MP2
Decontextualizing turns the data-plan situation into the inequality 47 + 3h ≤ 120, which can be solved without thinking about phones. Contextualizing brings the result back: h ≤ 24.33... is not the answer until we remember that h counts full hours of video, so the answer is 24 hours.
Diagram 2: What the Numbers in V = 25,000(0.84)ᵗ Mean
The value of a car, V = 25,000(0.84)ᵗ dollars after t years, plotted to scale for t = 0 to 8. Contextualizing the expression: 25,000 is the value at t = 0 (the price when new), and 0.84 means each year the car keeps 84% of its value, so it loses 16% of the previous year's value, not $4,000 every year.
04
Homework Assignment
~30 min
MP2 Homework: Symbols, Meaning and Units
Directions: Start each problem by naming the quantities with their units ("Let ___ = ___"). Show your work with the symbols, then finish with a sentence that answers the question in context, with units.
Part 1: From Situations to Symbols (Problems 1-3)
A bike courier earns $16 per hour plus $1.50 per delivery. Write an expression for the pay for h hours and d deliveries, and give the unit of each number. Then find the pay for a 6-hour shift with 22 deliveries.
A pool holds 2,400 gallons. It already has 300 gallons in it and is being filled at 15 gallons per minute. Write and solve an equation for the time until it is full. Give the answer in hours and minutes.
A taxi charges $3.50 plus $2.25 per mile. Represent the cost with a table (0 to 4 miles), a graph and an equation. Find the cost of an 8-mile ride. Which representation shows the $3.50 most clearly, and where?
Part 2: What the Numbers Mean (Problems 4-6)
The expression 1,200(1.04)ᵗ gives the balance, in dollars, of a savings account after t years. Explain what 1,200, 1.04 and t mean. Then compute 1,200(1.04)⁵ - 1,200 and explain what that number represents.
A cyclist rides 18 km in 45 minutes. Kai divides and says, "Her speed is 0.4." Explain what 0.4 means, with units. Convert the speed to kilometers per hour and decide whether it is realistic for a cyclist.
Use properties of operations to show that 4(3x - 2) + 2(5 - x) is equivalent to 10x + 2. Name the property you use at each step. Then test both expressions with x = 3.
Rubric
Criterion
Full Credit (2 pts)
Partial Credit (1 pt)
No Credit (0 pts)
Naming Quantities
Every variable and number is named with its unit
Some quantities named or units missing
Not named
Symbols and Work
Correct expressions or equations, solved correctly
Correct setup with an error in the work
Incorrect setup
Meaning in Context
Each answer is a sentence in context, with units, and impossible values are rejected
Answer given without context or units
No interpretation
Properties
Each step is justified with the correct property
Steps correct but properties missing or misnamed
Steps incorrect
05
Quiz: 20 Questions
Interactive, with answers
Instructions
Each question asks you to move between a situation and its symbols, to check units, or to explain what a quantity means. Your score updates as you answer, and Reset quiz clears everything.
Multiple choice: pick an option to check it. Short answer: write your answer, then reveal the model answer.
0 of 20 answered · 0 correct
Question 1 of 20 · Multiple Choice
A theater sells child tickets for $8 and adult tickets for $12. Let c be the number of child tickets and a the number of adult tickets. What does 8c + 12a = 960 say?
Answer: B
8c is the money from child tickets and 12a the money from adult tickets, in dollars, so the sum is the total ticket money. Choice A confuses the number of tickets (c + a) with the money. Choice D is true about the prices, but it is not what the equation says.
Question 2 of 20 · Multiple Choice
Sofia has $250 and saves $35 per week. Marco has $460 and spends $25 per week. Which equation finds the week w when they have the same amount?
Answer: A
Sofia's amount grows by 35 each week and Marco's shrinks by 25, so set 250 + 35w equal to 460 - 25w (w = 3.5, so they are equal halfway through week 4). Choice B reverses saving and spending. Choice D leaves out the variable, so it describes only one week.
Question 3 of 20 · Multiple Choice
A ride-share costs C = 2.5 + 1.75m dollars for m miles. Solving 2.5 + 1.75m = 30 gives m ≈ 15.7. What does that mean?
Answer: C
m is the number of miles, and the equation sets the cost equal to $30, so m ≈ 15.7 means a $30 ride covers about 15.7 miles. Choice A reads m as a price per mile; the price per mile is the 1.75. Choice D confuses m with the 2.5 starting fee.
Question 4 of 20 · Multiple Choice
A recipe uses 450 g of flour for 12 muffins. Which calculation gives the flour per muffin, with correct units?
Answer: D
Flour per muffin is grams divided by muffins: 450 g ÷ 12 muffins = 37.5 g per muffin. Choice C has the right number with the units upside down. Choice A answers a different question: muffins per gram of flour.
Question 5 of 20 · Multiple Choice
A faucet drips 2 mL every 5 seconds. About how much water is that per day?
Answer: C
The rate is 2/5 = 0.4 mL per second, and a day has 86,400 seconds: 0.4 × 86,400 = 34,560 mL, or 34.56 L. Choice B is the amount per hour (0.4 × 3,600 = 1,440 mL). Choice A treats 0.4 mL per second as liters. Choice D slips the decimal point when converting mL to liters.
Question 6 of 20 · Multiple Choice
A survey of the cars entering a school parking lot finds a mean of 1.6 people per car. Which interpretation is correct?
Answer: D
The mean is the total number of people divided by the number of cars: the amount per car if the people were shared out evenly. Choice A confuses the mean with the mode, the value that occurs most often. Choice C invents a percent the mean does not give.
Question 7 of 20 · Multiple Choice
A ball's height is h = -16t² + 48t + 5 feet after t seconds. What does the 5 mean?
Answer: A
At t = 0 the height is 5 feet, so 5 is the starting height. Choice B reads the constant as a time. Choice D confuses the starting height with the maximum, which is 41 feet at t = 1.5.
Question 8 of 20 · Multiple Choice
A student finds 17 × 4 × 25 mentally by computing 17 × (4 × 25) = 17 × 100 = 1,700. Which property makes this regrouping valid?
Answer: B
Regrouping factors, (17 × 4) × 25 = 17 × (4 × 25), is the associative property of multiplication. Choice A would split a sum, and there is no sum here. Choice C is about adding, not multiplying.
Question 9 of 20 · Multiple Choice
Which expression is equivalent to 5(2x - 3) - 2(x - 4)?
Answer: D
5(2x - 3) = 10x - 15 and -2(x - 4) = -2x + 8, so the total is 8x - 7. Choice A uses -2 × -4 = -8, a sign error. Choice C adds 2x instead of subtracting it. Choice B multiplies only the x by -2 and keeps +4, giving 10x - 15 - 2x + 4.
Question 10 of 20 · Multiple Choice
A tank holds 45 liters and drains at 3 liters per minute. Which graph matches, with time on the horizontal axis?
Answer: C
The tank starts at 45 L and is empty after 45 ÷ 3 = 15 minutes. Choice A shows a tank filling. Choice B uses the rate as the time. Choice D multiplies 45 by 3 instead of dividing.
Question 11 of 20 · Multiple Choice
A rectangular room is 4.2 m by 3.5 m, and carpet costs $28 per square meter. Which expression gives the cost of carpeting the floor, in dollars?
Answer: C
The area is 4.2 × 3.5 = 14.7 m², and (dollars per m²) × m² gives dollars: 28 × 14.7 = $411.60. Choice B uses the perimeter in meters, which does not cancel square meters. Choice D divides square meters by dollars per square meter, giving units that are not dollars.
Question 12 of 20 · Multiple Choice
A rectangle has width x cm and length x + 9 cm, and its area is 36 cm². The equation x(x + 9) = 36 has solutions 3 and -12. Which conclusion is right?
Answer: B
Both numbers solve the equation, but in context x is a length, so only x = 3 makes sense: a 3 cm by 12 cm rectangle with area 36 cm². Choice A stops before contextualizing. Choice C drops the sign, and a 12 cm by 21 cm rectangle has area 252 cm², not 36.
Question 13 of 20 · Multiple Choice
A plane flies 2,700 km in 3.6 hours. A student computes 2,700 ÷ 3.6 = 750. What does 750 measure?
Answer: A
Kilometers divided by hours gives kilometers per hour, a speed. Choice D inverts the units. Choice B treats the quotient as a time, but dividing a distance by a time cannot give a time.
Question 14 of 20 · Multiple Choice
Which equation represents "When 7 is added to a number and the sum is doubled, the result is 50"?
Answer: D
The sum n + 7 is doubled, so the whole sum is multiplied by 2: 2(n + 7) = 50, and n = 18. Choice A doubles only n. Choice C doubles the result instead of the sum.
Question 15 of 20 · Short Answer
A club sells candles for $12 each and spent $180 on supplies. Write an inequality for making a profit of at least $600, solve it, and state the answer in context.
Let c = the number of candles sold. 12c - 180 ≥ 600, so 12c ≥ 780 and c ≥ 65. In context: the club must sell at least 65 candles. Because c counts candles, only whole numbers make sense.
Question 16 of 20 · Short Answer
Convert 65 miles per hour to feet per second. Show the units in each step so that you can see them cancel. (1 mile = 5,280 feet.)
(65 mi / 1 h) × (5,280 ft / 1 mi) × (1 h / 3,600 s) = 343,200 ft / 3,600 s ≈ 95.3 feet per second. Miles cancel with miles and hours cancel with hours, leaving feet per second.
Question 17 of 20 · Short Answer
A monthly electric bill is C = 0.12k + 9.50 dollars, where k is the number of kilowatt-hours used. Explain what 0.12 and 9.50 mean, with units, and find the bill for 650 kilowatt-hours.
0.12 is the price of electricity, $0.12 per kilowatt-hour. 9.50 is a fixed monthly charge, $9.50, paid even if no electricity is used. For 650 kWh: 0.12 × 650 + 9.50 = 78 + 9.50 = $87.50.
Question 18 of 20 · Short Answer
Use the distributive property to compute 98 × 15 without a calculator. Show the steps.
98 × 15 = (100 - 2) × 15 = 100 × 15 - 2 × 15 = 1,500 - 30 = 1,470. Writing 98 as 100 - 2 turns a hard product into two easy ones.
Question 19 of 20 · Short Answer
Plan A costs $20 per month plus $0.10 per text. Plan B costs $35 per month with unlimited texts. Write an equation for each plan, find the number of texts for which the costs are equal, and say which plan is cheaper above that number.
Plan A: C = 20 + 0.10t. Plan B: C = 35. Setting 20 + 0.10t = 35 gives t = 150 texts. Above 150 texts a month, Plan B is cheaper; below 150, Plan A is cheaper.
Question 20 of 20 · Short Answer
A town's population is modeled by P = 18,000 + 450t, where t is the number of years since 2020. What does 450 mean? Find P(10) - P(0) and explain what it represents.
450 is the growth rate: the population increases by 450 people per year. P(10) - P(0) = 22,500 - 18,000 = 4,500, the number of people the town gains in the 10 years from 2020 to 2030 under this model.
0 of 20 answered · 0 correct
06
Frequently Asked Questions
10 Questions
What does MP2 mean in math?
MP2 is the Standard for Mathematical Practice "Reason abstractly and quantitatively." Students move between a situation and its symbols: they write and work with expressions and equations (abstract reasoning) and keep asking what the numbers, units and results mean in the situation (quantitative reasoning).
What do decontextualize and contextualize mean in MP2?
To decontextualize is to turn a situation into symbols and work with them "as if they have a life of their own," for example solving 47 + 3h ≤ 120 as pure algebra. To contextualize is to pause and ask what the symbols mean, for example remembering that h counts full hours of video.
Why do units matter so much in MP2?
Units tell you what a number measures and whether a calculation makes sense. Miles times hours is not a speed, and grams divided by muffins is grams per muffin. Writing units as fractions and canceling them is a quick check that the operation is the right one.
Is MP2 the same as solving word problems?
Not quite. Word problems are one place to use MP2, but the practice also covers interpreting expressions, rejecting solutions that do not fit, and using properties of operations flexibly. A student can solve a word problem without MP2 by grabbing numbers; MP2 asks for meaning at each step.
How does MP2 look different in grade 6 and in Algebra I?
In grade 6, students write expressions such as 6n - 140 for a ticket sale and explain each number. In Algebra I, they interpret parts of expressions such as 25,000(0.84)ᵗ and decide which solutions of a quadratic make sense. The habit of asking "What does this number mean?" is the same.
How do I help students who just want the answer?
Ask for a sentence in context with units as part of every answer, and give credit for it. Ask "What does that number mean?" more often than "What did you get?" Short tasks such as writing a story for an expression make contextualizing a routine.
What is a "coherent representation" of a problem?
It is a representation (a table, a diagram, a graph or a set of equations) in which every part matches the situation and the parts fit together. In the water-park problem, the table, the two equations and the final check all describe the same 11 people and the same $274.
Is MP2 tested?
Not as a separate item. Tests built on the content standards include many items that ask students to interpret a number or expression in context or to choose a model for a situation, and those items depend on MP2. Check your state test's published blueprint for how it describes them.
Which content standards are good for practicing MP2?
Good fits include writing and evaluating expressions (6.EE.A.2), proportional relationships (7.RP.A.2), rate of change and initial value (8.F.B.4), interpreting expressions in context (HSA.SSE.A.1) and using units to guide problem solving (HSN.Q.A.1).
How is MP2 different from MP4, Model with mathematics?
MP2 is the back-and-forth between symbols and meaning that happens in any problem with quantities. MP4 is the larger cycle of building a model of a real situation: making assumptions, choosing a representation, analyzing it and improving the model. Modeling uses MP2 at every step.
07
Related Standards
5 standards
These content standards are good places to practice MP2: earlier standards to start with, standards at the same level, and later courses where the practice keeps paying off.
Before this lesson
6.EE.A.2Prerequisite
Write, read, and evaluate expressions in which letters stand for numbers
