In plain English: MP4 is the Common Core Standard for Mathematical Practice about modeling. Students apply the math they know to problems from everyday life, society and the workplace: they identify the important quantities, make assumptions, map relationships with tables, graphs, flowcharts and formulas, analyze them, interpret the results in context, and improve the model when it fails. It applies in every grade 6-12 course.
Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.
Common Core State Standards for Mathematics · Domain: Standards for Mathematical Practice (MP) · Practice group: Modeling and using tools Also written as CCSS.MATH.PRACTICE.MP4 · Official standard
MP4 asks students to apply the mathematics they know to problems "arising in everyday life, society, and the workplace." A model is a mathematical description of a real situation: a table, a graph, a two-way table, a flowchart or a formula. To build one, students identify the important quantities and make assumptions and approximations (simplifications they choose on purpose, knowing they may need to change them). They analyze the model, interpret the results in context, ask whether the results make sense, and improve the model if it has not served its purpose. Diagram 1 shows this cycle.
The official text gives examples at each level: in middle grades, proportional reasoning to plan a school event or analyze a community problem; by high school, geometry to solve a design problem or a function to describe how one quantity depends on another. This lesson uses all of them, and each task is labeled with a typical course.
Learning Objectives
By the end of this lesson, students will be able to:
Identify the important quantities in a real situation and state the assumptions a model makes
Represent relationships with a table, two-way table, graph, flowchart or formula
Use proportional reasoning, geometry or a function to analyze a model and draw conclusions
Interpret a model's results in context and decide whether they make sense
Improve a model when its predictions do not fit the situation or new data
Prior Knowledge Required
Students should already be comfortable with:
Multistep ratio and percent problems 7.RP.A.3
Volume of cylinders 8.G.C.9
Using a linear model of data and interpreting its slope and intercept 8.SP.A.3
For the Algebra I tasks: exponential functions HSF.LE.A.1
Pose a question with no numbers in it. Pairs have five minutes to list what they would need to know and what they would assume.
Warm-Up Prompt
"About how many liters of water does our school use on a school day? Do not look anything up yet. What quantities matter? What will you assume? What is a reasonable range for the answer?"
Collect quantities on the board (number of people, toilet flushes, drinking water, the kitchen, cleaning) and assumptions (each person flushes about 3 times at school, at about 6 L per flush). One rough model: 1,200 people × (3 flushes × 6 L + 2 L for hands and drinking) = 1,200 × 20 = 24,000 L. Ask what would change the estimate most. Point out that the class just did the first two steps of Diagram 1 before computing anything.
Direct Instruction20 minutes
Walk through the modeling cycle in Diagram 1 with five examples. For each one, name the quantities, the assumptions and the representation before computing.
Quantities: list what matters and what can be ignored.
Assumptions: write each simplification as a sentence, so it can be checked later.
Formulate: choose a representation that shows the relationships: a table, two-way table, graph, flowchart or formula.
Analyze and interpret: compute, then say what the result means in the situation.
Validate and improve: compare with reality or new data; revise the assumptions or the formula if needed.
Plan a school event: proportional reasoning (Grade 6-7)
The 8th grade is ordering pizza for a party for 180 students. Assume 90% attend, each eats 2.5 slices, and a pizza has 8 slices.
Equation: 180 × 0.9 = 162 students; 162 × 2.5 = 405 slices; 405 ÷ 8 = 50.6, so order 51 pizzas. If many pizzas are left over, revise the 2.5 slices for next time.
Two-way table: a question for the community (Grade 8)
A survey of 200 students asks whether school should start later. Grades 9-10: 60 yes, 40 no. Grades 11-12: 75 yes, 25 no.
Equation: Yes: 60 of 100 younger students (60%) and 75 of 100 older students (75%). Conclusion: support is higher among older students, in this sample.
A function, then an improved function (Algebra I)
Tea at 85°C cools to 73°C in 5 minutes in a 21°C room. Model 1: the line through those two points.
Equation: T = 85 - 2.4t predicts 13°C at t = 30, colder than the room, which is impossible. Model 2 assumes the tea cools toward 21°C: T = 21 + 64(0.96)ᵗ gives about 40°C at t = 30 (Diagram 2).
A geometry design problem (Grade 8 / Geometry)
Design a cylindrical can that holds 473 cm³ (16 fluid ounces) using as little metal as possible. Assume the can is a perfect cylinder and ignore the seams.
Equation: h = 473 ÷ (πr²). Surface area 2πr² + 2πrh: r = 3 cm gives about 372 cm², r = 4.2 cm about 336 cm², r = 5.5 cm about 362 cm². A radius near 4.2 cm uses the least metal.
A flowchart for a workplace rule (Grade 7)
An online store charges $8.50 to ship up to 2 lb, plus $1.75 for each extra pound or part of a pound. Orders over $75 ship free. Ship a 5.3 lb package on a $40 order.
Equation: Flowchart: Is the order over $75? No. Is the weight over 2 lb? Yes: 3.3 extra lb counts as 4 pounds. Cost: 8.50 + 4 × 1.75 = $15.50.
After Example 3, show Diagram 2. Ask: "Which assumption made Model 1 fail?" (That the tea keeps losing 2.4°C every minute forever.) After Example 4, show a real 16-ounce can: its radius is about 3.3 cm, not 4.2 cm. Ask why a real design might not use the least metal (it must fit a hand and a vending machine, and its ends are thicker).
Guided Practice15 minutes
Pairs model one problem from society, writing each step of the cycle.
Problem (Grade 7): A class wants to grow tomatoes for a local food pantry in a 6 m by 4 m garden. Paths will take up 20% of the garden. Each plant needs 0.5 m² and yields about 4 kg of tomatoes in a season. About how many kilograms can the class donate?
Quantities: garden area, path share, space per plant, yield per plant.
Assumptions: every plant survives and gives the average yield; nothing is eaten by the class.
Analyze: 24 m² × 0.8 = 19.2 m² for plants; 19.2 ÷ 0.5 = 38.4, so 38 plants; 38 × 4 = 152 kg.
Interpret and validate: about 150 kg. If some plants die or pests eat part of the crop, the true amount will be lower, so the class might promise about 120 kg.
Independent Practice15 minutes
Students improve a model that did not serve its purpose.
Task (Grade 7-8): A lemonade stand used the model profit = 1.50c - 20 for c cups sold at $1.50 each with $20 of supplies. On Saturday it sold 60 cups, so the model predicted $70, but the stand made only $55.
Find a missing cost that explains the difference. (The $15 gap is $0.25 per cup, for example the cost of cups and ice.)
Write an improved model and test it. (profit = 1.25c - 20; with c = 60 it gives $55.)
Use the improved model to find how many cups the stand must sell to make $80. (1.25c - 20 = 80, so c = 80 cups.)
Closure5-10 minutes
Exit ticket:
Name one assumption you made today and how you would check it.
Describe a model from today that had to be improved. What was wrong with the first version?
Which representation (table, two-way table, graph, flowchart or formula) would you use to plan the next class party, and why?
Differentiation Strategies
For Struggling Students
Give a modeling organizer with one box per step of Diagram 1
Provide the list of quantities and ask students only to choose which ones matter and to write the assumptions
Use whole numbers first, then the real decimals
For Advanced Students
Ask students to find the radius of the 473 cm³ can with the least surface area to the nearest 0.1 cm using a table or a graphing tool, and to explain why a real can differs
Ask for a third model of the cooling tea and a comparison of its errors with Model 2
Ask students to find real data for a community question (such as bus ridership) and build and critique a model of it
Assessment Guidance
What to Look For
Look for students who write their assumptions down before computing and who interpret every result in context, with units. Strong students choose a representation that fits the relationships (a two-way table for two categories, a flowchart for rules with conditions, a formula for a dependence) and revise a model when its prediction is impossible or does not fit new data. Watch for answers such as 50.6 pizzas, for predictions far outside the data range accepted without comment, and for models that are never checked.
02
Classroom Activities
3 Activities
1
Plan the Spring Bake Sale
20 minGroups of 3-4
Groups use proportional reasoning to plan a school bake sale: how many cookies to bake, what profit to expect, and how many cookies they must sell to break even. This is the official middle-grades example of MP4: planning a school event.
Data Card (invented)
Each cookie costs $0.35 to make and sells for $1.25.
The table at the school fair costs $30.
About 300 people come to the fair. Last year, about 40% of visitors bought cookies, and buyers bought 2.5 cookies on average.
Break-even: each cookie earns $0.90 above its cost, so 30 ÷ 0.90 = 33.3, and the group must sell 34 cookies.
Procedure
List the quantities and write every assumption as a sentence (for example, "this year's visitors buy like last year's")
Build a table of profit for 100, 200, 300 and 400 cookies sold
Decide how many cookies to bake and justify it, including what happens to unsold cookies
Discussion Questions
Which assumption is the riskiest? How would the plan change if only 30% of visitors bought cookies?
Why might a group bake more than 300 cookies? Fewer?
What would you record at the sale to improve the model next year?
2
The Least-Metal Can
20 minPairs
Pairs solve a geometry design problem, the official high school example of MP4: find a cylinder that holds 473 cm³ with the least metal, then compare their design with a real can.
Procedure
Write the volume and surface-area formulas and the assumptions (a perfect cylinder, the same metal thickness everywhere)
Make a table for r = 2, 3, 3.5, 4, 5 and 6 cm: the height h = 473 ÷ (πr²) and the surface area 2πr² + 2πrh
Graph surface area against radius and estimate the best radius
Measure a real can and compare
Answer Key for the Teacher
r = 2 cm: h ≈ 37.6 cm, area ≈ 498 cm²; r = 3 cm: area ≈ 372 cm²; r = 4 cm: h ≈ 9.4 cm, area ≈ 337 cm²; r = 6 cm: area ≈ 384 cm².
The least area is near r = 4.2 cm (with h about 8.4 cm). A real 16-ounce can has r ≈ 3.3 cm and is taller.
Discussion Questions
Which assumption is least true for a real can?
If the top and bottom are twice as thick as the side, should the best can be taller or shorter? Why?
What other goals (grip, stacking, shipping) could change the design?
Modification for Distance Learning
Pairs build the table in a shared spreadsheet and graph it there, then measure a can at home.
3
Cooling Tea: Build, Test and Improve
20 minGroups of 3
Groups use a function to describe how temperature depends on time, the official high school example of using a function in MP4. They fit a first model, test it against the data, and improve it. If the teacher runs the optional demonstration, use warm tap water, not boiling water.
Data (invented)
A mug of tea in a 21°C room. Time in minutes and temperature in °C: (0, 85), (5, 73), (10, 64), (15, 56), (20, 49), (25, 44), (30, 40).
Procedure
Model 1: write the line through the first two points and use it to predict the temperature at 30 minutes
Compare the prediction with the data and with the room temperature
Model 2: assume the difference between the tea and the room shrinks by the same percent each minute. Test T = 21 + 64(0.96)ᵗ at t = 10, 20 and 30
Write which model you would use to predict when the tea reaches 30°C, and why
Discussion Questions
Why does Model 2 never go below 21°C?
Where is Model 2 farthest from the data? Is that close enough for the purpose?
What would change in Model 2 if the room were 18°C?
Challenge Variation
Use Model 2 to find when the tea reaches 30°C, by a table, a graph or logarithms, and decide whether the answer is believable.
03
Diagrams & Visual Aids
2 diagrams
Diagram 1: The Modeling Cycle
Modeling is a cycle, not a single calculation. Students choose the quantities that matter, make assumptions to simplify the situation, formulate a model, analyze it, interpret the result in context and validate it. If the result does not make sense or does not fit new data, they go back and improve the model.
Diagram 2: Improving a Model of Cooling Tea
Invented data: a mug of tea cools in a 21°C room (navy dots). Model 1, the line through the first two points, predicts 13°C at 30 minutes, colder than the room, so it fails the "does it make sense?" test. Model 2, T = 21 + 64(0.96)ᵗ, uses the assumption that the tea cools toward room temperature and fits all seven points within 1°C.
04
Homework Assignment
~30 min
MP4 Homework: Build, Use and Improve Models
Directions: For each problem, list the important quantities and your assumptions before you compute. End with a sentence that interprets your result in context and says whether it makes sense.
Part 1: Build the Model (Problems 1-3)
A community pool schedules 1 lifeguard for every 40 swimmers, with at least 2 on duty. On hot Saturdays, about 260 swimmers are in the pool at the busiest time. List the quantities and assumptions, and find how many lifeguards to schedule.
In an invented survey of 150 students, 70 live within 2 miles of school: 48 of them walk or bike, and 22 ride. Of the 80 who live farther away, 12 walk or bike, and 68 ride. Make a two-way table, find the percent of each group that walks or bikes, and state a conclusion.
A phone shows 100% battery at 9:00 a.m. and 76% at 11:00 a.m. Assume the battery drains at a steady rate. Write a function for the battery level after t hours, and predict when it reaches 20%. What assumption could make the prediction wrong?
Part 2: Analyze, Interpret and Improve (Problems 4-6)
A model for a sunflower's height is h = 10 + 12w centimeters after w weeks. What does it predict after 52 weeks? Does that make sense for a sunflower? Explain how you would improve the model, for example by limiting its domain.
A gardener has 24 m of fencing for three sides of a rectangular bed; a wall forms the fourth side. Find the dimensions that give the largest area, using a table or a function, and give that area.
For a field day, a school planned 0.5 L of water per student for 240 students. The water ran out after 2 hours of a 3-hour event. Explain which assumption failed, and use proportional reasoning to revise the plan.
Rubric
Criterion
Full Credit (2 pts)
Partial Credit (1 pt)
No Credit (0 pts)
Quantities and Assumptions
Important quantities and reasonable assumptions are stated
Some quantities or assumptions missing
None stated
Representation
A table, two-way table, graph or formula that fits the relationships
A representation with errors
No representation
Analysis
Correct calculations with units
Minor errors
Major errors
Interpretation and Revision
Results interpreted in context; unrealistic results lead to a revised model
Results interpreted but not checked
No interpretation
05
Quiz: 20 Questions
Interactive, with answers
Instructions
Each question asks you to choose quantities or assumptions, pick a representation, analyze a model, or interpret and improve it. 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 team is modeling how much paint it needs to repaint the walls of a classroom. Which quantity can the model safely leave out?
Answer: D
Paint depends on the wall area, the number of coats and the coverage per liter. The desks do not change how much paint the walls need. Leaving out the coats (choice B) would make the model underestimate by half for a two-coat job.
Question 2 of 20 · Multiple Choice
Which assumption is most reasonable for estimating how long a 300 km highway trip by car will take?
Answer: A
A highway trip with a stop or two averages well under the speed limit, and 90 km/h gives about 3 hours and 20 minutes. Choice B is far faster than any car on a highway. Choice C describes city traffic, not a highway.
Question 3 of 20 · Multiple Choice
Shipping costs depend on rules with conditions: free above $75, otherwise a base charge plus a charge per extra pound. Which representation shows such rules most clearly?
Answer: B
A flowchart shows each decision ("Is the order over $75?") and what happens next. A two-way table (choice C) summarizes counts for two categories, and a scatter plot shows paired numerical data.
Question 4 of 20 · Multiple Choice
A survey records, for each student, whether the student has a part-time job and whether the student plays a school sport. Which representation best shows the relationship?
Answer: C
Both variables are categories (job or no job; sport or no sport), and a two-way table shows the count for each combination, so row or column percents can be compared. A line graph (choice A) needs a quantity that changes over time.
Question 5 of 20 · Multiple Choice
A gym charges a $35 fee to join plus $12 per month. The model is C = 35 + 12m. What does it predict for 8 months?
Answer: C
C = 35 + 12(8) = 35 + 96 = $131. Choice A multiplies (35 + 12) by 8, charging the fee every month. Choice B leaves out the fee. Choice D uses 9 months.
Question 6 of 20 · Multiple Choice
A model of a town's population, P = 52,000(1.03)ᵗ, predicts about 2.4 million people in 130 years. What is the best reflection on that prediction?
Answer: B
The model may describe the next few years well, but growth rates change over long periods, so a prediction 130 years ahead is doubtful. Choice A treats a model as exact. Choice D changes the number without questioning the assumption behind it.
Question 7 of 20 · Multiple Choice
A model for the line outside a concert, L = 400 - 15t (people, t minutes after the doors open), predicts -50 people at t = 30. What is the best improvement?
Answer: C
The line is empty when 400 - 15t = 0, at t ≈ 26.7 minutes, so the model only makes sense up to then. Choice A reports an impossible count. Choice B changes the data rather than the domain. Choice D throws away the useful rate of 15 people per minute.
Question 8 of 20 · Multiple Choice
A class trip needs 1 adult chaperone for every 9 students, and 115 students are going. How many chaperones are needed?
Answer: D
115 ÷ 9 ≈ 12.8, and 12 chaperones can cover only 108 students, so 13 are needed. Choice A rounds down and leaves 7 students without coverage. Choice B is not a possible number of people.
Question 9 of 20 · Multiple Choice
Which statement about assumptions in a mathematical model is true?
Answer: A
Every model simplifies reality, and MP4 says proficient students make assumptions "realizing that these may need revision later." Stating them openly (unlike choice C) is what makes them possible to check.
Question 10 of 20 · Multiple Choice
A rectangular garden has 40 m of fencing on three sides, and a wall forms the fourth side. Which dimensions give the largest area?
Answer: D
With x meters on each side from the wall, the side along the wall is 40 - 2x, and the area x(40 - 2x) is largest at x = 10: 10 × 20 = 200 m². The square in choice A uses all 40 m but has area about 178 m². Choices B and C each give 150 m².
Question 11 of 20 · Multiple Choice
A recipe model says a scaled-up batch needs 7.5 eggs. What is the most sensible way to interpret this?
Answer: B
Eggs come whole, so the cook rounds to 8 (or uses 7 and a little extra liquid). Interpreting results in context means adjusting answers that cannot be carried out exactly. Choice D rejects a model that is close enough for its purpose.
Question 12 of 20 · Multiple Choice
A candle is 24 cm tall when lit. After 1, 2 and 3 hours it is 21.5 cm, 19 cm and 16.5 cm tall. Which function models its height h after t hours?
Answer: A
The height drops by the same 2.5 cm each hour, from 24 cm at t = 0, so the model is linear: h = 24 - 2.5t. Choice B would drop by a smaller amount each hour. Choice D starts from the 1-hour height. Choice C drops too fast.
Question 13 of 20 · Multiple Choice
A nurse must give 250 mg of a medicine that comes as a liquid with 125 mg in every 5 mL. How many milliliters should the nurse give?
Answer: D
The liquid has 125 ÷ 5 = 25 mg per mL, so 250 mg needs 250 ÷ 25 = 10 mL. Choice A divides 250 by 125 and forgets the 5 mL. Choice B divides 250 by 5, treating the 5 mL as if it were the strength in mg per mL. Workplace models must be right the first time.
Question 14 of 20 · Multiple Choice
A store's model predicted it would sell 300 umbrellas in July, but it sold 40. Which revision is the best improvement?
Answer: C
The model missed a quantity that drives umbrella sales: rain. A dry July means few umbrella sales, so adding expected rainfall improves the model. Choice A ignores evidence that the model failed. Choice B makes the July error even bigger.
Question 15 of 20 · Short Answer
A school picnic is planned for 320 students and 25 staff. Hot dogs come in packs of 8. Build a model for how many packs to buy: name the quantities, state your assumptions, and give your answer.
Quantities: number of people, share who attend, hot dogs per person, pack size. Sample assumptions: 85% attend and each eats 1.5 hot dogs. Model: 345 × 0.85 × 1.5 ≈ 440 hot dogs, and 440 ÷ 8 = 55, so about 55 packs. Other answers are fine if the assumptions are stated and the arithmetic follows from them.
Question 16 of 20 · Short Answer
Of 120 students, 50 have a pet. 30 of the pet owners and 20 of the students without pets say science is their favorite subject. Make a two-way table and compare the percent of each group whose favorite is science.
Pet: 30 science, 20 other (50). No pet: 20 science, 50 other (70). Science is the favorite of 30/50 = 60% of pet owners and 20/70 ≈ 28.6% of students without pets. In this group, pet owners are more likely to prefer science; the table does not show that pets cause the preference.
Question 17 of 20 · Short Answer
A sign maker charges a $3.00 setup fee plus $0.40 for each letter on a banner. Write a function for the cost of a banner with n letters and find the cost of a 25-letter banner.
C(n) = 3 + 0.40n, where n is the number of letters. C(25) = 3 + 0.40 × 25 = 3 + 10 = $13.00.
Question 18 of 20 · Short Answer
A model for a small-breed puppy's weight is w = 2 + 1.5m kilograms after m months. It predicts 38 kg at 24 months, but adult dogs of this breed weigh about 8 kg. What is wrong with the model, and how would you improve it?
2 + 1.5 × 24 = 38 kg, almost five times the adult weight. The model assumes the puppy gains 1.5 kg every month forever, but growth slows and stops. Improvements: limit the domain to the first few months (2 + 1.5m reaches 8 kg at m = 4), or use a model that levels off near 8 kg.
Question 19 of 20 · Short Answer
A closed box with a square base must hold 576 cm³. Compare the cardboard (surface area) needed for a base 12 cm on a side and a base 8 cm on a side. Which uses less?
Base 12 cm: height 576 ÷ 144 = 4 cm, area 2(144) + 4(12)(4) = 288 + 192 = 480 cm². Base 8 cm: height 576 ÷ 64 = 9 cm, area 2(64) + 4(8)(9) = 128 + 288 = 416 cm². The 8 cm base, the box closer to a cube, uses less cardboard.
Question 20 of 20 · Short Answer
A family drives about 14,000 miles a year. Car A gets 25 miles per gallon and Car B gets 40. If gas costs $3.60 per gallon, about how much would the family save per year with Car B? State one assumption.
Car A: 14,000 ÷ 25 = 560 gallons, costing $2,016. Car B: 14,000 ÷ 40 = 350 gallons, costing $1,260. Savings: about $756 per year. Assumptions: the gas price and the miles driven stay about the same, and the mileage ratings match real driving.
0 of 20 answered · 0 correct
06
Frequently Asked Questions
10 Questions
What does MP4 mean in math?
MP4 is the Standard for Mathematical Practice "Model with mathematics." Students use the math they know to describe and solve real problems: they choose quantities, make assumptions, build a representation, analyze it, interpret the result and improve the model if needed.
What counts as a mathematical model?
Any mathematical description of a real situation: an equation, a function, a table, a graph, a two-way table, a flowchart or a geometric diagram. The text of MP4 names "diagrams, two-way tables, graphs, flowcharts and formulas" as tools for mapping relationships.
Is a word problem the same as modeling?
Not always. Many word problems give every number and only one possible model. Modeling asks students to decide what matters, make assumptions and check whether the answer makes sense. A word problem becomes a modeling task when students make those decisions themselves.
How does MP4 look in middle school?
The official text gives the example of using proportional reasoning to plan a school event or analyze a problem in the community. Planning food for a party, a bake sale budget or a garden for a food pantry are typical grade 6-8 modeling tasks.
How does MP4 look in high school?
The text gives two examples: using geometry to solve a design problem, and using a function to describe how one quantity depends on another. Designing a can with the least metal and modeling how a drink cools are typical high school tasks.
Why do models need to be improved?
Every model rests on assumptions, and some of them turn out to be wrong. When a model predicts something impossible, such as tea colder than the room, or misses new data, students change an assumption or the formula. The text says students improve the model "if it has not served its purpose."
How is modeling with mathematics related to the modeling standards in high school?
The high school Common Core standards mark many content standards with a star symbol for modeling. MP4 is the practice students use when working on those standards, and it also applies in grades 6-8, where there are no stars.
How do I assess MP4?
Grade the whole cycle, not only the final number: quantities and assumptions, the representation, the analysis, and the interpretation and revision. The homework rubric above has one row for each. Accept different answers when they follow from clearly stated, reasonable assumptions.
Which content standards are good for practicing MP4?
Good fits include multistep ratio and percent problems (7.RP.A.3), linear models of data (8.SP.A.3), writing functions for relationships (HSF.BF.A.1), geometric design problems (HSG.MG.A.3) and scatter plots with fitted functions (HSS.ID.B.6).
How is MP4 different from MP1 and MP2?
MP1 is about persevering with any problem, and MP2 is about moving between symbols and meaning. MP4 adds the real-world cycle: simplifying a messy situation with assumptions and checking the model against reality. A good modeling task uses all three.
07
Related Standards
5 standards
These content standards are good places to practice MP4: earlier standards to start with, standards at the same level, and later courses where the practice keeps paying off.
Before this lesson
7.RP.A.3Prerequisite
Use proportional relationships to solve multistep ratio and percent problems
