In plain English: MP5 is the Common Core Standard for Mathematical Practice about tools. Students choose among pencil and paper, rulers and protractors, calculators, spreadsheets, graphing and geometry software, and online resources; they know what each tool reveals and where it misleads; they check tool results by estimation; and they use technology to explore models and concepts. It applies in every grade 6-12 course.
Use appropriate tools strategically. Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts.
Common Core State Standards for Mathematics · Domain: Standards for Mathematical Practice (MP) · Practice group: Modeling and using tools Also written as CCSS.MATH.PRACTICE.MP5 · Official standard
MP5 is about choosing and using tools on purpose. The official text lists "pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software." Proficient students know their tools well enough to decide when each one helps, and they know each tool's limitations: a calculator rounds, a graph window can hide a solution, a drawing is only as accurate as the hand that made it. They check tool results with estimation, use technology to see how a model responds to different assumptions, find reliable resources such as data on a website, and use technology to explore concepts.
This lesson moves through tools for different grade 6-12 domains: geometry drawings, arithmetic, graphs of functions, spreadsheets and data. Each task is labeled with a typical course. Students need access to at least one graphing tool and one spreadsheet, shared in groups if necessary.
Learning Objectives
By the end of this lesson, students will be able to:
Choose a tool for a task and justify the choice, naming what the tool shows and what it can hide
Interpret graphs and solutions produced by a graphing calculator, including checking for missed solutions
Use estimation to detect errors in calculator or spreadsheet results
Use a spreadsheet to test how a model's results change with its assumptions and compare predictions with data
Use reliable external resources and technology to pose problems and explore concepts
Prior Knowledge Required
Students should already be comfortable with:
Drawing shapes with a ruler and protractor 7.G.A.2
Scatter plots of two quantities 8.SP.A.1
Rounding and estimating with decimals
For the Algebra I tasks: graphs of linear, quadratic and exponential functions HSF.IF.C.7
Show five tasks. Students pick the best tool for each one and write one reason, without doing the tasks.
Warm-Up Prompt
"Which tool would you use for each task, and why? (a) 25% of 80. (b) 17.3² × 4.91. (c) The size of an angle in a printed triangle. (d) The average of 500 survey answers. (e) How the graph of y = ax² changes as a changes."
Discuss. Likely choices: mental math for (a), since a calculator is slower than knowing that 25% is a quarter (20); a calculator for (b), about 1,470; a protractor for (c); a spreadsheet for (d); a graphing tool with a slider for (e). Ask: "When would a calculator be the wrong choice for (a)?" (When you would type faster than you think, and a typing error would go unnoticed.) Introduce Diagram 1.
Direct Instruction20 minutes
Model five tool decisions. For each, say what the tool shows, what it could hide, and how you check the result.
List the available tools before starting, including pencil and paper.
Choose for the task: exactness, speed, the size of the data, or the need to see a picture.
Estimate first, so a tool's answer can be checked against it.
Read tool output critically: decimals are approximations, and a window shows only part of a graph.
Use technology to explore: change an assumption or drag a shape and watch what stays the same.
Choosing between drawing and calculating (Grade 7 / Geometry)
Is a triangle with sides 4 cm, 6 cm and 9 cm acute, right or obtuse?
Equation: A ruler-and-compass drawing shows a wide angle quickly. Calculation confirms it: 4² + 6² = 52, which is less than 9² = 81, so the triangle is obtuse; the largest angle is about 127°.
Solve 2ˣ = x + 4. There is no algebraic method in Algebra I, so graph y = 2ˣ and y = x + 4.
Equation: The intersect tool gives x ≈ -3.93 and x ≈ 2.76 (Diagram 2). Check: 2^2.76 ≈ 6.77 and 2.76 + 4 = 6.76. The left solution is easy to miss in a window that starts at x = 0.
Estimation detects a typing error (Grade 6-7)
A student needs 48.6 × 0.52 and the calculator shows 252.72.
Equation: Estimate: 50 × 0.5 = 25. The screen is about 10 times too big; the student typed 486. The correct product is 25.272.
A spreadsheet what-if (Algebra I)
Deposit $50 each month for 24 months. Compare a monthly interest rate of 0.5% with one of 0.3%.
Equation: Column B: new balance = old balance × (1 + rate) + 50. After 24 months: about $1,271.60 at 0.5% and about $1,242.33 at 0.3%. Changing one cell shows how much the assumption matters.
Exploring a concept with dynamic geometry (Geometry)
Draw a triangle, its three medians and their meeting point, then drag the vertices.
Equation: The medians always meet at one point, the centroid, two-thirds of the way from each vertex. For vertices (0, 0), (6, 0) and (2, 6), the centroid is (8/3, 2).
After Example 2, show Diagram 2 and ask: "How do you know there are no more solutions?" (For large x, 2ˣ grows faster than x + 4 and stays above it; for very negative x, 2ˣ is near 0 and x + 4 is negative.) After Example 5, stress that dragging gives evidence and understanding, and that a proof explains why it always works.
Guided Practice15 minutes
Pairs study three cases where a tool can mislead, decide what went wrong, and say how a strategic user would catch it.
(Grade 6) A calculator shows 2 ÷ 3 × 3 = 1.9999999. (The calculator stores 2 ÷ 3 as a rounded decimal. The exact answer is 2.)
(Algebra I) A graphing calculator in connected mode shows a vertical line at x = 2 on the graph of y = 1/(x - 2). (The calculator joined points on both sides of x = 2. The function is undefined there; the line is not part of the graph.)
(Grade 7) A spreadsheet average of quiz scores is 64, but most scores are in the 80s. (Blank cells for absent students were typed as 0 and counted. Remove them or leave them blank.)
For each case, the class writes one sentence starting "A strategic user would..."
Independent Practice15 minutes
Students use an external resource to solve and pose problems.
Use a reliable unit-conversion source (a textbook table or a government measurement website) to find how many miles a 10 km race is. Before trusting it, check with 1 mile ≈ 1.6 km. (10 ÷ 1.6 ≈ 6.2, and the exact value is about 6.21 miles.)
Find a reliable table of data on a website, such as a government data site, about a topic you care about. Record the source, then pose one question the data could answer and one it cannot.
Write two sentences on how you decided the source was reliable (who published it, and whether it says where the numbers came from).
Closure5-10 minutes
Exit ticket:
Name a task from today where a tool gave a misleading result, and how you caught it.
Give one task where you would not use a calculator, and explain why.
Complete: "Before I trust a graphing calculator's solution, I..."
Differentiation Strategies
For Struggling Students
Give a tool menu card with a picture of each tool and one example task
Ask for an estimate in words first ("about 25") before any tool is used
Pair students so one operates the tool and the other checks against the estimate, then switch
For Advanced Students
Ask students to find a graph window in which y = 2ˣ and y = x + 4 seem to meet only once, and explain how a user could be fooled
Ask students to build a spreadsheet that compares two loan payment plans and write a one-paragraph recommendation
Ask students to use dynamic geometry to discover a fact about quadrilaterals, then prove it
Assessment Guidance
What to Look For
Listen for reasons when students pick a tool ("the numbers are messy," "I need to see the whole graph," "there are 500 values"). Strong students estimate before they compute, question a tool's output that disagrees with the estimate, look for solutions a window may hide, and say that a dragged figure is evidence, not a proof. Watch for students who copy a calculator display without rounding sensibly, who accept a graph that shows only part of the picture, or who use a calculator for 25% of 80.
02
Classroom Activities
3 Activities
1
Tool Choice Stations
20 minGroups of 3-4, rotating
Five stations each hold one task and several tools. Groups choose a tool, solve the task, and record why that tool was the best choice and what its limitation was.
The Five Stations (with answers for the teacher)
Station 1 (Grade 7-8): A wheelchair ramp rises 1 ft over a 12 ft run. Find its angle. (Scale drawing and protractor: about 5°. Calculator: tan⁻¹(1/12) ≈ 4.76°.)
Station 2 (Grade 6): How many whole numbers from 1 to 1,000 are divisible by 7? (Paper: 1,000 ÷ 7 = 142.9, so 142. A spreadsheet works but is slower.)
Station 3 (Grade 6-7 statistics): Find the mean of 40 reaction times stored in a file. (Spreadsheet or statistics tool; typing 40 numbers into a calculator invites errors.)
Station 4 (Geometry): Construct the perpendicular bisector of a segment. (Compass and straightedge, or dynamic geometry software.)
Station 5 (Algebra I): Solve x³ - 6x + 2 = 0. (Graphing tool: about -2.60, 0.34 and 2.26. There is no quick paper method.)
Procedure
At each station, make an estimate or a sketch before using any tool
Record: the tool, the answer, one insight the tool gave, one limitation
At Station 5, check one solution by substituting it
Discussion Questions
At which station did two groups choose different tools? Were both reasonable?
Where did paper beat technology?
At Station 1, why do the protractor and calculator answers differ slightly?
2
Graphing Calculator Detective
20 minPairs
Pairs analyze what a graphing calculator shows for the equation x² = 2ˣ and decide whether the calculator has found every solution. This is the official high school example of MP5: analyzing graphs of functions and solutions generated using a graphing calculator.
Procedure
Graph y = x² and y = 2ˣ in the window x from 0 to 5, y from 0 to 20, and use the intersect tool
Check each solution by substituting it into both sides
Change the window to x from -3 to 5. Do new solutions appear?
Write a sentence on how you know there are no more solutions
Answer Key for the Teacher
The first window shows x = 2 and x = 4: 2² = 2² = 4 and 4² = 2⁴ = 16.
The wider window shows a third solution, x ≈ -0.77, where the falling left branch of x² meets 2ˣ.
For x > 4, 2ˣ grows faster than x² and stays above it, so there are exactly three solutions.
Discussion Questions
Which solution would a student miss with the first window?
Why are two of the solutions exact and one only a decimal?
What did the table feature show that the graph did not?
Modification for Distance Learning
Pairs use a free online graphing tool in a shared screen and paste screenshots of both windows into a shared document.
3
Spreadsheet What-If: Fish in a Pond
20 minGroups of 3
Groups build a spreadsheet model of a fish population, vary its assumptions, and compare its predictions with counts (invented data). Technology lets them "visualize the results of varying assumptions, explore consequences, and compare predictions with data."
The Model (Algebra II)
A pond can support about 1,000 fish. Each year the population grows by 30% of the room that is left: next = P + 0.3 × P × (1 - P/1,000). Start with 100 fish. Counts (invented) for years 0 to 3: 100, 129, 158 and 203.
Procedure
Put the year in column A and the model in column B (first cell 100, then the formula filled down for 15 years)
Put the counts in column C and the differences B - C in column D
Change the growth rate in one cell to 0.2 and to 0.4 and watch the graph change
Decide which rate fits the counts best
Answer Key for the Teacher
With a rate of 0.3, the model gives 100, 127, 160.3 and 200.6 for years 0 to 3, within about 3 fish of every count. Rates of 0.2 and 0.4 miss by more. With every rate, the population levels off near 1,000.
Discussion Questions
What happens to the population after many years? Why?
How would you change the spreadsheet if 50 fish were caught every year?
What would be hard to see without the spreadsheet's graph?
03
Diagrams & Visual Aids
2 diagrams
Diagram 1: Choosing a Tool: Insight and Limits
MP5 asks students to recognize "both the insight to be gained and their limitations" for each tool. The left column lists common tools, the middle column what each one does well, and the right column the error it invites. A strategic student picks the tool for the job and checks its result with estimation or a second tool.
Diagram 2: Reading a Graphing Tool's Solutions to 2ˣ = x + 4
The graphs of y = 2ˣ and y = x + 4, drawn to scale. A graphing tool's intersect command gives x ≈ -3.93 and x ≈ 2.76, the two solutions of 2ˣ = x + 4. The left intersection is close to the x-axis and easy to miss in a careless window. The tool gives decimals, not exact values, so students check each one by substituting.
04
Homework Assignment
~30 min
MP5 Homework: Choose, Use and Check Tools
Directions: Name the tool you use for each problem and why. Estimate before you compute, and say how you checked any result a tool gave you.
Part 1: Choose and Use Tools (Problems 1-3)
For each task, name the best tool and one limitation of that tool: (a) the volume of a cereal box; (b) the median of 2,000 test scores in a file; (c) whether lengths of 4 cm, 9 cm and 12 cm can form a triangle; (d) 15% of $60.
A graphing calculator shows the graphs of y = x³ - 5x and y = 1 crossing three times. Find the three solutions of x³ - 5x = 1 to two decimal places with a graphing tool, and check one of them by substituting it.
Estimate first, then decide which of these calculator results must be wrong, and explain how your estimate shows it: (a) 39.8 × 21.2 = 843.76; (b) 612 ÷ 0.48 = 127.5; (c) √850 = 29.15; (d) (3.1 × 10⁴)(2 × 10³) = 6.2 × 10⁷.
Part 2: Technology to Model and Explore (Problems 4-6)
A $9,000 car loan has a monthly interest rate of 0.6% and a payment of $250. Each month, new balance = 1.006 × old balance - 250. Use a spreadsheet or a calculator to find the balance after 3 months. Then change the payment to $300 and compare the two balances.
Use a reliable online source, such as the U.S. Census Bureau website, to find your state's population in 2010 and in 2020. Compute the percent change, name your source, and pose one question these data could help answer.
Use dynamic geometry software or careful drawings of three different quadrilaterals. In each, connect the midpoints of consecutive sides. What kind of shape appears every time? For the quadrilateral with vertices (0, 0), (8, 0), (6, 6) and (0, 4), find the midpoints and show that the shape has that property.
Rubric
Criterion
Full Credit (2 pts)
Partial Credit (1 pt)
No Credit (0 pts)
Tool Choice
A sensible tool with a reason and a limitation
A sensible tool without a reason
No tool named or an unsuitable one
Estimation and Checking
Estimates made first and used to accept or reject results
Some estimates or checks
No checks
Accuracy
Results correct and rounded sensibly
Minor errors
Major errors
Exploration and Sources
Spreadsheet or geometry work explained; source named and judged
Partly explained
Missing
05
Quiz: 20 Questions
Interactive, with answers
Instructions
Each question asks you to choose a tool, read what a tool shows, check a tool's result, or use technology to model or explore. 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
Which tool is the best choice for finding the mean of 600 survey responses stored in a file?
Answer: C
A spreadsheet can average 600 values in one formula without retyping them. Mental math (choice B) is a good tool for small, friendly numbers, not for 600 values.
Question 2 of 20 · Multiple Choice
A calculator shows 1 ÷ 3 × 3 = 0.9999999. What does this show?
Answer: A
The calculator rounds 1 ÷ 3 to a finite decimal, and multiplying the rounded value by 3 gives a result just under 1. Knowing this limitation is part of MP5. Choice B is false: (1/3) × 3 = 1 exactly. Choice C overreacts to a normal rounding effect.
Question 3 of 20 · Multiple Choice
A graphing calculator's intersect tool shows (1.73, 3) for the graphs of y = x² and y = 3. What should a student conclude?
Answer: D
The tool found only the intersection near the cursor. By symmetry, x² = 3 has two solutions, ±√3 ≈ ±1.73. Choice A trusts the tool without thinking about the graph. Choice B reads the y-coordinate as the solution. Choice C confuses "not a whole number" with "no exact value": √3 is exact.
Question 4 of 20 · Multiple Choice
A calculator shows 0.6 × 4.5 = 27. Which estimate shows the result is wrong?
Answer: B
Half of 4.5 is 2.25, and 0.6 is a little more than half, so the product is a little more than 2.25 (it is 2.7). The display, 27, is 10 times too big: the decimal point in 0.6 was probably dropped. Choice A repeats the typing error. Choice D rounds 0.6 to 6, dropping the same decimal point, so its estimate is also 10 times too big.
Question 5 of 20 · Multiple Choice
Which statement about measuring an angle in a drawing with a protractor is true?
Answer: A
A protractor reading is limited by the drawing and by the scale, so it is an estimate that a calculation can confirm. Choice C is false: protractors measure obtuse angles. Choice B ignores the tool's limitation.
Question 6 of 20 · Multiple Choice
Kai graphs y = 3/(x + 1) in connected mode and sees a vertical line at x = -1. What is the best interpretation?
Answer: D
At x = -1 the denominator is 0, so the function has no value there. In connected mode the calculator draws a segment between the last point on one side and the first point on the other. Choice A trusts the display over the algebra. Choice B confuses "undefined" with 0. Choice C ignores the denominator.
Question 7 of 20 · Multiple Choice
A student's spreadsheet models savings with the interest rate in one cell. She changes the rate from 2% to 4%. What does this let her do?
Answer: B
Changing one cell recalculates every row, so she can compare results under different assumptions. This is what MP5 means by visualizing "the results of varying assumptions." Choice A claims too much: a model is still an approximation.
Question 8 of 20 · Multiple Choice
A student is writing a report on how the population of her state has changed. Which source is the most appropriate?
Answer: C
An official census site publishes data with its methods and dates, so it is a reliable external resource. Choices A and B give no way to check where the numbers came from.
Question 9 of 20 · Multiple Choice
In dynamic geometry software, a student drags the vertices of a triangle and sees the displayed sum of its angles stay at 180°. What does this give her?
Answer: C
Dragging many triangles builds understanding and evidence, but it checks only the triangles drawn and the software's rounding; a proof with parallel lines explains why it is always true. Choice A overstates what the tool shows. Choice D contradicts what she saw.
Question 10 of 20 · Multiple Choice
A student finds the hypotenuse of a right triangle with legs 9 cm and 12 cm and gets 4.58 cm. Which reasoning best detects the error?
Answer: B
The hypotenuse is the longest side, so it must be more than 12 cm; the correct value is √(81 + 144) = 15 cm. The student found √(9 + 12) = √21 ≈ 4.58 and forgot to square the legs. Choice D adds the legs, which ignores the Pythagorean Theorem.
Question 11 of 20 · Multiple Choice
Which task is best done with mental math rather than a calculator?
Answer: A
25% is one quarter, and a quarter of 120 is 30, faster in your head than on a keypad. Choices B, C and D involve messy numbers, many values or a picture, which is where technology helps.
Question 12 of 20 · Multiple Choice
A graphing calculator table for y = x² - 12x + 35 shows y = 3, 0, -1, 0, 3 at x = 4, 5, 6, 7, 8. What can the student conclude?
Answer: D
The y-values are 0 at x = 5 and x = 7, and the table is symmetric about x = 6, where y = -1 is the smallest value. Choice A reads the x-values where y = 3. Choice B confuses the largest shown value with the minimum.
Question 13 of 20 · Multiple Choice
A student wants to compare a model's predictions with measured data in a spreadsheet. Which setup helps most?
Answer: A
Side-by-side columns and a difference column show at a glance where the model fits and where it misses, which is how technology helps "compare predictions with data." Choices B and C make the comparison impossible.
Question 14 of 20 · Multiple Choice
Which is a real limitation of a graphing calculator?
Answer: C
A poor window can hide intersections or turning points, and the solutions it reports are rounded decimals. Choices A and D are false: graphing calculators graph lines and make tables. Choice B is the opposite of the truth.
Question 15 of 20 · Short Answer
A carpenter needs to cut a board at a 35° angle and also find the length of the diagonal brace for a rectangular frame 1.2 m by 0.9 m. Which tool would you use for each job, and why? Find the length of the brace.
For the 35° cut, a protractor or an angle gauge (a speed square) measures and marks the angle directly. For the brace, calculate with the Pythagorean Theorem, since a tape measure on a frame that is not yet built is less accurate: √(1.2² + 0.9²) = √2.25 = 1.5 m.
Question 16 of 20 · Short Answer
Find every solution of x² = 2x + 8. Explain how a graphing tool would show the solutions, and check them without the tool.
Graph y = x² and y = 2x + 8; the intersect tool shows points at x = -2 and x = 4. Check by factoring: x² - 2x - 8 = (x - 4)(x + 2) = 0, so x = 4 or x = -2. Substitution: 16 = 8 + 8 and 4 = -4 + 8.
Question 17 of 20 · Short Answer
Before using a calculator, estimate 0.52 × 389 and 389 ÷ 0.52. Then compute both. Explain how the estimates would catch a student who pressed the wrong operation key.
Estimates: 0.52 × 389 ≈ 0.5 × 400 = 200, and 389 ÷ 0.52 ≈ 400 ÷ 0.5 = 800. Exact: 202.28 and about 748.08. Multiplying by a number near one half makes the result about half as big, and dividing by it makes the result about twice as big, so a student who pressed × instead of ÷ would see 202 when expecting about 800.
Question 18 of 20 · Short Answer
A deer population is modeled in a spreadsheet by P(next) = 1.2P - 50, starting with P = 400. Find the population after 3 years. Then change the yearly harvest from 50 to 90 and describe what happens.
With 50: 430, 466, 509.2 (about 509 deer), so the herd grows. With 90: 390, 378, 363.6 (about 364 deer), so the herd shrinks each year. The spreadsheet shows that the harvest decides whether the population grows or declines.
Question 19 of 20 · Short Answer
Use dynamic geometry software or a careful drawing: draw a circle with a diameter AB and choose any other point C on the circle. Measure angle ACB for several positions of C. What do you find, and how could you check it with coordinates?
Angle ACB is always 90°. Coordinate check with the unit circle: A = (-1, 0), B = (1, 0), C = (0.6, 0.8). Vector CA = (-1.6, -0.8) and vector CB = (0.4, -0.8); their dot product is -0.64 + 0.64 = 0, so the angle is a right angle.
Question 20 of 20 · Short Answer
A website's unit converter says that 3 miles = 48.28 km. Use what you know to decide whether to trust it, and give the correct value.
A mile is about 1.6 km, so 3 miles is about 3 × 1.6 ≈ 4.8 km, not 48. The converter (or the way it was read) is off by a factor of 10. Correct value: about 4.828 km. Checking an external resource against an estimate is part of using it strategically.
0 of 20 answered · 0 correct
06
Frequently Asked Questions
10 Questions
What does MP5 mean in math?
MP5 is the Standard for Mathematical Practice "Use appropriate tools strategically." Students choose the right tool for a task, from pencil and paper to spreadsheets and geometry software, know what each tool shows and where it can mislead, and check results with estimation.
Does MP5 mean students should always use technology?
No. Strategic use includes deciding not to use a tool. Finding 25% of 80 is faster in your head, and a quick sketch often shows more than a calculator. MP5 asks for "sound decisions about when each of these tools might be helpful."
What tools does MP5 list?
The text names pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package and dynamic geometry software. It also mentions external resources such as digital content on a website.
How do students check a graphing calculator's answer?
Substitute each reported solution into the original equation, look at a wider window for solutions the screen may hide, and compare with an estimate or the shape of the graphs. The tool gives rounded decimals, so a check should come out close, not exact.
Why does MP5 mention estimation?
Because estimation is how students catch tool errors. If 48.6 × 0.52 should be about 25 and the screen shows 252.72, the student knows to look for a typing mistake. The text says students "detect possible errors by strategically using estimation and other mathematical knowledge."
How can spreadsheets support MP5?
Spreadsheets handle large data sets and let students change one assumption, such as an interest rate or a growth rate, and see the effect on a whole model at once. Putting predictions next to data makes it easy to compare them.
Is using a website a math practice?
Yes, when it is done carefully. MP5 says students identify relevant external resources, "such as digital content located on a website," and use them to pose or solve problems. The skill includes judging whether a source is reliable and checking its numbers.
Is dynamic geometry software a substitute for proof?
No. Dragging a figure gives strong evidence and helps students see what stays the same, which deepens understanding. A proof explains why the property holds for every figure. The two work well together: explore first, then prove.
Which content standards are good for practicing MP5?
Good fits include drawing shapes with ruler, protractor and technology (7.G.A.2), scatter plots (8.SP.A.1), finding solutions with graphs (HSA.REI.D.11), graphing functions by hand and with technology (HSF.IF.C.7) and geometric constructions with many tools (HSG.CO.D.12).
How can I assess MP5 on a test without calculators?
Ask students which tool they would use and why, give them a calculator display or a graph and ask whether it can be right, or ask for an estimate that checks a given result. These questions test tool judgment without the tool.
07
Related Standards
5 standards
These content standards are good places to practice MP5: earlier standards to start with, standards at the same level, and later courses where the practice keeps paying off.
Before this lesson
7.G.A.2Prerequisite
Draw geometric shapes with ruler, protractor and technology from given conditions
