Six units with complete lessons, examples, practice, challenge work, and mastery checks.

Beginner explanation

A rational number can be written as a fraction. Irrational numbers, like pi and sqrt(2), never end or repeat in a pattern.

Vocabulary

rational, irrational, decimal expansion, number line, approximation

Equations / formulas

a/b where b is not 0 | sqrt(2) ≈ 1.414

Nashville example

Compare approximate walking distances around Centennial Park using decimals and square-root distances.

Mastery check

Classify 10 mixed numbers and explain two classifications.

AI tutor behavior

Ask for fraction evidence before revealing whether a number is rational.

10 practice problems

1. Solve a basic number classification problem with whole numbers.
2. Solve a number classification problem with a negative value.
3. Explain the first step for a number classification problem.
4. Choose the correct formula or rule for number classification.
5. Find and fix a mistake in a worked number classification example.
6. Compare two answers from a number classification problem.
7. Write a sentence explaining what the answer means.
8. Represent a number classification problem with a table, graph, diagram, or number line.
9. Solve a Nashville real-world number classification problem.
10. Write your own number classification problem and solve it.

3 challenge problems

1. Order sqrt(10), 3.1, and pi.
2. Create two rational numbers between sqrt(2) and 1.5.
3. Explain why every integer is rational.

Common mistakes

• Thinking every decimal is irrational.
• Forgetting repeating decimals are rational.
• Assuming every square root is irrational.

Hints

• Restate the question in your own words.
• Circle the numbers, variables, graph features, or units you know.
• Choose one rule, equation, graph move, or formula before calculating.
• Do one clean step, then check if the result makes sense.

Step-by-step answer frame

1. Label the known information.
2. Choose the matching rule, model, or formula.
3. Substitute values carefully.
4. Simplify one line at a time.
5. Write the answer with units or a short explanation.

Beginner explanation

Roots undo powers. Square roots undo squaring; cube roots undo cubing.

Vocabulary

square root, cube root, perfect square, perfect cube, estimate

Equations / formulas

sqrt(64)=8 | cuberoot(125)=5 | x^2=p | x^3=p

Nashville example

Estimate the diagonal distance across a square stage area for a Nashville school performance.

Mastery check

Evaluate or estimate 12 roots with at least 10 correct.

AI tutor behavior

Use perfect-square anchors and number-line language before decimals.

10 practice problems

1. Solve a basic root estimation problem with whole numbers.
2. Solve a root estimation problem with a negative value.
3. Explain the first step for a root estimation problem.
4. Choose the correct formula or rule for root estimation.
5. Find and fix a mistake in a worked root estimation example.
6. Compare two answers from a root estimation problem.
7. Write a sentence explaining what the answer means.
8. Represent a root estimation problem with a table, graph, diagram, or number line.
9. Solve a Nashville real-world root estimation problem.
10. Write your own root estimation problem and solve it.

3 challenge problems

1. Solve x^2=81.
2. Estimate sqrt(130).
3. Find the edge of a cube with volume 216.

Common mistakes

• Using half the number as the root.
• Forgetting negative solutions for x^2=p.
• Confusing square roots and cube roots.

Hints

• Restate the question in your own words.
• Circle the numbers, variables, graph features, or units you know.
• Choose one rule, equation, graph move, or formula before calculating.
• Do one clean step, then check if the result makes sense.

Step-by-step answer frame

1. Label the known information.
2. Choose the matching rule, model, or formula.
3. Substitute values carefully.
4. Simplify one line at a time.
5. Write the answer with units or a short explanation.

Beginner explanation

Scientific notation writes a number as a value from 1 to 10 times a power of 10.

Vocabulary

base, exponent, power of ten, coefficient, scientific notation

Equations / formulas

a x 10^n where 1 <= a < 10 | 10^-3=0.001 | x^a x x^b=x^(a+b)

Nashville example

Use scientific notation to compare Tennessee population to water molecules in a Cumberland River sample.

Mastery check

Convert, compare, and multiply scientific notation values with 80% accuracy.

AI tutor behavior

Ask if the original number is large or tiny before choosing exponent sign.

10 practice problems

1. Solve a basic scientific notation problem with whole numbers.
2. Solve a scientific notation problem with a negative value.
3. Explain the first step for a scientific notation problem.
4. Choose the correct formula or rule for scientific notation.
5. Find and fix a mistake in a worked scientific notation example.
6. Compare two answers from a scientific notation problem.
7. Write a sentence explaining what the answer means.
8. Represent a scientific notation problem with a table, graph, diagram, or number line.
9. Solve a Nashville real-world scientific notation problem.
10. Write your own scientific notation problem and solve it.

3 challenge problems

1. Compare 3.2 x 10^5 and 8.1 x 10^4.
2. Simplify 2 x 10^3 times 4 x 10^5.
3. Write 0.000072 in scientific notation.

Common mistakes

• Moving the decimal the wrong direction.
• Using a coefficient greater than 10.
• Adding exponents when adding numbers.

Hints

• Restate the question in your own words.
• Circle the numbers, variables, graph features, or units you know.
• Choose one rule, equation, graph move, or formula before calculating.
• Do one clean step, then check if the result makes sense.

Step-by-step answer frame

1. Label the known information.
2. Choose the matching rule, model, or formula.
3. Substitute values carefully.
4. Simplify one line at a time.
5. Write the answer with units or a short explanation.

Beginner explanation

Like terms have the same variable part. Distribution means multiplying every term inside parentheses.

Vocabulary

term, coefficient, like terms, distributive property, simplify

Equations / formulas

a(b+c)=ab+ac | 3x+5x=8x

Nashville example

Simplify the cost expression for snacks plus a delivery fee for a Nashville study group.

Mastery check

Simplify 10 expressions with distribution and like terms.

AI tutor behavior

Use arrows for distribution and color-code like terms.

10 practice problems

1. Solve a basic expression simplification problem with whole numbers.
2. Solve a expression simplification problem with a negative value.
3. Explain the first step for a expression simplification problem.
4. Choose the correct formula or rule for expression simplification.
5. Find and fix a mistake in a worked expression simplification example.
6. Compare two answers from a expression simplification problem.
7. Write a sentence explaining what the answer means.
8. Represent a expression simplification problem with a table, graph, diagram, or number line.
9. Solve a Nashville real-world expression simplification problem.
10. Write your own expression simplification problem and solve it.

3 challenge problems

1. Simplify -2(3x-5)+4x.
2. Find the error: 5(x+2)=5x+2.
3. Create two equivalent expressions for 12x+18.

Common mistakes

• Only distributing to the first term.
• Combining unlike terms.
• Dropping negative signs.

Hints

• Restate the question in your own words.
• Circle the numbers, variables, graph features, or units you know.
• Choose one rule, equation, graph move, or formula before calculating.
• Do one clean step, then check if the result makes sense.

Step-by-step answer frame

1. Label the known information.
2. Choose the matching rule, model, or formula.
3. Substitute values carefully.
4. Simplify one line at a time.
5. Write the answer with units or a short explanation.

Beginner explanation

An equation is balanced. Undo operations until the variable is alone, then check the answer.

Vocabulary

equation, inverse operation, solution, variable, check

Equations / formulas

2x+5=17 | 5x+4=2x+19

Nashville example

Compare two Nashville tutoring plans and find when the total cost is the same.

Mastery check

Solve 8 of 10 equations and check at least 2 by substitution.

AI tutor behavior

Ask students to name the undo step before doing arithmetic.

10 practice problems

1. Solve a basic linear equation solving problem with whole numbers.
2. Solve a linear equation solving problem with a negative value.
3. Explain the first step for a linear equation solving problem.
4. Choose the correct formula or rule for linear equation solving.
5. Find and fix a mistake in a worked linear equation solving example.
6. Compare two answers from a linear equation solving problem.
7. Write a sentence explaining what the answer means.
8. Represent a linear equation solving problem with a table, graph, diagram, or number line.
9. Solve a Nashville real-world linear equation solving problem.
10. Write your own linear equation solving problem and solve it.

3 challenge problems

1. Solve 2(3x-4)=5x+10.
2. Create an equation with no solution.
3. Create an equation with infinitely many solutions.

Common mistakes

• Changing only one side.
• Forgetting to distribute first.
• Not checking solutions.

Hints

• Restate the question in your own words.
• Circle the numbers, variables, graph features, or units you know.
• Choose one rule, equation, graph move, or formula before calculating.
• Do one clean step, then check if the result makes sense.

Step-by-step answer frame

1. Label the known information.
2. Choose the matching rule, model, or formula.
3. Substitute values carefully.
4. Simplify one line at a time.
5. Write the answer with units or a short explanation.

Beginner explanation

Inequalities show a range of answers. A system solution is where two rules are true at the same time.

Vocabulary

inequality, solution set, system, intersection, boundary

Equations / formulas

-3x>15 | y=2x+1 | y=-x+7

Nashville example

Use a budget inequality to plan a downtown Nashville class trip.

Mastery check

Solve 5 inequalities and interpret 3 systems from graphs.

AI tutor behavior

Use number-line visuals for inequalities and intersection language for systems.

10 practice problems

1. Solve a basic inequalities and systems problem with whole numbers.
2. Solve a inequalities and systems problem with a negative value.
3. Explain the first step for a inequalities and systems problem.
4. Choose the correct formula or rule for inequalities and systems.
5. Find and fix a mistake in a worked inequalities and systems example.
6. Compare two answers from a inequalities and systems problem.
7. Write a sentence explaining what the answer means.
8. Represent a inequalities and systems problem with a table, graph, diagram, or number line.
9. Solve a Nashville real-world inequalities and systems problem.
10. Write your own inequalities and systems problem and solve it.

3 challenge problems

1. Graph x >= -2.
2. Find the intersection of y=x+1 and y=-x+5.
3. Explain no solution for parallel lines.

Common mistakes

• Not flipping the sign with negatives.
• Reading the wrong intersection point.
• Confusing x and y.

Hints

• Restate the question in your own words.
• Circle the numbers, variables, graph features, or units you know.
• Choose one rule, equation, graph move, or formula before calculating.
• Do one clean step, then check if the result makes sense.

Step-by-step answer frame

1. Label the known information.
2. Choose the matching rule, model, or formula.
3. Substitute values carefully.
4. Simplify one line at a time.
5. Write the answer with units or a short explanation.

Beginner explanation

A function is a rule where each input has exactly one output.

Vocabulary

function, input, output, rule, ordered pair

Equations / formulas

y=2x+3 | f(x) names the output for input x

Nashville example

Model scooter rental cost near downtown Nashville as a function of minutes used.

Mastery check

Complete two function tables and identify two non-functions.

AI tutor behavior

Use a function machine and ask whether one input gets two outputs.

10 practice problems

1. Solve a basic function tables problem with whole numbers.
2. Solve a function tables problem with a negative value.
3. Explain the first step for a function tables problem.
4. Choose the correct formula or rule for function tables.
5. Find and fix a mistake in a worked function tables example.
6. Compare two answers from a function tables problem.
7. Write a sentence explaining what the answer means.
8. Represent a function tables problem with a table, graph, diagram, or number line.
9. Solve a Nashville real-world function tables problem.
10. Write your own function tables problem and solve it.

3 challenge problems

1. Create a table for y=-x+6.
2. Identify a non-function from ordered pairs.
3. Find x when y=15 for y=3x.

Common mistakes

• Mixing up input and output.
• Treating f(x) as multiplication.
• Missing repeated inputs with different outputs.

Hints

• Restate the question in your own words.
• Circle the numbers, variables, graph features, or units you know.
• Choose one rule, equation, graph move, or formula before calculating.
• Do one clean step, then check if the result makes sense.

Step-by-step answer frame

1. Label the known information.
2. Choose the matching rule, model, or formula.
3. Substitute values carefully.
4. Simplify one line at a time.
5. Write the answer with units or a short explanation.

Beginner explanation

To compare functions, look at starting value and rate of change, not just one point.

Vocabulary

linear, nonlinear, rate of change, initial value, representation

Equations / formulas

rate = change in y / change in x | y=mx+b

Nashville example

Compare two Nashville music lesson payment plans.

Mastery check

Compare four functions across different representations.

AI tutor behavior

Ask for rate and starting value separately before choosing.

10 practice problems

1. Solve a basic comparing functions problem with whole numbers.
2. Solve a comparing functions problem with a negative value.
3. Explain the first step for a comparing functions problem.
4. Choose the correct formula or rule for comparing functions.
5. Find and fix a mistake in a worked comparing functions example.
6. Compare two answers from a comparing functions problem.
7. Write a sentence explaining what the answer means.
8. Represent a comparing functions problem with a table, graph, diagram, or number line.
9. Solve a Nashville real-world comparing functions problem.
10. Write your own comparing functions problem and solve it.

3 challenge problems

1. Compare a graph and equation.
2. Find which plan is cheaper after 10 hours.
3. Explain why y=x^2 is not linear.

Common mistakes

• Comparing intercepts instead of rates.
• Using only one point.
• Calling every graph linear.

Hints

• Restate the question in your own words.
• Circle the numbers, variables, graph features, or units you know.
• Choose one rule, equation, graph move, or formula before calculating.
• Do one clean step, then check if the result makes sense.

Step-by-step answer frame

1. Label the known information.
2. Choose the matching rule, model, or formula.
3. Substitute values carefully.
4. Simplify one line at a time.
5. Write the answer with units or a short explanation.

Beginner explanation

A graph tells a story from left to right. Steeper parts mean faster change; flat parts mean no change.

Vocabulary

increasing, decreasing, constant, interval, qualitative

Equations / formulas

slope = rise/run

Nashville example

Describe travel distance from East Nashville to Bridgestone Arena.

Mastery check

Write accurate stories for three graphs and sketch one from a story.

AI tutor behavior

Have students point to the graph section and say what is happening in ordinary language.

10 practice problems

1. Solve a basic graph interpretation problem with whole numbers.
2. Solve a graph interpretation problem with a negative value.
3. Explain the first step for a graph interpretation problem.
4. Choose the correct formula or rule for graph interpretation.
5. Find and fix a mistake in a worked graph interpretation example.
6. Compare two answers from a graph interpretation problem.
7. Write a sentence explaining what the answer means.
8. Represent a graph interpretation problem with a table, graph, diagram, or number line.
9. Solve a Nashville real-world graph interpretation problem.
10. Write your own graph interpretation problem and solve it.

3 challenge problems

1. Sketch a bus stopping at two lights.
2. Describe an impossible distance graph.
3. Match three graphs to stories.

Common mistakes

• Reading graphs right-to-left.
• Confusing height with speed.
• Ignoring axis labels.

Hints

• Restate the question in your own words.
• Circle the numbers, variables, graph features, or units you know.
• Choose one rule, equation, graph move, or formula before calculating.
• Do one clean step, then check if the result makes sense.

Step-by-step answer frame

1. Label the known information.
2. Choose the matching rule, model, or formula.
3. Substitute values carefully.
4. Simplify one line at a time.
5. Write the answer with units or a short explanation.

Beginner explanation

The coordinate plane is a map. Proportional graphs pass through (0,0).

Vocabulary

coordinate, origin, quadrant, proportional, unit rate

Equations / formulas

y=kx | (x,y)

Nashville example

Graph ticket cost if each Nashville Sounds ticket costs the same amount.

Mastery check

Plot points and identify unit rate from three proportional graphs.

AI tutor behavior

Use x-before-y language and ask what happens when x is zero.

10 practice problems

1. Solve a basic coordinate graphing problem with whole numbers.
2. Solve a coordinate graphing problem with a negative value.
3. Explain the first step for a coordinate graphing problem.
4. Choose the correct formula or rule for coordinate graphing.
5. Find and fix a mistake in a worked coordinate graphing example.
6. Compare two answers from a coordinate graphing problem.
7. Write a sentence explaining what the answer means.
8. Represent a coordinate graphing problem with a table, graph, diagram, or number line.
9. Solve a Nashville real-world coordinate graphing problem.
10. Write your own coordinate graphing problem and solve it.

3 challenge problems

1. Compare y=2x and y=5x.
2. Find unit rate from a graph.
3. Explain why proportional graphs start at the origin.

Common mistakes

• Reversing x and y.
• Skipping the origin.
• Using total instead of unit rate.

Hints

• Restate the question in your own words.
• Circle the numbers, variables, graph features, or units you know.
• Choose one rule, equation, graph move, or formula before calculating.
• Do one clean step, then check if the result makes sense.

Step-by-step answer frame

1. Label the known information.
2. Choose the matching rule, model, or formula.
3. Substitute values carefully.
4. Simplify one line at a time.
5. Write the answer with units or a short explanation.

Beginner explanation

Slope is steepness or rate of change. The y-intercept is where the line starts on the y-axis.

Vocabulary

slope, rise, run, y-intercept, initial value

Equations / formulas

m=(y2-y1)/(x2-x1) | y=mx+b

Nashville example

Model a downtown Nashville parking garage with a starting fee plus hourly cost.

Mastery check

Find slope and intercept from four representations.

AI tutor behavior

Draw rise/run arrows and separate starting value from rate.

10 practice problems

1. Solve a basic slope and intercepts problem with whole numbers.
2. Solve a slope and intercepts problem with a negative value.
3. Explain the first step for a slope and intercepts problem.
4. Choose the correct formula or rule for slope and intercepts.
5. Find and fix a mistake in a worked slope and intercepts example.
6. Compare two answers from a slope and intercepts problem.
7. Write a sentence explaining what the answer means.
8. Represent a slope and intercepts problem with a table, graph, diagram, or number line.
9. Solve a Nashville real-world slope and intercepts problem.
10. Write your own slope and intercepts problem and solve it.

3 challenge problems

1. Find slope from (-2,5) and (4,-1).
2. Explain zero slope.
3. Write a line with slope -2 and y-intercept 7.

Common mistakes

• Using run over rise.
• Plotting intercept on the x-axis.
• Missing negative slope.

Hints

• Restate the question in your own words.
• Circle the numbers, variables, graph features, or units you know.
• Choose one rule, equation, graph move, or formula before calculating.
• Do one clean step, then check if the result makes sense.

Step-by-step answer frame

1. Label the known information.
2. Choose the matching rule, model, or formula.
3. Substitute values carefully.
4. Simplify one line at a time.
5. Write the answer with units or a short explanation.

Beginner explanation

Slope-intercept form tells you where to start and how to move: start at b, then use m.

Vocabulary

slope-intercept form, linear model, rate, initial value, solution

Equations / formulas

y=mx+b

Nashville example

Model rideshare cost from Germantown to downtown Nashville.

Mastery check

Graph three equations and write one equation from a story.

AI tutor behavior

Ask students to identify b first, then use slope as movement.

10 practice problems

1. Solve a basic linear modeling problem with whole numbers.
2. Solve a linear modeling problem with a negative value.
3. Explain the first step for a linear modeling problem.
4. Choose the correct formula or rule for linear modeling.
5. Find and fix a mistake in a worked linear modeling example.
6. Compare two answers from a linear modeling problem.
7. Write a sentence explaining what the answer means.
8. Represent a linear modeling problem with a table, graph, diagram, or number line.
9. Solve a Nashville real-world linear modeling problem.
10. Write your own linear modeling problem and solve it.

3 challenge problems

1. Write equation for $4 start fee plus $2 per mile.
2. Check if (3,7) is on y=2x+1.
3. Compare two linear models.

Common mistakes

• Starting at the wrong intercept.
• Forgetting slope as rise/run.
• Missing units.

Hints

• Restate the question in your own words.
• Circle the numbers, variables, graph features, or units you know.
• Choose one rule, equation, graph move, or formula before calculating.
• Do one clean step, then check if the result makes sense.

Step-by-step answer frame

1. Label the known information.
2. Choose the matching rule, model, or formula.
3. Substitute values carefully.
4. Simplify one line at a time.
5. Write the answer with units or a short explanation.

Beginner explanation

Transformations move or resize shapes. Similar figures have the same shape and proportional sides.

Vocabulary

translation, rotation, reflection, dilation, scale factor, similar

Equations / formulas

(x,y)->(x+a,y+b) | (x,y)->(kx,ky)

Nashville example

Resize a simple Nashville school event logo using dilations.

Mastery check

Transform four points and explain whether size changed.

AI tutor behavior

Ask whether the shape moved, flipped, turned, or resized.

10 practice problems

1. Solve a basic transformations problem with whole numbers.
2. Solve a transformations problem with a negative value.
3. Explain the first step for a transformations problem.
4. Choose the correct formula or rule for transformations.
5. Find and fix a mistake in a worked transformations example.
6. Compare two answers from a transformations problem.
7. Write a sentence explaining what the answer means.
8. Represent a transformations problem with a table, graph, diagram, or number line.
9. Solve a Nashville real-world transformations problem.
10. Write your own transformations problem and solve it.

3 challenge problems

1. Reflect a triangle over the y-axis.
2. Find a missing side in similar triangles.
3. Describe two transformations between figures.

Common mistakes

• Rotating the wrong direction.
• Reflecting over the wrong axis.
• Scaling only one coordinate.

Hints

• Restate the question in your own words.
• Circle the numbers, variables, graph features, or units you know.
• Choose one rule, equation, graph move, or formula before calculating.
• Do one clean step, then check if the result makes sense.

Step-by-step answer frame

1. Label the known information.
2. Choose the matching rule, model, or formula.
3. Substitute values carefully.
4. Simplify one line at a time.
5. Write the answer with units or a short explanation.

Beginner explanation

In a right triangle, the squares of the two shorter sides add to the square of the longest side.

Vocabulary

right triangle, leg, hypotenuse, distance, converse

Equations / formulas

a^2+b^2=c^2

Nashville example

Estimate straight-line distance between two points on a Nashville neighborhood map.

Mastery check

Solve three side-length problems and one coordinate-distance problem.

AI tutor behavior

Have students identify the hypotenuse before substituting numbers.

10 practice problems

1. Solve a basic Pythagorean theorem problem with whole numbers.
2. Solve a Pythagorean theorem problem with a negative value.
3. Explain the first step for a Pythagorean theorem problem.
4. Choose the correct formula or rule for Pythagorean theorem.
5. Find and fix a mistake in a worked Pythagorean theorem example.
6. Compare two answers from a Pythagorean theorem problem.
7. Write a sentence explaining what the answer means.
8. Represent a Pythagorean theorem problem with a table, graph, diagram, or number line.
9. Solve a Nashville real-world Pythagorean theorem problem.
10. Write your own Pythagorean theorem problem and solve it.

3 challenge problems

1. Find distance between (-2,5) and (4,-3).
2. Decide if 7,24,25 is right.
3. Find missing leg when c=13 and a=5.

Common mistakes

• Using the wrong side as c.
• Adding sides instead of squares.
• Forgetting the square root.

Hints

• Restate the question in your own words.
• Circle the numbers, variables, graph features, or units you know.
• Choose one rule, equation, graph move, or formula before calculating.
• Do one clean step, then check if the result makes sense.

Step-by-step answer frame

1. Label the known information.
2. Choose the matching rule, model, or formula.
3. Substitute values carefully.
4. Simplify one line at a time.
5. Write the answer with units or a short explanation.

Beginner explanation

Volume measures how much space a 3D shape holds.

Vocabulary

volume, radius, height, cylinder, cone, sphere

Equations / formulas

V=pi r^2h | V=(1/3)pi r^2h | V=(4/3)pi r^3

Nashville example

Estimate a cylindrical water tank volume for an outdoor Nashville festival.

Mastery check

Choose and apply the correct volume formula for each solid.

AI tutor behavior

Ask students to name the solid first, then choose the formula.

10 practice problems

1. Solve a basic volume formulas problem with whole numbers.
2. Solve a volume formulas problem with a negative value.
3. Explain the first step for a volume formulas problem.
4. Choose the correct formula or rule for volume formulas.
5. Find and fix a mistake in a worked volume formulas example.
6. Compare two answers from a volume formulas problem.
7. Write a sentence explaining what the answer means.
8. Represent a volume formulas problem with a table, graph, diagram, or number line.
9. Solve a Nashville real-world volume formulas problem.
10. Write your own volume formulas problem and solve it.

3 challenge problems

1. Compare a cone and cylinder with same radius and height.
2. Find sphere volume when r=4.
3. Design a container near 200 cubic units.

Common mistakes

• Using diameter instead of radius.
• Forgetting one-third for cones.
• Mixing area and volume units.

Hints

• Restate the question in your own words.
• Circle the numbers, variables, graph features, or units you know.
• Choose one rule, equation, graph move, or formula before calculating.
• Do one clean step, then check if the result makes sense.

Step-by-step answer frame

1. Label the known information.
2. Choose the matching rule, model, or formula.
3. Substitute values carefully.
4. Simplify one line at a time.
5. Write the answer with units or a short explanation.

Beginner explanation

Scatter plots show pairs of data. The pattern can be positive, negative, linear, nonlinear, or unclear.

Vocabulary

scatter plot, association, cluster, outlier, linear

Equations / formulas

trend line is an informal model

Nashville example

Analyze study time and quiz score data from a Nashville after-school program.

Mastery check

Interpret three scatter plots using correct association vocabulary.

AI tutor behavior

Ask what happens to y as x increases and remind students association is not proof of cause.

10 practice problems

1. Solve a basic scatter plots problem with whole numbers.
2. Solve a scatter plots problem with a negative value.
3. Explain the first step for a scatter plots problem.
4. Choose the correct formula or rule for scatter plots.
5. Find and fix a mistake in a worked scatter plots example.
6. Compare two answers from a scatter plots problem.
7. Write a sentence explaining what the answer means.
8. Represent a scatter plots problem with a table, graph, diagram, or number line.
9. Solve a Nashville real-world scatter plots problem.
10. Write your own scatter plots problem and solve it.

3 challenge problems

1. Create data with negative association.
2. Identify an outlier.
3. Judge whether a trend line fits well.

Common mistakes

• Saying association proves cause.
• Forcing a line through every point.
• Ignoring outliers.

Hints

• Restate the question in your own words.
• Circle the numbers, variables, graph features, or units you know.
• Choose one rule, equation, graph move, or formula before calculating.
• Do one clean step, then check if the result makes sense.

Step-by-step answer frame

1. Label the known information.
2. Choose the matching rule, model, or formula.
3. Substitute values carefully.
4. Simplify one line at a time.
5. Write the answer with units or a short explanation.

Beginner explanation

A trend line can model data. Tables organize counts so groups can be compared clearly.

Vocabulary

linear model, slope, intercept, two-way table, relative frequency

Equations / formulas

y=mx+b | relative frequency = part / total

Nashville example

Use a trend line to predict attendance at a Nashville school club meeting.

Mastery check

Use one linear model and one table to answer evidence questions.

AI tutor behavior

Ask what slope means in the story, not just the number.

10 practice problems

1. Solve a basic linear data models problem with whole numbers.
2. Solve a linear data models problem with a negative value.
3. Explain the first step for a linear data models problem.
4. Choose the correct formula or rule for linear data models.
5. Find and fix a mistake in a worked linear data models example.
6. Compare two answers from a linear data models problem.
7. Write a sentence explaining what the answer means.
8. Represent a linear data models problem with a table, graph, diagram, or number line.
9. Solve a Nashville real-world linear data models problem.
10. Write your own linear data models problem and solve it.

3 challenge problems

1. Interpret slope in a study-time model.
2. Complete a two-way table.
3. Compare two conditional percentages.

Common mistakes

• Treating intercept as rate.
• Using raw counts when percentages are needed.
• Forgetting units.

Hints

• Restate the question in your own words.
• Circle the numbers, variables, graph features, or units you know.
• Choose one rule, equation, graph move, or formula before calculating.
• Do one clean step, then check if the result makes sense.

Step-by-step answer frame

1. Label the known information.
2. Choose the matching rule, model, or formula.
3. Substitute values carefully.
4. Simplify one line at a time.
5. Write the answer with units or a short explanation.

Beginner explanation

Probability is chance from 0 to 1. Compound events combine more than one action.

Vocabulary

probability, sample space, compound event, outcome, simulation

Equations / formulas

P(event)=favorable outcomes/total outcomes

Nashville example

Design a fair probability game for a Nashville school fundraiser booth.

Mastery check

Represent sample spaces three ways and calculate compound probabilities.

AI tutor behavior

Have students list the sample space before calculating probability.

10 practice problems

1. Solve a basic compound probability problem with whole numbers.
2. Solve a compound probability problem with a negative value.
3. Explain the first step for a compound probability problem.
4. Choose the correct formula or rule for compound probability.
5. Find and fix a mistake in a worked compound probability example.
6. Compare two answers from a compound probability problem.
7. Write a sentence explaining what the answer means.
8. Represent a compound probability problem with a table, graph, diagram, or number line.
9. Solve a Nashville real-world compound probability problem.
10. Write your own compound probability problem and solve it.

3 challenge problems

1. Build a tree diagram for two coin flips.
2. Design a fair game.
3. Compare theoretical and experimental probability.

Common mistakes

• Counting only one event.
• Letting probability exceed 1.
• Confusing experimental and theoretical probability.

Hints

• Restate the question in your own words.
• Circle the numbers, variables, graph features, or units you know.
• Choose one rule, equation, graph move, or formula before calculating.
• Do one clean step, then check if the result makes sense.

Step-by-step answer frame

1. Label the known information.
2. Choose the matching rule, model, or formula.
3. Substitute values carefully.
4. Simplify one line at a time.
5. Write the answer with units or a short explanation.