This Index is meant to help you select questions to use for Test Talks in your classroom. Above all, select questions that you have not explicitly taught your students how to do and that they have the skills and understandings needed to find a way into the question. You can choose questions related to current class content or ones that are not. The Introduction of the Will This Be on the Test? packet has more guidance on selecting questions. Here you can quickly locate questions that address specific domains or content areas or provide opportunities to use specific tools, strategies, and Standards for Mathematical Practice.
For each question, you will find:
- A content summary that briefly describes the math content of the question.
- A list of strategies outlined in the teacher pages for the question. There are always more strategies for any question beyond those listed.
- Specific tools that can be used with the question, including number lines, bar models, area models, and tables.
- Standards for Mathematical Practice (SMPs) fostered by the strategies outlined in the teacher pages. Other strategies might foster other SMPs.
- Note: MP.1 and MP.3 are not tagged because they are present whenever you do a Test Talk, regardless of the question. MP.1, “Make sense of problems and persevere in solving them,” is at the heart of Test Talks because Test Talks require students to make sense of an unfamiliar question and determine a strategy to solve it. MP.3, “Construct viable arguments and critique the reasoning of others,” is present in the strategy sharing of a Test Talk, where students explain their reasoning and critically evaluate the reasoning of their peers.
- College and Career Readiness Standards for Adult Education (CCRSAE) domains. While test questions are often written to a specific content standard within a specific domain, the strategies used to solve them may be drawn from multiple domains. The domains cited are domains the listed strategies come from.
- The CCRSAE content standard most closely aligned to the question.
Each question has a link to a Will This Be on the Test? blog post, and some questions are also in the Will This Be on the Test? packet. In the packet, there is a brief description of the basic understandings students need to find a way into the question.
This page will be updated as more Will This Be on the Test? blogs are posted.
| Title | Content Summary | Strategies | Tools | SMPs | CCRSAE Domains | CCRSAE Content Std |
| Julia’s Photocopy (Packet question #1) | ● Proportional reasoning in the context of enlarging a photograph ● Similar figures | ● Draw pictures ● Work from known information ● Compare fractions visually ● Look for structure | Bar models | MP.2 MP.4 MP.5 MP.7 | Geometry Ratios and Proportional Relationships Number and Operations: Fractions | 7.RP.2 7.G.1 |
| José’s Backyard (Packet question #2) | ● Area of a rectangle ● Unit conversions with square units | ● Estimate ● Draw pictures – reasoning about feet and yards ● Draw pictures – reasoning about square units | MP.4 MP.6 | Geometry Measurement and Data | 3.MD.5 3.MD.6 | |
| Job Training Application (Packet question #3) | Fraction of a set – find the whole | ● Estimate ● Draw ratios ● Draw a bar model | Bar models | MP.4 MP.5 MP.7 | Ratios and Proportional Relationships Number and Operations: Fractions | 3.NF.1 |
| Pencils & Erasers (Packet question #4) | ● Algebraic reasoning ● Systems of equations in context (accessible at lower levels) | ● Reason proportionally ● Guess and Check | Tables | MP.4 MP.7 | Ratios and Proportional Relationships Expressions and Equations | 8.EE.8 (accessible at lower levels) |
| Exponent Equivalence (Packet question #5) | ● Meaning of an exponent ● Multiplying expressions with exponents | ● Try a concrete case ● Write out exponents as multiplication ● Figure out a rule using structure | MP.5 MP.7 | Expressions and Equations | 8.EE.1 | |
| Snail Trail I (friendly numbers) (Packet question #6) | ● Reasoning about distance, rate, and time with fractions ● Benchmark fractions ● Fractions of an hour as minutes | ● Estimate ● Use a bar model ● Reason proportionally | Number lines Bar models | MP.4 MP.5 | Ratios and Proportional Relationships Number and Operations: Fractions | 6.RP.3 |
| Snail Trail II (less friendly numbers) (Packet question #7) | ● Reasoning about distance, rate, and time with fractions ● Benchmark fractions ● Fractions of an hour as minutes | ● Estimate ● Use a bar model ● Reason proportionally | Number lines Bar models | MP.4 MP.5 | Ratios and Proportional Relationships Number and Operations: Fractions | 6.RP.3 |
| Souvenir Sales (Packet question #8) | ● Angles in a circle graph ● Percents ● Angle measurements | ● Estimate ● Measure by comparing to a right angle ● Guess and check ● Reason proportionally | Improvised angle measurer | MP.2 MP.5 MP.6 | Measurement and Data Geometry Ratios and Proportional Relationships | 4.MD.5 |
| Running Laps (Packet question #9) | ● Meaning of a fraction ● Division by a fraction | ● Estimate ● Draw a picture ● Reason about division with repeated addition ● Reason proportionally ● Use a bar model | Tables Number lines Bar models | MP.2 MP.5 MP.8 | Number and Operations: Fractions The Number System | 6.NS.1 |
| Choosing Your Marbles (Packet question #10) | Probability expressed as a fraction | ● Estimate ● Play “what if?” ● Draw a picture | MP.4 MP.7 | Statistics and Probability | 7.SP.5 7.SP.7 | |
| Finding “x” (Packet question #11) | ● Solving equations ● Equivalent fractions | ● Visualize equivalent fractions with bar models ● Reason about equivalent fractions by multiplying across numerators and denominators ● Iterate ratios ● Draw pictures | Bar models | MP.2 MP.7 | Expressions and Equations | 8.EE.7 |
| Park Playground (Packet question #12) | ● Area of a rectangle ● Percents | ● Estimate visually ● Redraw the diagram ● Estimate with benchmark fractions ● Manipulate fractions to get a denominator of 100 | Bar models | MP.2 MP.4 | Geometry Measurement and Data Ratios and Proportional Relationships | 3.MD.7 6.RP.3 |
| Dorothy’s Test Scores (Packet question #13) | Finding a missing value given the mean of a set | ● Estimate ● Visualize distances on a number line ● Make equal piles ● Reason about the total ● Guess and check | Number lines Tables | MP.2 MP.5 MP.7 | Statistics and Probability | 6.SP.5 |
| Alicia’s Earnings (Packet question #14) | Write an expression to represent a situation | ● Use symbols to tell a story ● Read an expression as a story | MP.2 MP.7 | Operations and Algebraic Thinking | 5.OA.2 | |
| Icicles by the Inch (Packet question #15) | ● Proportional reasoning ● Multiplication or division with fractions ● Rates | ● Estimate ● Take small steps ● Think in chunks ● Reason about rates | Tables Bar models | MP.7 MP.8 | Number and Operations: Fractions The Number System Ratios and Proportional Relationships | 6RP.3 |
| Mark’s Garden (Packet question #16) | ● Inequality in two variables ● Ordered pairs (coordinates) | ● Reason in context ● Write out the possibilities ● Make a chart | Tables | MP.2 | Expressions and Equations | 6.EE.6 |
| Ordered Pairs (Packet question #17) | Systems of equations | ● Turn it into a story ● Draw a picture ● Reframe subtraction as “distance between” or “more than” ● Make logical inferences ● Make a table | Tables | MP.2 | Expressions and Equations | 8.EE.8 |
| TV Speed (Packet question #18) | ● Proportional reasoning ● Benchmark percents | ● Make sense/Think about reasonableness ● Try simpler numbers ● Look for and make use of structure (MP.7) ● Estimate with a bar model | Tables | MP.2 MP.7 | Ratios and Proportional Relationships | 6.RP.3 |
| How Old is Paulina (Packet question #19) | One-step word problem | ● Make sense/Think about reasonableness ● Use a number line ● Use a bar model ● Make an analogy to a known situation | Number lines Bar models | MP.2 MP.5 | Operations and Algebraic Thinking | 2.OA.1 |
| The Price of Pens (Packet question #20) | Two-step word problem | ● Estimate ● Work down to the needed information ● Draw a bar model ● Write and solve an equation | Bar models | MP.2 | Operations and Algebraic Thinking | 3.OA.8 |
| Kitty Litter (Packet question #21) | Comparing rates in context | ● Estimate (multiple strategies) ● Calculate unit rates | Tables | MP.4 MP.6 | Ratios and Proportional Relationships | 6.RP.1 6.RP.2 |
| Alicia’s Appliances (Packet question #22) | Find the whole, given the percent | ● Estimate ● Draw pictures ● Use a bar model | Bar models | MP.4 MP.6 | Ratios and Proportional Relationships | 6.RP.3 |
| A Perimeter Problem (Packet question #23) | Area and perimeter of a rectangle | ● Play with area using gridded diagrams (Guess and check) ● Play with area using ungridded diagrams (Guess and check) ● Play with perimeter ● Make use of structure | Tables | MP.7 | Geometry Measurement and Data | 3.MD.8 |
| Class Enrollment | Percent increase | ● Make sense of the question ● Estimate ● Reason from benchmarks ● Use a bar model ● Work backwards | Bar models | MP.2 MP.4 | Ratios and Proportional Relationships | 7.RP.3 |
| Joy’s Garden | Area of a rectangle | ● Collect data ● Choose numbers and experiment ● Draw generalized pictures | MP.8 | Geometry Measurement and Data | 3.MD.7 | |
| Zari’s Ladder | ● Similar triangles ● Proportional reasoning | ● Investigate structure with a sketch ● Estimate with a sketch ● Reason with benchmarks and a double number line ● Reason with fractions or percents | Number lines Bar models | MP.4 | Geometry Measurement and Data Ratios and Proportional Relationships | 8.G.4 |
| Splitting the Cost | Algebraic thinking | ● Consider reasonableness ● Start with a fair split and work from there ● Guess and check ● Use a bar model | Bar models | MP.2 MP.4 MP.7 | Operations and Algebraic Thinking | 8.EE.8 |
| Smallest to Largest | Comparing and ordering fractions, decimals, and percents | ● Estimate – consider small and big ● Estimate – compare to a benchmark ● Draw pictures ● Visualize using number lines | Number lines | MP.7 | Number and Operations: Fractions | 4.NF.2 |
| Goat’s Grazing Area | ● Area of a region defined by constraints including circles ● Writing expressions | ● Draw a picture to make sense ● Draw a picture to estimate – check with a calculator ● Tell a story ● Consider what is relevant | MP.4 | Geometry Measurement and Data | 7.G.4 | |
| Trapezoid Area | Area of a trapezoid | ● Estimate from inside and outside ● Estimate by finding a shape with a similar area ● Chunk it up ● Subtract from a rectangle | MP.7 | Geometry Measurement and Data | 6.G.1 | |
| Hospital Wards | Comparing ratios | ● Make sense and estimate ● Draw ratios ● Take advantage of friendly numbers ● Reason about “leftovers” | Tables | MP.2 MP.4 | Ratios and Proportional Relationships | 6.RP.3 |
| Circle Area | Area of a circle | ● Estimate with an outside square ● Estimate with four outside squares ● Estimate with inside triangles ● Estimate inside and outside | MP.7 | Geometry Measurement and Data | 7.G.4 | |
| Class Data | Finding an average (mean) from a frequency table | ● Make sense of the question ● Estimate ● Visualize the data in a different way | MP.2 MP.6 | Statistics and Probability | 6.SP.5 | |
| Class Data II | Finding the median from a frequency table | ● Think about reasonableness ● Write out the data the long way ● Visualize with a different data display | Tables | MP.2 MP.6 | Statistics and Probability | 6.SP.5 |
| Beach Ball | Find the radius of a sphere, given the volume | ● Estimate with an answer choice ● Estimate with friendly numbers ● Use a story table | Story tables | MP.2 | Geometry: Geometric Measurement and Dimension | G.GMD.3 |
| Find the Slope | Find the slope, given two points | ● Use benchmarks – Estimate with a quick sketch ● Draw a triangle to figure out the vertical and horizontal change ● Reason about up and over ● Create a context | MP.2 | Functions | 8.EE.5 | |
| Part of a Whole | Find one fraction of a number, given another | ● Make sense and estimate with benchmarks ● Make sense and estimate by thinking about relationships ● Use a bar model | Bar models | MP.7 | Number and Operations – Fractions | 3.NF.1 |
| Slope-Intercept Form | Write an equation in slope-intercept form, given two points | ● Make a rough sketch ● Reason visually about slope ● Use slope steps from one point to find the y-intercept | MP.7 | Functions | 8.F.3 | |
| Data Plan | Two-step word problem with decimal division | ● Make sense with a bar model ● Estimate ● Play “What if?” ● Divide a little bit at a time | Bar models Tables | MP.4 | Number and Operations in Base Ten | 5.NBT.7 |
| Estimate with Fractions | Estimating a fraction sum | ● Estimate with benchmarks ● Reason about the sizes of the answer choices without calculating ● Calculate and compare | Bar models | MP.7 | Number and Operations – Fractions | 3.NF.1 |
| Chocolate “Bar” | Surface area of a triangular prism | ● Make sense and estimate ● Rearrange shapes ● Think about what is visible and invisible | MP.4 MP.7 | Geometry | 6.G.1 | |
| Distance | Find the distance between two points on a coordinate plane | ● Estimate based on looks ● Estimate based on triangle relationships ● Build a right triangle and use the Pythagorean Theorem | MP.7 | Geometry | 8.G.8 | |
| Converting Temperature | Use a formula to convert Fahrenheit to Celsius | ● Use an approximate story table ● Use a precise story table ● Sketch the action on a number line ● Rely on known relationships | Story tables Number lines | MP.4 MP.5 | Measurement and Data Expressions and Equations | 6.EE.2 |
| Book Drive | Find the percent represented by one bar in a bar graph | ● Estimate by reasoning about the sizes of the parts ● Estimate the total the part ● Visualize chunking up the graph | MP.2 MP.7 | Measurement and Data Ratios and proportional relationships | 3.MD.3 6.RP.3 | |
| Taxi Fares | Write a linear function to model data in a table | ● Ask: Is it proportional ● Sketch a graph and estimate the y-intercept ● Figure out the rate per mile by comparing two rides ● Check the answer choices efficiently | MP.2 MP.7 | Expressions and Equations Ratios and Proportional Relationships Functions | 8.F.3 | |
| Cost of Gum | Estimate division within 100 | ● Estimate ● Play “What if?” ● Use a bar model ● Use a number line for rounding | Bar models Number Lines | MP.4 MP.5 | Number and Operations in Base Ten Operations and Algebraic Thinking | 3.OA.7 |
| Nick’s Tip | Calculate an 18% tip on a restaurant bill | ● Think of percent as “for every hundred” ● Estimate with a benchmark ● Build the percent with chunks ● Estimate with a double number line | Number lines | MP.2 MP.7 | Ratios and Proportional Relationships | 6.RP.3 |
| Lifeguards | Proportional reasoning in a context requiring a whole number answer | ● Draw a picture ● Make a table ● Check the answer choices | Tables | MP.2 MP.7 | Ratios and Proportional Relationships | 6.RP.3 |
| Solve for x | Solve a two step linear equation | ● Make sense of the story – chunk it up ● Use a story table ● Use a bar model ● Illustrate the action on a number line | Story tables Bar models Number lines | MP.7 | Expressions and equations | 6.EE.5 7.EE.4 |
| Sebastian’s Racquetball Record | Find a part given a whole and a part:part ratio | ● Use a bar model ● Tally the games in a t-chart ● Make “piles” and move games around ● Think about parts on a number line | Bar models Tables Number lines | MP.2 MP.7 | Ratios and Proportional Relationships | |
| Arithmetic Sequence | Find the 15th number in an arithmetic sequence | ● Use a concrete approach: Model with counters ● Use a representational approach: Draw the sequence on a number line ● Use a representational approach: Draw the hops ● Use an abstract approach: Reason about and extend the change ● Use an abstract approach: Reason about a related sequence | Number lines | MP.7 MP.8 | Operations and Algebraic Thinking | 4.OA.5 |
| Multiplying Decimals | Multiply 4.8 x 7.2 | ● Estimate by truncating ● Estimate with nearby whole numbers ● Draw an area model | Area models | MP.5 MP.7 | Number and Operations in Base Ten | 5.NBT.7 |
| Fractions on a Number Line | ● Locate a fraction on a number line ● Reason about improper fractions | ● Draw a picture ● Reason about wholes ● Mark and count thirds on the number line | Number lines | MP.7 | Number and Operations – Fractions | 3.NF.2 |