# 31

This card game helps students learn to add numbers in their heads. The objective of the game is to get as close to 31 with any number of cards, without going over 31.

**Grades covered:**1 through 12

**Curriculum Topics:**Math, Addition, Probability

### Standards

Idea Sheets are cross-referenced to subjects listed in the Common Core, Next Generation Science Standards, and California Content Standards.

Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||Common Core Mathematics||Grade 1||Mathematical Practices|||1.NBT.4. Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.||Common Core Mathematics||Grade 1||Number And Operations In Base Ten||Use Place Value Understanding And Properties Of Operations To Add And Subtract|||1.OA.1. Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.2||Common Core Mathematics||Grade 1||Operations And Algebraic Thinking||Represent And Solve Problems Involving Addition And Subtraction|||1.OA.6. Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 ? 4 = 13 ? 3 ? 1 = 10 ? 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 ? 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).||Common Core Mathematics||Grade 1||Operations And Algebraic Thinking||Add And Subtract Within 20|||Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||Common Core Mathematics||Grade 2||Mathematical Practices|||2.NBT.5. Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.||Common Core Mathematics||Grade 2||Number And Operations In Base Ten||Use Place Value Understanding And Properties Of Operations To Add And Subtract|||2.OA.2. Fluently add and subtract within 20 using mental strategies.2 By end of Grade 2, know from memory all sums of two one-digit numbers.||Common Core Mathematics||Grade 2||Operations And Algebraic Thinking||Add And Subtract Within 20|||Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||Common Core Mathematics||Grade 3||Mathematical Practices|||Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||Common Core Mathematics||Grade 4||Mathematical Practices|||Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||Common Core Mathematics||Grade 5||Mathematical Practices|||Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||Common Core Mathematics||Grade 6||Mathematical Practices|||Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||Common Core Mathematics||Grade 7||Mathematical Practices|||7.SP.5. Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.||Common Core Mathematics||Grade 7||Statistics And Probability||Investigate Chance Processes And Develop, Use, And Evaluate Probability Models|||7.SP.6. Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.||Common Core Mathematics||Grade 7||Statistics And Probability||Investigate Chance Processes And Develop, Use, And Evaluate Probability Models|||Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||Common Core Mathematics||Grade 8||Mathematical Practices|||Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||Common Core Mathematics||High School||Mathematical Practices|||HS.S.CP.2. Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.||Common Core Mathematics||High School||Conditional Probability And The Rules Of Probability||Understand Independence And Conditional Probability And Use Them To Interpret Data

2.1 Know the addition facts (sums to 20) and the corresponding subtraction facts and commit them to memory.||CA Mathematics||Grade 1||01. Number Sense||2.0 Students demonstrate the meaning of addition and subtraction and use these operations to solve problems.|||2.6 Solve addition and subtraction problems with one- and two-digit numbers (e.g., 5 + 58 = __).||CA Mathematics||Grade 1||01. Number Sense||2.0 Students demonstrate the meaning of addition and subtraction and use these operations to solve problems.|||2.2 Express outcomes of experimental probability situations verbally and numerically (e.g., 3 out of 4; 3/4).||CA Mathematics||Grade 4||04. Statistics, Data Analysis, and Probability||2.0 Students make predictions for simple probability situations.|||3.4 Understand that the probability of either of two disjoint events occurring is the sum of the two individual probabilities and that the probability of one event following another, in independent trials, is the product of the two probabilities.||CA Mathematics||Grade 6||04. Statistics, Data Analysis, and Probability||3.0 Students determine theoretical and experimental probabilities and use these to make predictions about events.|||3.5 Understand the difference between independent and dependent events.||CA Mathematics||Grade 6||04. Statistics, Data Analysis, and Probability||3.0 Students determine theoretical and experimental probabilities and use these to make predictions about events.|||1.0 Students know the definition of the notion of independent events and can use the rules for addition, multiplication, and complementation to solve for probabilities of particular events in finite sample spaces.||CA Mathematics||Grade 8 – 12||04. Probability and Statistics|||2.0 Students know the definition of conditional probability and use it to solve for probabilities in finite sample spaces.||CA Mathematics||Grade 8 – 12||04. Probability and Statistics

**Categories include:**

- Grades K-2
- Grades 3-5
- Grades 6-8
- Math

**Tags:**Problem Solving, Addition & Subtraction, Probability

**Subjects covered:**["Math"]