Number Talk Guidance

Number Talks is a time for students to explore strategies based upon place value, relationship between operations and deepen their understanding of the properties. Students need to know how to be flexible, efficient and accurate, in other words fluent, when calculating.

The standards are written as a progression first having students create deep conceptual understanding by exploring strategies based upon place value, relationship between operations, deepen their understanding of the properties, and justifying and drawing/illustrating their mathematical reasoning. This progression then steps to application and fluency, which typically happens at the next grade level. If opportunities are missed to explore numbers with deep conceptual understanding and progress to procedure fluency too quickly, students lack building explicit connections and possibly accessing higher-level mathematics.

Page 158-160 in the Number Talks by Parrish, discusses the strategies that are worked on during a Number Talks session

Third Grade Guidance
Third grade students need to be fluent with the strategy of all four operations and be able to name them before you move on to the next strategy. These strategies start on page 189. The focus should be on Category 1 and 2. When students struggle with single digit multiplication, you can use the multiplication subitizing cards and number stings found on the district website.
MCC3.NBT.2 Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
MCC3.OA.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
Understand properties of multiplication and the relationship between multiplication and division.
MCC3.OA.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.1 / MCC3.OA.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers. What does each number in the equation mean?
MCC3.OA.5 Apply properties of operations as strategies to multiply and divide. (Commutative property of multiplication, Associative property of multiplication, Distributive property.)
MCC3.OA.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. Use place value understanding and properties of operations to perform multi-digit arithmetic.
MCC3.NBT.3 Multiply one-digit whole numbers by multiples of 10 in the range 10–90 using strategies based on place value and properties of operations.
Fourth Grade Guidance
Fourth grade starts with addition/subtraction but the focus needs to be on category 3, if used. 4th grade should be into multiplication and division strategies, p 230. There needs to be a focus on illustration with arrays, open arrays, base ten pieces, and/or visual strategies. This will be tested in Claim 3-communicating reasoning.
Use place value understanding and properties of operations to perform multi-digit arithmetic.
MCC4.NBT.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm.
MCC4.OA.2 Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.[1]
Use place value understanding and properties of operations to perform multi-digit arithmetic. / MCC4.NBT.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
MCC4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
Fifth Grade Guidance
As Fifth grade reviews whole number strategies with all four operations, a focus should be on the visual model, properties and naming the strategies. Students should be comfortable with category 3. After the Georgia unit of decimal and fractions, start incorporating the work from Making Number Talks Matter by Humphreys. Revisit category 1 strategies from Number Talks and simply adding a decimal in to facilitate students connecting the previous strategy with the new number system.
Perform operations with multi-digit whole numbers and with decimals to hundredths.
MCC5.NBT.5 Fluently multiply multi-digit whole numbers using the standard algorithm.
MCC5.NBT.6. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. / MCC5.NBT.7 Add, subtract, multiply, and divide decimals to hundredths, 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.
MCC5.NF.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. [2]

[1] See Glossary, Table 2.

[2] Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade.