Topic+Five

= Topic Five: Number Sense: Multiplying by 1-Digit Numbers = Pacing (Duration of Unit): 1. Makes 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. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||
 * ~ = Desired Results = ||
 * __**Transfer:**__
 * 5. Use appropriate tools strategically.**
 * __**Established Goals:**__


 * 4.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 operation. Illustrate and explain the calculations by using equations, rectangular arrays, and/or area models.
 * 4.OA.3: Solve multi-step word problems posted with whole numbers and having whole -number answers using the four operations including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

__**I Can Statements:**__
 * I can multiply two digit numbers.
 * I can use what I know about addition, subtraction, multiplication and division to solve multi-step word problems involving whole numbers.
 * I can represent word problems by using equations with a letter standing for the unknown number.
 * I can determine how reasonable my answers to word problems are by using estimation, mental math and rounding.

__**Pre-Requisite Standards:**__ __**Vocabulary:**__ partial product, compensation || __**Students will be skilled at...**__ __**[|Performance Assessment Task-4.OA.3, 4.NBT.5-The Baker]**__ || __**Other Evidence:**__ || 5-1:Making an array with place-value blocks provides a way to visualize and find products. 5-2: Basic facts and place-value patterns can be used to find products when one factor is 10 or 100. 5-3: Making an array with place value blocks provides a way to visualize and find products. A 2-digit by 1-digit multiplication calculation can be broken into simpler problems: a basic and and a 1-digit number times a multiple of 10. Answers to the simpler problems can be added to give the product. 5-4:There is more than one way to do a mental math calculation. Techniques for doing multiplication calculations mentally involve changing the numbers or the expression so the calculation is easy to do mentally. 5-5: Rounding is one way to estimate products. 5-6: Answers to problems should always be checked for reasonableness and this can be done in different ways. Two ways are to use estimation and to check the answer against the questions and conditions in the problem. || __Home-School Connection__
 * 3.NBT.3: Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 ´ 80, 5 ´ 60) using strategies based on place value and properties of operations.
 * 3.OA.1: Interpret products of whole numbers, e.g., interpret 5 ´  7 as the total number of objects in 5 groups of 7 objects each. //For example, describe a context in which a total number of objects can be expressed as 5// // ´  7. //
 * 3.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//.//
 * 3.OA.4: Determine the unknown whole number in a multiplication or division equation relating three whole numbers. //For example, determine the unknown number that makes the equation true in each of the equations 8// // ´  ? = 48, 5 =  ¸  3, 6 ´  6 = ?. //
 * 3.OA.5: Apply properties of operations as strategies to multiply and divide.//Examples: If 6// // ´ 4 = 24 is known, then 4// // ´ 6 = 24 is also known. (Commutative property of multiplication.) 3// // ´ 5// // ´ 2 can be found by 3// // ´ 5 = 15 then 15// // ´ 2 = 30, or by 5// // ´ 2 = 10 then 3// // ´ 10 = 30. (Associative property of multiplication.) Knowing that 8// // ´ 5 = 40 and 8// // ´ 2 = 16, one can find 8x////7 as 8// // ´ (5 + 2) = (8// // ´ 5) + (8// // ´ 2) = 40 + 16 = 56. (Distributive property.)// ||
 * __**Big Ideas:**__
 * __Basic Facts and Algorithms:__ There is more than one algorithm for each of the operations with rational numbers. Some strategies for basic facts and most algorithms for operations with rational numbers, both mental math and paper and pencil, use equivalence to transform calculations into simpler ones.
 * __Patterns, Relations, and Functions__: Relationships can be described and generalizations made for mathematical situations that have numbers or objects that repeat in predictable ways. For some relationships, mathematical expressions and equations can be used to describe how members of one set are related to members of a second set.
 * __Estimation__: Numbers can be approximated by numbers that are close. Numerical calculations can be approximated by replacing numbers with other numbers that are close and easy to compute mentally. Some measurements can be approximated using known referents as the unit in the measurement process. || __**Essential Questions:**__
 * How can some products be found mentally?
 * How can products be estimated? ||
 * __**Students will know...**__
 * Making an array with place-value blocks provides a way to visualize and find products.
 * Basic facts and place-value patterns can be used to find products when one factor is 10 or 100.
 * Making an array with place value blocks provides a way to visualize and find products. A 2-digit by 1-digit multiplication calculation can be broken into simpler problems: a basic and and a 1-digit number times a multiple of 10. Answers to the simpler problems can be added to give the product.
 * There is more than one way to do a mental math calculation. Techniques for doing multiplication calculations mentally involve changing the numbers or the expression so the calculation is easy to do mentally.
 * Rounding is one way to estimate products.
 * Answers to problems should always be checked for reasonableness and this can be done in different ways. Two ways are to use estimation and to check the answer against the questions and conditions in the problem.
 * Using arrays and multiplying by 10 and 100.
 * Using basic multiplication facts and number patterns to multiply by multiples of 10 and 100.
 * Breaking apart numbers and using arrays to multiply 2-digit by 1-digit numbers.
 * Using compensation to multiply numbers mentally.
 * Using rounding to estimate solutions to multiplication problems.
 * Checking for reasonableness by making sure their calculations answer the questions asked an by using estimation to make sure the calculation was performed correctly. ||
 * ~ = Assessment Evidence = ||
 * __**Performance Assessment:**__
 * ~ = Learning Plan = ||
 * __**Learning Activities:**__
 * __**Resources:**__

__Problem of the Month:__ [|4.OA.3: Digging Dinosaurs] [|4.OA.3: Friends You Can Count On] [|4.OA.3: Squirreling it Away] [|4.OA.3: The Wheel Shop] [|4.NBT.5: Measuring Up]

__**Centers:**__ [|4.NBT.5: Multiplication Strategy: Doubling and Halving] [|4.NBT.5: Multiplication Number Story] [|4.NBT.5: Multiplication Bump (x100)] ||