Topic+Three

= Topic Three: Multiplying Whole Numbers = 1. Makes sense of problems and perseve re in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 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 .**
 * 6. Attend to precision. **
 * __**Established Goals:**__
 * 5.NBT.2: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.
 * 5.NBT.5: Fluently multiply multi-digit whole numbers using the standard algorithm.
 * 5.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.


 * __Student I Can Statements: __**
 * I can explain patterns when multiplying a number by powers of 10.
 * I can multiply multi-digit whole numbers.
 * I can divide four-digit dividends by two-digit divisors.
 * I can illustrate and explain a division problem using equations, arrays and/or models.

__**Prerequisite Standards:**__
 * 4.NBT.1: Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. // For example, recognize that 700 ¸  70 = 10 by applying concepts of place value and division. //
 * 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 of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. ||
 * __**Big Ideas:**__


 * Properties:** For a given set of numbers there are relationships that are always true called properties, and these are the rules that govern arithmetic and algebra.


 * Patterns, Relationships, and Functions:** Relationships can be described and generalizations made for mathematical situations that have numbers or objects that repeat in predictable ways.


 * 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 with mentally.


 * Number Uses, Classification, and Representation:** Numbers can be used for different purposes, and numbers can be classified and represented in different ways.


 * Algorithms: E**ach operation with rational numbers has more that one algorithm. Most algorithms for operations with rational numbers, both mental math and paper and pencil, use equivalence to transform calculations into simpler ones.


 * Practice, Processes, and Proficiencies:** Mathematics content and practice can be applied to solve problems. || __**Essential Questions:**__


 * What are the standard procedures for estimating and multiplying whole numbers? ||
 * __**Students will know...**__


 * The properties of multiplication can be used to simplify computation and to verify mental math and paper and pencil algorithms.
 * Basic facts and place-value patterns can be used to find products when one factor is a multiple of 10 or a multiple of 100.
 * There is more than one way to estimate a product. Each estimation technique gives one way to estimate by replacing numbers with other numbers that are close and easy to compute with mentally.
 * Some numbers can be represented using a base number and an exponent.
 * The standard multiplication algorithm breaks the calculation into simpler caculations using place value starting with the ones, then the tens, and so on.
 * Information is a problem can often be shown using a diagram and used to solve the problem. Some problems can be solved by writing and completing a number sentence or equation.


 * __Vocabulary:__** Commutative Property of Multiplication, Associative Property of Multiplication, Identity Property of Multiplication, Zero Property of Multiplication, Distributive Property, factors, product, multiple, overestimate, underestimate, partial product, base, exponent, power, exponential notation, expanded form, standard form, squared, cubed

|| **Students will be skilled at...**

__**[|Performance Assessment Task-5.NBT.5, 5.NBT.6-Fruits and Vegetables]**__ || __**Other Evidence:**__ ||
 * Identifying and applying the Commutative, Associative, Identity, and Zero Properties of Multiplication.
 * Mentally computing products of whole numbers using place-value patterns and the properties of multiplication.
 * Using rounding or compatible numbers to estimate products of whole numbers.
 * Using exponential notation.
 * Using the Distributive Property to simplify expressions and solve equations.
 * Using partial products or the traditional algorithm to multiply multi-digit numbers by a one-digit number.
 * Multiplying two-digit numbers by two-digit numbers.
 * Multiplying two-digit numbers by factors with more than two digits.
 * Using diagrams and write equations to solve problems. ||
 * ~ = Assessment Evidence = ||
 * __**Performance Assessment:**__
 * ~ = Learning Plan = ||
 * __**Learning Activities:**__

__**3-1:**__ The properties of multiplication can be used to simplify computation and to verify mental math and paper and pencil algorithms. __**3-2:**__ Basic facts and place-value patterns can be used to find products when one factor is a multiple of 10 or a multiple of 100. __**3-3:**__ There is more than one way to estimate a product. Each estimation technique gives one way to estimate by replacing numbers with other numbers that are close and easy to compute with mentally __**3-4:**__ Some numbers can be represented using a base number and an exponent. __**3-5:**__ The properties of multiplication can be used to simplify computation and to verify mental math and paper and pencil algorithms. __**3-6:**__ The standard multiplication algorithm breaks the calculation into simpler calculations using place value starting with the ones, then the tens, and so on. __**3-7:**__ The standard multiplication algorithm breaks the calculation into simpler calculations using place value starting with the ones, then the tens, and so on. __**3-8:**__ The standard multiplication algorithm breaks the calculation into simpler calculations using place value starting with the ones, then the tens, and so on. __**3-9**__: Information is a problem can often be shown using a diagram and used to solve the problem. Some problems can be solved by writing and completing a number sentence or equation. ||
 * __**Resources:**__

__Home-School Connection__

__Problem of the Month:__ __[|5.NBT.5, 5.NBT.6-Through the Grapevine]__

__Centers:__ __[|5.NBT.2: Multiplying a whole number by a power of ten]__ __ [|5.NBT.5: Make the Largest Product] __ __[|5.NBT.5: Make the smallest product]__

__Smart Board Resources:__ __[|Speed Grid Multiplication Challenge]__ __[|Sum Sense Multiplication]__ __[|Ghostblasters Multiplication]__ ||