Topic+Six

= Topic Six: Multiplying Decimals =
 * ~ = Desired Results = ||
 * __**Transfer:**__

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. 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. ** ||
 * __**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.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.

__** I Can Statements: **__
 * I can explain patterns when multiplying a number by powers of 10.
 * I can explain patterns when a decimal is multiplied or divided by a power of 10.
 * I can add, subtract, multiply, and divide decimals to hundredths. I can use concrete models or drawings to explain the method used.

__** Pre-Requisite Standards: **__
 * 5.NBT.1: Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and **1 **/ **10 ** of what it represents in the place to its left.
 * 5.NBT.5: Fluently multiply multi-digit whole numbers using the standard algorithm. ||
 * __**Big Ideas:**__
 * __ 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.
 * __ 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.
 * __ Practices, Processes, and Proficiencies __ : Mathematics content and practices can be applied to solve problems. || __**Essential Questions:**__
 * What are the standard procedures for estimating and finding products involving decimals? ||
 * __**Students will know...**__
 * Patterns can be used to mentally multiply decimals by 10, 100, and 1, 000.
 * Rounding and compatible numbers can be used to estimate the product of a whole number and a decimal.
 * The location of decimal points in decimal multiplication calculations can sometimes be decided by reasoning about the relatize size of the given numbers.
 * The standard multiplication algorithm involving decimals is an extension of the standard algorithm for multiplying whole numbers.
 * The steps for multiplying whole numbers by decimals are similar to the steps for multiplying two whole numbers. Place value determines the placement of the decimal point in a product.
 * Steps for multiplying decimals are similar to steps for multiplying whole numbers. Place value determines the placement of the decimal point in a product. The product of two decimals less than one is less than either factor.
 * Some problems can be solved by first finding and solving a sub-problem(s) and then using that answer(s) to solve the original problem. || __**Students will be skilled at...**__
 * Mentally multiplying decimals by 10, 100, and 1,000.
 * Using rounding and compatible numbers to estimate products of whole numbers and decimals.
 * Identifying estimates as overestimates or underestimates.
 * Using number sense and place value to multiply decimals.
 * Finding products of whole numbers and decimals to ten thousandths.
 * Using a standard algorithm to multiply a whole number and a decimal.
 * Using the standard algorithm to multiply decimals by decimals.
 * Finding the hidden question or questions to solve multiple-step problems. ||
 * ~ = Assessment Evidence = ||
 * __**Performance Assessment:**__

|| Other Evidence: ||
 * ~ = Learning Plan = ||
 * __**Learning Activities:**__

6-1: Patterns can be used to mentally multiply decimals by 10, 100, and 1, 000. 6-2: Rounding and compatible numbers can be used to estimate the product of a whole number and a decimal. 6-3: Compare each factor to 1 as a way of determining if you have placed the decimal point reasonably. 6-4: The standard multiplication algorithm involving decimals is an extension of the standard algorithm for multiplying whole numbers. 6-5: The steps for multiplying whole numbers by decimals are similar to the steps for multiplying two whole numbers. Place value determines the placement of the decimal point in a product. 6-6: Steps for multiplying decimals are similar to steps for multiplying whole numbers. Place value determines the placement of the decimal point in a product. The product of two decimals less than one is less than either factor. 6-7: Some problems can be solved by first finding and solving a sub-problem(s) and then using that answer(s) to solve the original problem. ||
 * __**Resources:**__

__**Problem of the Month:**__ __**[|5.NBT.7: Diminishing Return]**__ __**[|5.NBT.7: Got Your Number]**__

__**Number Activities:**__ __**[|5.NBT.2: Multiply a Decimal by a Power of Ten]**__ __**[|5.NBT.7: Decimal of the Week]**__ ||