CCGPS Mathematics Fifth Grade Update Webinar Unit 3: Multiplying and Dividing with Decimals October 14, 2013 Update presentations are the result of collaboration between members of 2012 and 2013 Unit Review and Revision Teams and classroom teachers Microphone and speakers can be configured by going to: Tools – Audio – Audio setup wizard Turtle Toms- Elementary Mathematics Specialist These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.

Today’s presenters Emily Heck – Gwinnett County Trudy Ives – Gwinnett County Michelle Parker - Gordon County Michael Wiernicki - Henry County

Webinar Guide Unit 3 Overview  Critical areas within this unit  Content standards  Practice standards  Decimal number talks Changes to Unit 3 tasks Resources

Critical Areas in 5 th Grade Unit 3 Falls under the 2 nd Critical Area Students should be given ample opportunities to keep their unit 3 skills sharp throughout the remainder of the year.

Unit 3 Content, Strategies and Misconceptions Understand the place value system. MCC5.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. Content: o As students multiply and divide decimals by powers of tens, they should notice a pattern occurring in the number of zeros in the product or quotient, as well as a pattern in the placement of the decimal point in the resulting product or quotient. o Students need to explain why these patterns are occurring when a decimal number is multiplied or divided by a power of ten. o Students should become aware that 1, 10, 100 and 1,000 are powers of ten and that these numbers can be expressed as whole number exponents.

Unit 3 Content, Strategies and Misconceptions MCC5.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. Strategies: o Elicit student’s prior knowledge about MCC5.NBT.1 – recognizing 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 one tenth of what it represents in the place to its left. o Use base ten blocks or hundreds grids to help students create models or representations of problems where exponents are used. Change the value of the base ten blocks to create decimal numbers instead of whole numbers. o Compare and contrast the process of multiplying and dividing whole numbers by powers of ten to multiplying and dividing decimal numbers by powers of ten. Help students see the similarities and differences between the two.

Unit 3 Content, Strategies and Misconceptions

MCC5.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. Student Misconceptions: o Students are familiar with how multiplying or dividing a whole number by a power of ten affects a product or quotient. They visually see the zeros being added to the product or being dropped from the quotient. Some students take that knowledge and try to apply it to multiplying and dividing decimals by powers of ten. Students need to be aware that while adding or dropping zeros to the product or quotient may happen, it is also possible that they may just see a shift in the decimal point in the product or quotient.

Unit 3 Content, Strategies and Misconceptions Perform operations with multi-digit whole numbers and with decimals to the hundredths. 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. Content: o Students multiply and divide decimal numbers to the hundredths place. o Students should develop an understanding of how the algorithm works through the use of concrete models and representations. o Students should make connections between the algorithm and partial products and partial quotients.

Unit 3 Content, Strategies and Misconceptions 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. Strategies: o Work with base ten blocks and decimal grids so that students connect visually to the process of multiplying and dividing decimal numbers. o Area models are also a very powerful tool for promoting student understanding of decimal multiplication and division. o Students can generate an estimate of the product or quotient to determine if their exact answer is reasonable or not.

Unit 3 Content, Strategies and Misconceptions

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. Student Misconceptions: o Students’ prior experiences have led them to understand that when multiplying whole numbers the product is always larger than the factors. They also have experienced that dividing whole numbers always results in a quotient that is smaller than the dividend. They may experience disequilibrium when multiplying and dividing by decimal numbers because these beliefs will no longer always be true.

Standards for Mathematical Practice

Number Talks

Decimal Multiplication Number Talks Strategies for Multiplying Decimals  Estimation  Fractions and Decimals as Operators  Associative & Commutative Properties  Eliminating the Decimal / Maintaining Equivalence  Partial Products  Distributive Property  Using Landmark Numbers (think money)  Using Place Value Array models are an important tool used to develop these strategies Adapted from Number Talks by Sherry Parrish

Decimal Division Number Talks Strategies for Dividing Decimals  Estimation  Think multiplication / Find the missing factor  Eliminating the decimal / Maintaining equivalence Student models are important here as well. The models students choose to use show their level of understanding of operations with decimals. Adapted from Number Talks by Sherry Parrish

Unit 3 Tasks - Unchanged Power-ful Exponents What Comes Next? Patterns-R-Us Base Ten Activity Missing Numbers Multiplication Teasers How Much Money? Super Slugger Award What’s My Rule? Do You See an Error? Road Trip Teacher for a Day Bargain Shopping

Task – Base 10 Activity MCC5.NBT x 3

Task – Base 10 Activity MCC5.NBT x 3

Task – Base 10 Activity MCC5.NBT x 5.4

Task – Base 10 Activity MCC5.NBT ÷ 1.2

Task – Base 10 Activity MCC5.NBT ÷ 2.1

Revised Task - Place the Point MCC5.NBT.2 & MCC5.NBT.7

Revised Task - Number Puzzles MCC5.NBT.7

New Task - Multiplying and Dividing Decimals FAL – Formative Assessment Lesson

New Task - Multiplying and Dividing Decimals

New Culminating Task – Field Trip MCC5.NBT.4 & MCC5.NBT.7

Resources K-5 Mathematics Wiki OAS Formative Assessment Bank (NBT.2) Illustrative Mathematics (NBT.2&7) K-5 Math Teaching Resources (NBT.2) Learn Zillion Decimal Multiplication (change to multiplication, 1-3 grids, 10 rows, 10 columns) ions.swf

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