Scaffolding/Constructing Task: Patterns-R-Us In this task, students are asked to identify, describe, and explain any patterns they notice when multiplying or dividing numbers by 1000, 100, 10, 0.1, and 0.01. STANDARDS FOR MATHEMATICAL CONTENT Understand the place value system. Explain patterns in the number of zeros of the product when multiplying a number by MCC5.NBT.2 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. 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. STANDARDS FOR MATHEMATICAL PRACTICE SMP 1. Make sense of problems and persevere in solving them. SMP 2. Reason abstractly and quantitatively. SMP 3. Construct viable arguments and critique the reasoning of others. SMP 4. Model with mathematics. SMP 5. Use appropriate tools strategically. SMP 6. Attend to precision. SMP 7. Look for and make use of structure. SMP 8. Look for and express regularity in repeated reasoning. BACKGROUND KNOWLEDGE Students should develop an understanding that when a number is multiplied by a number less than 1, the product is less than the original number, and when a number is divided by a decimal number less than 1, the quotient will be greater than the dividend. This is important, yet difficult for students to understand because it is counterintuitive based on students’ previous experiences with multiplication and division. Because students have not yet learned how to multiply or divide decimals, calculators are recommended for this investigation. Students will be more likely to explore a variety of numbers and be able to recognize patterns more efficiently with the use of a calculator. Require students to record what they put into the calculator and the result. If students have learned how to multiply and divide
Scaffolding/Constructing Task: Patterns-R-Us In this task, students are asked to identify, describe, and explain any patterns they notice when multiplying or dividing numbers by 1000, 100, 10, 0.1, and 0.01. STANDARDS FOR MATHEMATICAL CONTENT 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. 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. STANDARDS FOR MATHEMATICAL PRACTICE SMP 1. Make sense of problems and persevere in solving them. SMP 2. Reason abstractly and quantitatively. SMP 3. Construct viable arguments and critique the reasoning of others. SMP 4. Model with mathematics. SMP 5. Use appropriate tools strategically. SMP 6. Attend to precision. SMP 7. Look for and make use of structure. SMP 8. Look for and express regularity in repeated reasoning. BACKGROUND KNOWLEDGE Students should develop an understanding that when a number is multiplied by a number less than 1, the product is less than the original number, and when a number is divided by a decimal number less than 1, the quotient will be greater than the dividend. This is important, yet difficult for students to understand because it is counterintuitive based on students’ previous experiences with multiplication and division. Because students have not yet learned how to multiply or divide decimals, calculators are recommended for this investigation. Students will be more likely to explore a variety of numbers and be able to recognize patterns more efficiently with the use of a calculator. Require students to record what they put into the calculator and the result. If students have learned how to multiply and divide
CCGPS_Math_5_Unit3Framework.docx