6th Grade American Math First page of your notebook Mrs. Moser – mosermathematics@gmail.com melissa.borgmann@archimedean.org All homework will be on Archie Go to website (sis.archimedean.org)  Hover over “Homework”  Hover over “AMC”  Hover over “6th Grade”  Click the appropriate section If you know how to access homework from Archie already, you don’t have to write this part.

Table of Contents STILL the first page of your notebook Page # 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - ….. DO NOT WRITE ON THE BACK OF THIS PAGE… We will continue the Table of Contents there when the time comes.

Guide to Note Taking Take turns reading aloud or try a problem all together. Write in your notes. Exercises to try on your own in your notebooks. If the text is in green, you don’t have to write it.

1. Computing with Multi-Digit Numbers Put the title and the page number in your ToC 1. Computing with Multi-Digit Numbers Adding and Subtracting Decimals Multiplying Decimals Dividing Multi-Digit Numbers Dividing Decimals

* Adding and Subtracting Decimals Line up the decimal points. You may need to add zeros at the end of a decimal to properly line them up. Estimate the answer before solving to see if your answer is reasonable. Find the sum of 23.1 and 5.8. Estimate 23 + 6 = 29 23.1 +5.8 28.9 28.9 ≈ 29 The sum of 23.1 and 5.8 is 28.9. Find the difference of 5.774 and 2.371 Estimate 6 - 2 = 4 5.774 – 2.371 3.403 3.403 ≈ 4 The difference of 5.774 and 2.371 is 3.403.

1) Find 29.6 + 14.7. Estimate + = + Check: ≈ 2) Find 6 – 4.78 Estimate - = - Check: ≈ Find each sum or difference. 3) 54.72 + 21.4 4) 14.2 + 23.51 5) 9.54 – 3.671 6) $50.62 – $39.81

* Multiplying Decimals *Ignore decimals and multiply. *To place the decimal point, find the sum of the number of decimal places in each factor and move the decimal in the product to the right accordingly. Find the product of 3.6 and 0.05. Estimate 4 x 0 = 0 3.6  one decimal place x 0.05  two decimal places 0.180  1+2 = 3, three decimal places 0.180 ≈ 0 The product 3.6 and 0.05 is 0.180 or 0.18. Since we count the decimal places, we do NOT have to align the decimals.

0. 1 1 2 The product should have x 7. 2 decimal places. 0 · 7 = 0 1) Find 0.112 · 7.2. Estimate 0. 1 1 2 The product should have x 7. 2 decimal places. + 0 · 7 = 0 4 Sometimes you will see a “dot” instead of an “x” to represent multiplication. Check: ≈ 0 Find each product. 2) 5.7 · 2.8 3) 0.04 · 0.32 4) 4.12 · 0.05 5) 0.26 · 0.205 Add extra zeros on the left of an answer if you need to.

*Dividing using American Math Quotient *Make sure your place values line up. Since 9 does not go into 4, place an “x” to hold the place. One number in the quotient should be on top of one number in the divisor. Don’t squish your answer! x47 9 ) 423 -36 63 -63 Divisor Dividend *Estimate the answer using compatible numbers (either divisor or dividend). 423  450 450 ÷ 9 = 50 47 ≈ 50 Remind students that “American Division” is the same as “Greek Division” just set up differently. “American” division and “Greek” division are the same! Watch!

*Dividing using American Math *Make sure your place values line up. Since 9 does not go into 4, place an “x” to hold the place. One number in the quotient should be on top of one number in the divisor. Don’t squish your answer! 423 9 -36 47 63 -63 Divisor Dividend Quotient Remind students that “American Division” is the same as “Greek Division” just set up differently. The work is the same! The only difference is where the divisor and quotient go. “American” division and “Greek” division are the same! Watch!

17 ) 408 15 ) 556 YOU MUST USE AMERICAN DIVISION! NOT GREEK!!! The average person has 1,460 dreams a year. What is the average number of dreams a person has each night?

* Dividing by Decimals *Change the divisor into a whole number. * Multiply both the divisor and the dividend by the same power of 10. Then divide like normal. *If a decimal remains, move it directly up into the quotient. Multiply BOTH by 10 to make divisor a whole number Multiply BOTH by 100 to make divisor a whole number

(Round to the nearest tenth if necessary.) 2) 0.338 ÷ 0.26 Dividend ÷ Divisor Dividend ÷ Divisor 2.64 ÷ 0.6 6.24 ÷ 200 0.6 ) 2.64 6 ) 26.4 200 ) 6.24 *Divisor is already a whole number. No need to multiply by power of 10. 1) Alaska has a coastline of about 6.64 thousand miles. Florida has about 1.35 thousand miles of coastline. How many times more coastline does Alaska have than Florida? (Round to the nearest tenth if necessary.) 2) 0.338 ÷ 0.26

Quick note: Don’t rely on “key words” to tell you what operation to do. When multiplying: When Dividing: You are given the parts and are looking for the total. Ex: “How many in all?” You are given the total and are looking for the parts. Ex: “How many groups?” “How many in each group?”