Unit 4: Decimal Operations
|
In this unit students will add, subtract, multiply and divide decimals. Students must be able to complete these operations fluently. Students will have to apply their knowledge of computation with decimals to fluently solve real world word problems with decimals. Students will extend their knowledge of equivalent ratios/rates and unit rate from Unit 2, and complete more complex application problems. Students will have to apply their knowledge of percentages to real world situations including, but not limited to, determining the best deal, finding a quicker pace, determine sale prices from a percent discount and determine a total amount number amount from a percentage.
|
Learning Target |
NYS Standard |
Engage NY |
Textbook Resources |
1: I can add and subtract decimals. |
6.NS.3 |
CMP3 Decimals Ops Go Math 5.2 |
|
2: I can multiply decimals. |
6.NS.3 |
CMP3 Decimal Ops Go Math 5.3 |
|
3: I can divide a decimal by a whole number. |
6.NS.3 |
CMP3 Decimal Ops Go Math 5.4 |
|
4: I can divide a whole number by a decimal. |
6.NS.3 |
Value |
CMP3 Decimal Ops Go Math 5.4 |
5: I can divide a decimal by a decimal. |
6.NS.3 |
Value |
CMP3 Decimal Ops Go Math 5.4 |
6: I can solve real world problems with decimals. |
MP.1 MP.4 |
Go Math 5.5 |
|
7: I can solve real world unit rate problems with decimals. |
6.RP.2 6.RP.3a 6.RP.3b |
Go Math 6.2 Go Math 6.3 |
|
8: I can solve real world percent problems. |
6.RP.3c |
Go Math 8.3 |
Learning Target 1: I can add and subtract decimals.
Learning Target & Objectives |
Misconceptions/ Common Errors |
Instructional Resources |
Learning Activities |
4.1.A: I can identify place values. |
(1) Inaccurately labeling the place values to the right of the decimal point because the first one is "tenths"; as opposed to "ones" being the first to the left of the decimal and "tens" being the second. |
(1) Place Value; notes sheet with examples (2) Understanding place value ; Video (3) Place Value Practice; Practice Sheets |
(1) |
4.1.B: I can add or subtract decimals following the standard algorithm. |
(1) Students may line up the digits of the values instead of lining up the decimal points of the numbers. It is necessary to line up the decimal point to preserve the value of each number’s digits. |
(1) Adding and Subtracting Decimals; Activinspire (2) Adding and Subtracting Decimals; Powerpoint Slides (3) Adding and Subtracting Decimals; Video |
|
4.1.C: I can explain why the sum or difference is correct. |
(1) Failing to understand that each digit's worth is determined by the place value so inaccurately aligning the place values leads to the wrong sum or difference |
(1) |
(1) |
4.1: I can add and subtract decimals. |
(1) Failing to properly align the place values (2) Failing to understand that each digit's worth is determined by the place value so inaccurately aligning the place values leads to the wrong sum or difference |
(1) Adding & Subtracting Menu Activity: Real Life Application (2) Adding & Subtracting Decimals Dice Activity; Game |
Learning Target 2: I can multiply decimals.
Learning Target & Objectives |
Misconceptions/ Common Errors |
Instructional Resources |
Learning Activities |
4.2.A: I can multiply multi-digit whole numbers following the standard algorithm. |
(1)Students may fail to input zeros as place-holders as they multiply beyond the first digit of the bottom factor. This will lead to an incorrect product if the digits are not put in the correct place value. |
(1) Multiplying multi-digit whole numbers (2 digit by 2 digit); Activinspire (2) Multiplying multi-digit whole numbers (3 digit by 3 digit); Activinspire (3) Multiplying multi-digit whole numbers(2 digit by 2 digit and 3 digit by 2 digit); Powerpoint Slides (4) Multiply multi-digit whole numbers; Practice Sheet |
(1) |
4.2.B: I can multiply decimals following the standard algorithm. |
(1) Students may incorrectly place the decimal point in the product. It is necessary for the students to understand the differences and weight of each place value. |
(1) Multiplying Decimals; Notes sheet with examples (2) Multiplying multi-digit decimals ; Video & Slides (3) Multiplying Decimals with models (part one); Activinspire (4) Multiplying Decimals (part two); Activinspire (5) Multiply Decimals; Notes Sheet with examples |
Value |
4.2.C: I can explain why the product is correct. |
(1) Multiplying Decimals; Do Now & Notes sheet where students shade in the product |
||
4.2: I can multiply decimals. |
Unit 4 Mastery Quiz 1: see assessment tabs
Learning Target 3: I can divide a decimal by a whole number.
Learning Target & Objectives |
Misconceptions/ Common Errors |
Instructional Resources |
Learning Activities |
4.3.A: I can divide multi-digit whole numbers following the standard algorithm. |
(1)Students may incorrectly place the digits of a quotient in the wrong place or forget to fill in the ones place with a zero. It is necessary for the students to understand the differences and weight of each place value. |
(1) Division (1-digit divisor); Activinspire (2) Dividing Multi-digit whole numbers; Powerpoint Slides (3) Divide multi-digit whole numbers; Notes Sheet |
(1) |
4.3.B: I can divide a decimal by a whole number following the standard algorithm. |
(1)Students may incorrectly place the digits of a quotient in the wrong place or bring the decimal up to the wrong spot. Some can forget to bring the decimal up at all. Students must bring the decimal point up vertically from the dividend to the quotient and it is necessary for the students to understand the differences and weight of each place value |
(1) Divide a decimal by a whole number; Powerpoint Slides (2) Divide decimal by a whole number; Notes Sheet |
Value |
4.3.C: I can explain why the quotient is correct. |
(1) |
(1) |
|
4.3: I can divide a decimal by a whole number. |
Learning Target 4: I can divide a whole number by a decimal.
Learning Target & Objectives |
Misconceptions/ Common Errors |
Instructional Resources |
Learning Activities |
4.4.A: I can divide a whole number by a decimal following the standard algorithm. |
(1) Students may fail to move the decimal point of the dividend after moving the decimal point of the divisor. It is necessary for the students to know to maintain proportionality by remembering to change the dividend and divisor equally. |
(1) |
|
4.4.B: I can explain why the quotient is correct. |
(1) |
(1) |
Value |
4.4: I can divide a whole number by a decimal. |
(1) |
Learning Target 5: I can divide a decimal by a decimal.
Learning Target & Objectives |
Misconceptions/ Common Errors |
Instructional Resources |
Learning Activities |
4.5.A: I can divide a decimal by a decimal following the standard algorithm. |
(1)Students may fail to move the decimal point of the dividend after moving the decimal point of the divisor. It is necessary for the students to know to maintain proportionality by remembering to change the dividend and divisor equally. |
(1) Dividing decimals ; Video (2) Divide a decimal by a decimal; Powerpoint Slides (3) Divide a decimal by a decimal; Notes sheet with practice problems |
(1) |
4.5.B: I can explain why the quotient is correct. |
(1) Confusing absolute value with a number's opposite. ex) |8| = -8 |
(1) |
Value |
4.5: I can divide a decimal by a decimal. |
(1) Assuming the the number with the larger absolute value is the larger number. ex) -9 > -2 |
(1) Dividing Decimals Pirate Game; Board Game |
Unit 4 Mastery Quiz 2: see assessment tab
Learning Target 6: I can solve real world problems involving decimals.
Learning Target & Objectives |
Misconceptions/ Common Errors |
Instructional Resources |
Learning Activities |
4.6.A: I can correctly identify and solve real world problems requiring addition and subtraction of decimals. |
(1) |
(1) Justify the Operation - M; addition or subtraction (2) Identify the correct operation and solve; Problem Set |
(1) Adding and Subtracting Decimals Word Problems- Problem Set |
4.6.B: I can correctly identify and solve real world problems requiring multiplication or division of decimals. **excluding unit rate |
(1) Incorrectly recognizing the relationship between place values. |
(1) |
(1) Multiplying Decimals; Matching Activity - match the equation to the word problem; PDF Version |
4.6: I can solve real world problems involving decimals. |
(1) Students choose the incorrect operation for the word problem Students must memorize the key words and operations they coincide with |
Learning Target 7: I can solve real world unit rate problems with decimals.
Learning Target & Objectives |
Misconceptions/ Common Errors |
Instructional Resources |
Learning Activities |
4.7.A: I can determine a unit rate involving decimals using a proportion. |
(1) Incorrectly setting up the proportion Students must remember to label when setting up the proportion |
(1) Unit Rate using a proportion; Notes with examples (2) Solve real world unit rate problems with decimals; Note Sheet with examples (3) Unit Rate; Entrance/exit ticket |
|
4.7.B: I can determine a unit rate involving decimals using a division equation. |
(1) Switching divisor and dividend Unit rate is amount per one of something and therefore divisor must represent unit value |
(1) |
Value |
4.7: I can solve real world unit rate problems with decimals. |
(1) |
(1) Real world unit rate problems with decimals Problem Set (2) Comparing costs using unit rate; Problem Set (3) Comparing Unit Rates; Problem Set |
Learning Target 8: I can solve real world percent problems.
Learning Target & Objectives |
Misconceptions/ Common Errors |
Instructional Resources |
Learning Activities |
4.8.A: I can solve percent problems using a proportion. |
(1) Incorrectly setting up the proportion Percents are out of 100 and the part is a portion out of the whole or the total |
(1) Percent problems using a proportion; Video (2) Percent problems using a proportion; Notes sheet with examples |
(1) |
4.8.B: I can calculate the percent of a number by converting the percent to a decimal and multiplying. |
(1) Students incorrectly move the decimal and multiplication errors Move the decimal twice to the left and use zeros as placeholders when multiplying |
(1) How to convert a percent to a decimal; Video (2) Converting the percent to a decimal and multiplying; Notes sheet with examples |
Value |
4.8.C: I can calculate the percent of a number by a converting the percent to a fraction and multiplying. |
(1) |
(1) How to convert the percent to a fraction; Video (2) Calculate the percent of a number; Notes sheet with examples |
|
4.8.D: I can solve real world discount and sale price problems. |
(1) Students will fail to complete ALL necessary steps to complete the question correctly. It is necessary for students to understand that tax and tip are added/sale and discount are subtracted from original price. It is also necessary for students to understand the sale price (part ) is part of the original price (whole) |
||
4.8.E: I can solve real world tax and tip problems. |
(1) Students will fail to complete ALL necessary steps to complete the question correctly. It is necessary for students to understand that tax and tip are added |
||
4.8.F: I can determine the original price given the percent discount and the sale price. |
(1) Students forget to subtract the percent discount from 100 and use that percentage in the proportion Students must understand that they need to find out what percentage was not discounted in order to determine the original price |
(1) Determine original price; Notes sheet with examples (2) Finding the Bill from the Tip; Practice problems |
Value |
4.8: I can solve real world percent problems. |
