Unit 3: Rational Numbers ANSWER KEY

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Maximilian Carroll
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1 Unit : ANSWER KEY The following unit includes: Adding/Subtracting Integers on a Number Line Adding/Subtracting Integers with Rules Multiplying/Dividing Integers Adding/Subtracting Decimals Multiplying Decimals Dividing Decimals Adding/Subtracting Fractions Multiplying Fractions Dividing Fractions

2 Get Connected with Math in Demand My Teachers Pay Teachers Read My Blog Click on the buttons to check out more from me. Visit My Pinterest Watch My Videos Me Thank you for purchasing my notebook! Please don t forget to rate me.

I like to use direct instruction and have my students fill in the blank template. However, I accommodate any of my students that have difficulty writing by providing the answer key.

3 Teacher Notes: Provided in this file is the answer key for Unit. There are a few things that you might find helpful: () You can differentiate for your students by deciding to print the blank template or answer key. I like to use direct instruction and have my students fill in the blank template. However, I accommodate any of my students that have difficulty writing by providing the answer key. () If you feel that I left anything out, you can ALWAYS have students add any additional notes. Every teacher likes to teach a concept differently than another. () You can use colored paper when printing the cutouts. This makes it less for students to color and it still makes the page look colorful! Also, have students color code important info with highlighters!! It looks great! () You can print the interactive notebook at 90% to make it fit into a smaller composition notebook. If you have any questions, please don t hesitate to me at jen_marie_8@hotmail.com. Thank you so much! Math in Demand

Unit Checklist () As you go through the unit, check off the concepts that you have mastered. Leave the other ones unchecked so that you know which concepts you need to study before a test!

4 Unit Checklist () As you go through the unit, check off the concepts that you have mastered. Leave the other ones unchecked so that you know which concepts you need to study before a test! The following unit includes: Adding/Subtracting Integers on a Number Line Adding/Subtracting Integers with Rules Multiplying/Dividing Integers Adding/Subtracting Decimals Multiplying Decimals Dividing Decimals Adding/Subtracting Fractions Multiplying Fractions Dividing Fractions

Unit Overview () This overview shows you important information that you will be learning throughout the unit. Make sure to fill out important dates and scores!

5 Unit Overview () This overview shows you important information that you will be learning throughout the unit. Make sure to fill out important dates and scores! Concepts(s): Adding/Subtracting Integers on a Number Line Adding/Subtracting Integers with Rules Multiplying/Dividing Integers Adding/Subtracting Decimals Multiplying Fractions Multiplying Decimals Dividing Fractions Dividing Decimals Adding/Subtracting Fractions Essential Questions: How are adding and subtracting integers similar? Why is it important to understand operations on rational numbers? How can number lines be used to interpret real world problems? Vocabulary: Rationals Integers Decimals Fractions Operations Numerator Denominator Reciprocal Quotient Important Dates: Pre-Test: Post-Test: Vocabulary Quiz: Scores: Pre-Test: Post-Test: Vocabulary Quiz:

(Adding/Subtracting Integers on a Number Line) Numbers get smaller! Numbers get bigger!

A number line is a great tool to use when adding or subtracting integers! Subtraction always comes back to addition!

dot on the number line for the first given number Step : Move from the dot either left or right according to the other

6 (Adding/Subtracting Integers on a Number Line) Numbers get smaller! Numbers get bigger! add and subtract integers I can on a number line. A number line is a great tool to use when adding or subtracting integers! Subtraction always comes back to addition!!! For example, 5 (-) becomes 5+ and becomes Follow these steps to add or subtract integers: Step : Place a dot on the number line for the first given number Step : Move from the dot either left or right according to the other given number. Move left when adding a negative integer Move right when adding a positive integer Your stopping point is your answer! Example: What is -6 (-9)?

7 (Adding/Subtracting Integers on a Number Line) On a rating of -5, how comfortable are you with this concept? (5 is the highest).) ) - (-) ) Reflection: I learned

add and subtract integers I can (Adding/Subtracting Integers with Rules) using the

) 7 (-) 7 + We can add integers by using rules Positive + Negative (Different Signs)

Negative + Negative OR Positive + Positive (Same Signs) Add the two numbers.

8 add and subtract integers I can (Adding/Subtracting Integers with Rules) using the addition rules. Change the following to addition:.) Addition Rules.) 7 (-) 7 + We can add integers by using rules Positive + Negative (Different Signs) Subtract the two numbers. Keep the sign of the largest absolute value number. Negative + Negative OR Positive + Positive (Same Signs) Add the two numbers. Keep the sign. We can also add or subtract integers by using counters: ) - (-7) Examples:.)

9 Intro to Algebra (Adding/Subtracting Integers with Rules) On a rating of -5, how comfortable are you with this concept? (5 is the highest) (-) (-) 6-9 (-6) (-) 9 Reflection: I learned

10 multiply and divide integers. I can (Multiplying/Dividing Integers) Multiplying Integers Dividing Integers Neg x Pos Neg Neg Pos Neg Pos x Neg Neg Pos Neg Neg Neg x Neg Pos Neg Neg Pos Pos x Pos Pos Pos Pos Pos Another Way to Think About Signs: # of Negatives Outcome Negative Positive Negative Positive What do you notice about the table? There is a pattern! If you have an odd number of negatives, then your answer is negative! If you have an even number of negatives, then your answer is positive!.) - -8 Examples:.) 5

11 Intro to Algebra (Multiplying/Dividing Integers) On a rating of -5, how comfortable are you with this concept? (5 is the highest) Reflection: I learned

We use decimals every day when we are purchasing items at the store, counting money or making change, and reading an odometer.

12 (Adding/Subtracting Decimals) add and subtract decimals. I can What is a decimal? A decimal is written in our base-ten number system. There are ten single-digit numbers: 0,,,,, 5, 6, 7, 8, and 9. Why are decimals important? Decimals are important in our everyday life. We use decimals every day when we are purchasing items at the store, counting money or making change, and reading an odometer. Follow these steps to add decimals: Step : Write down the numbers with one underneath the other so that the decimals are lined up. Step : If necessary, add in any zeros that are needed to fill in any empty spots. Step : Add the numbers using column addition. Make sure to bring down the decimal..) Examples:.)

13 (Adding/Subtracting Decimals) On a rating of -5, how comfortable are you with this concept? (5 is the highest).) ) ) (-.) Reflection: I learned

14 multiply decimals. I can (Multiplying Decimals) Multiplication Signs Negative x Positive Negative Positive x Negative Negative Negative x Negative Positive Positive x Positive Positive Follow these steps to multiply decimals: Step : Ignore the decimal and multiply as usual. Step : Count the total number of digits behind the decimal point(s). Step : Place the decimal according to the same number of digits you counted. Example: 0.5 x

15 (Multiplying Decimals) On a rating of -5, how comfortable are you with this concept? (5 is the highest).) 6.7 x ) -0.8 x ) -. x Reflection: I learned

16 divide decimals. I can (Dividing Decimals) Division Signs Negative Positive Negative Positive Negative Negative Negative Negative Positive Positive Positive Positive Follow these steps to divide decimals: Step : If divisor is not a whole number, move the decimal point to the right to make a whole number. Move the decimal in the dividend by the same number of places. Step : Divide as usual (long division). Step : Place the decimal point above the decimal point in the dividend. Example: ?

17 (Dividing Decimals) On a rating of -5, how comfortable are you with this concept? (5 is the highest).) ) ) Reflection: I learned

$add and subtract fractions. I can (Adding/Subtracting Fractions) What is a fraction? A fraction is a ratio of two numbers. In other words, an integer divided by an integer.$

18 add and subtract fractions. I can (Adding/Subtracting Fractions) What is a fraction? A fraction is a ratio of two numbers. In other words, an integer divided by an integer. Before we can add or subtract fractions, we must have: Common Denominators Follow these steps to add or subtract fractions: If denominators are different, find the least common denominator. Step : Step : Multiply the numerators AND denominators by a number to get the LCM. Step : Add the numerators. Keep the denominators the same. If possible, reduce. Example: What is + +?

19 (Adding/Subtracting Fractions) On a rating of -5, how comfortable are you with this concept? (5 is the highest).) +.) + 5.) + ++x.) 8 +5x a.) The expression has terms. b.) Underline the+variables c.) Box the coefficients constants d.) Circle the Reflection: I learned

20 (Multiplying Fractions) multiply fractions. I can Multiplication Signs Negative x Positive Negative Positive x Negative Negative Negative x Negative Postive Positive x Positive Positive How do we multiply fractions? Multiply the numerators together and multiply the denominators together!!! Make sure to SIMPLIFY your answers! Multiplying across is not the same thing as cross multiplication..) Examples:.)

21 (Multiplying Fractions) On a rating of -5, how comfortable are you with this concept? (5 is the highest).).).) 5 - Reflection: I learned

22 divide fractions. I can (Dividing Fractions) Division Signs Negative Positive Negative Positive Negative Negative Negative Negative Postive Positive Positive Positive How do we divide fractions? Step : Keep the first fraction the same. Step : Flip the second fraction. Step : Multiply the fractions. Step : Simplify..) Examples:.)

23 (Dividing Fractions) On a rating of -5, how comfortable are you with this concept? (5 is the highest).).).) 5 Reflection: I learned

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Decimal Reference Sheet

Decimal Reference Sheet The decimal reference sheet is a great resource for an interactive notebook or handout to be given in class for review. The Decimal Reference Sheet includes:!a!set!of!32!word!problem!task!cards!for!your!common!core!classroom!