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Name: _______________________________________________________ Date: ______________ Pd: ____ Make sure your handwriting can be read. Complete all work in PENCIL. Unit 1: The Number System Math in Careers: Read page 1 of your textbook. Then fill in the blanks below. Career: ________________________________________________________________________ 1. ______________________ perform cost-benefit analysis of projects, use ________________ and ____________________ when they design the layout of infrastructure, and use ____________________ and mathematical _______________ to predict the growth and future needs of a population. (page 1) 2. If you are interested in this career, you should take these four math classes: (page 1) a. ____________________________________ b. ____________________________________ c. ____________________________________ d. ____________________________________ Write down the three modules that are covered in Unit 1. (page 1) 1. Module 1: _________________________________________________________________ 2. Module 2: _________________________________________________________________ 3. Module 3: _________________________________________________________________ Unit Project Preview (pg 2) Use complete sentences to answer the questions below. 1. What is a real-life situation in which you would add two negative numbers? ___________________________________________________________________________ ___________________________________________________________________________ 2. What is a real-life situation when you would multiply two negative numbers? ___________________________________________________________________________ ___________________________________________________________________________ 3. What is a real-life situation when you would divide a negative integer by a positive integer? ___________________________________________________________________________ ___________________________________________________________________________ Complete problems 1 and 2 on page 2 of your textbook. 1 Name: _______________________________________________________ Date: ______________ Pd: ____ Write down the Domains and Clusters that are covered in this Unit. (page 2) 1. Domain: ___________ a. Cluster __________________________________________________ ________________________________________________________ ________________________________________________________ ________________________________________________________ ________________________________________________________ 2. Domain: ___________ a. Cluster __________________________________________________ ________________________________________________________ ________________________________________________________ ________________________________________________________ Are You Ready (page 4) Be sure page 4 #1-12 is done and leave in your textbook. Reading Start-Up (page 5) Complete the Reading Start-Up on page 5 in your textbook. Leave it in your textbook. Vocabulary for this Unit Absolute value Expression Positive number (integers) Additive inverse Integers Product Complex fraction Model Rational number Difference Negative number (integers) Repeating decimal Divide Operation Sum Dividend Opposites Terminating decimal Divisor Pattern Whole number 2 Name: _______________________________________________________ Date: ______________ Pd: ____ Module 1: EQ: _____________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ Watch the Real-World Video then answer the EQ. Answer: ___________________________________________________________________________ ___________________________________________________________________________ Scan the module. List the four topics you will learn in this module. (page 3) 1) ____________________________________________________________________________________ 2) ____________________________________________________________________________________ 3) ____________________________________________________________________________________ 4) ____________________________________________________________________________________ Vocabulary for this Module Complete the “Reading Start-up” from page 5 in your textbook. Do not tear it out. Write a brief definition for each word. Absolute value - _______________________________________________________________ Additive inverse - ______________________________________________________________ Difference - ___________________________________________________________________ Expression - __________________________________________________________________ Integer - _____________________________________________________________________ Graph - ______________________________________________________________________ Model - _______________________________________________________________________ Negative integer (number) - ______________________________________________________ Positive integer (number) - ______________________________________________________ Sum - ________________________________________________________________________ Whole number - _______________________________________________________________ Zero pair - ____________________________________________________________________ 3 Name: _______________________________________________________ Date: ______________ Pd: ____ Lesson 1.1 - _____________________________________________________ Make sure your handwriting can be read. Answer all questions using complete sentences. Standard 7.NS.1 Apply and extend previous understanding of addition and subtraction to add and subtract rational numbers, represent addition and subtraction on a horizontal or vertical number line diagram. EQ What You’ll Learn: Scan the lesson. List three headings you would use to make an outline of the lesson. 1) ________________________________________________________________________________ (p7) 2) ________________________________________________________________________________ (p8) 3) ________________________________________________________________________________ (p9) Review of Prior Knowledge Answer each question true or false. Prove your answer correct or provide a counterexample. Answer using complete sentences. 1. Subtraction of whole numbers is associative. 2. Division of whole numbers is commutative. Matching. Match each example on the left to the correct property on the right. Place the letter of the correct answer on the line next to the example. 3. 5 ∙ 3 ∙ 2 = 3 ∙ 5 ∙ 2 _____ A) Additive Identity 4. 5 + (3 + 2) = (5 + 3) + 2 _____ B) Associative Property 5. 5(3𝑥 − 4) = 15𝑥 − 20 _____ C) Commutative Property 6. 4𝑎 + 0 = 4𝑎 _____ D) Distributive Property 7. 4𝑎 ∙ 0 = 0 _____ E) Multiplicative Identity 8. 4𝑎 ∙ 1 = 4𝑎 _____ F) Multiplicative Property of Zero Solve. Show each step of your work. Circle your final answer. 9. 12 + (36 ÷ 32 ) 10. 30 − 2[4 + (9 ÷ 3)] 4 Name: _______________________________________________________ Date: ______________ Pd: ____ Given Notes integers – all whole numbers and their opposites … -3, -2, -1, 0, 1, 2, 3 … absolute value – the distance between the number and 0, ALWAYS POSITIVE…how far the number is from zero symbol -- │x │ │5 │ = 5 │-5 │ = 5 │1.2 │ = 1.2 │-1.2 │ = 1.2 opposites – two numbers that have the same absolute value but have different signs…the positive and negative of a number 5 and –5 are opposites ½ and –½ are opposites Modeling Sums of Integers with the Same Sign You can use colored counters to add positive integers and negative integers. = a positive integer (yellow) = a negative integer (red) (See Explore Activity 1 on page 7) You Try Model with two-color counters. 1. 1 + 4 2. −2 + (−4) Adding on a Number Line Just as you can add positive integers on a number line, you can add negative integers. Use a number line to add 2 + 3. Steps: 1) Mark the initial term on the number line with a dot. Label the point 2) Count on the number line to find the final answer. Place a dot there. Label the point. 3) Draw a line from the initial dot to the final dot. 4) Label the line with the second term. 5 Name: _______________________________________________________ Date: ______________ Pd: ____ Use a number line to add -2 + (-3). 1) Mark the initial term on the number line with a dot. Label the point 2) Count on the number line to find the final answer. Place a dot there. Label the point. 3) Draw a line from the initial dot to the final dot. 4) Label the line with the second term. You Try. Use a number line to find each sum. Show your work. 1. 1 + 4 2. −2 + (−4) (See Explore Activity 2 on page 8) Adding Integers with a Common Sign (Example 1) Rule: If the signs are the same, add the integers and keep the common sign. 5+3=8 6+2+1=9 -5 + -3 = -8 -6 + (-2) + (-1) = -9 You Try. 1. Add −𝟗 + (−𝟖). 2. Add 𝟏 + 𝟒. 3. Add −𝟕 + (−𝟕). (see Explore Activity 2 on page 8) 6 4. Add 𝟏𝟐𝟎 + 𝟕𝟓