Slide 1 / 191 Slide 2 / 191 5th Grade Algebraic Concepts 2015-10-16 www.njctl.org Slide 3 / 191 click on the topic to go Table of Contents to that section · What is Algebra? · Order of Operations · Grouping Symbols · Writing Simple Expressions & Interpreting Numerical Expressions · Writing & Interpreting Expressions Application Problems · Function Tables · Graphing Patterns & Relationships in the Coordinate Plane Glossary ·
Slide 3 (Answer) / 191 click on the topic to go Table of Contents to that section Vocabulary Words are Teacher Notes underlined with a dashed line · What is Algebra? in the presentation. This is · Order of Operations linked to the page at the end · Grouping Symbols of the presentation with the word defined on it. · Writing Simple Expressions & Interpreting Numerical Expressions · Writing & Interpreting Expressions Application Problems [This object is a pull tab] · Function Tables · Graphing Patterns & Relationships in the Coordinate Plane Glossary · Slide 4 / 191 What is Algebra? Return to Table of Contents Slide 5 / 191 The word "algebra" is taken from a book title al-jebr w'al-muqabalah (circa 825) by the Persian mathematician known as al-Khowarismi. This is considered to be the first book written about Algebra. Al'Khwarizmi was a Persian mathematician who wrote on Hindu-Arabic numerals (the numeral system we use today). He was also one of the first to use zero as a place holder. al-jebr (from the book title) means "reunion of broken parts". Kind of like puzzle pieces.
Slide 6 / 191 Algebra is a way of solving Math problems. It is basically like looking at the problem like a puzzle. Putting together the pieces you have, in order to figure out what is missing. What is the missing piece to this number puzzle? Slide 7 / 191 Algebra help us tie together many mathematical ideas. (Like hours worked and money earned.) Sarah earns $10 for every hour she works. ______ (hours) x $40 $10 What is the missing value? Slide 8 / 191 Things change. To describe things that change or vary, mathematicians invented Algebra. Algebra makes it easier to say exactly how two changing things (like dollars earned and hours worked) are related. Sarah earns $10 for every hour she works. $10 x = $40 (hours) If we change the amount Sarah earns, the number of hours she worked will change too. $10 x = $60 (hours)
Slide 9 / 191 Important Vocabulary: An expression is like a phrase and names a number. An equation is a number sentence that describe a relationship between two expressions. H x 6 is an example of an algebraic expression. An algebraic expression uses operation symbols (+,-,x,÷) to combine variables and numbers. A letter that stands for a number is called a variable. Some common variables are: l = length, w = width, h = height and x or y. Slide 10 / 191 Order of Operations Return to Table of Contents Slide 11 / 191 Imagine this: You put your shoes on, and then your socks. Wait... What? What's wrong with this picture? click It's out of order.
Slide 12 / 191 In life, there is an order in which we do things. Like putting our socks on first, before our shoes. Math is no different. When we perform operations (+,-,x, ) there is an order. Slide 13 / 191 In an expression with more than one operation, use the rules called Order of Operations. 1. Do all multiplication and division in order from left to right. 2. Do all addition and subtraction in order from left to right. Note: From left to right means first come, first served. Like reading a book. Start on the left, and work your way to the right. First, completing all x and . Then all + and -. Slide 14 / 191 Name the operation that should be done first. 6 x 3 + 4 multiplication click 3 + 4 x 6 multiplication click 5 - 3 + 6 subtraction click 9 - 6 3 division click
Slide 15 / 191 1 Do you add or multiply first? 6 + 3 x 2 + 7 A add B multiply Slide 15 (Answer) / 191 1 Do you add or multiply first? 6 + 3 x 2 + 7 A add B multiply Answer B [This object is a pull tab] Slide 16 / 191 2 Do you divide or add first? 12 + 3 ÷ 12 ÷ 4 A add B divide
Slide 16 (Answer) / 191 2 Do you divide or add first? 12 + 3 ÷ 12 ÷ 4 A add B divide Answer B [This object is a pull tab] Slide 17 / 191 3 10 - 6 x 6 + 4 x 10 Which operation do you do... 1st? 2nd? 3rd? + + + A D G - - - B E H x x x C F I Choose an operation for each step. Slide 17 (Answer) / 191 3 10 - 6 x 6 + 4 x 10 Which operation do you do... 1st? 2nd? 3rd? Answer + + + A D C,E,G G - - - E B H x x x F C I [This object is a pull tab] Choose an operation for each step.
Slide 18 / 191 Evaluate the expression using the Order of Operations. 4 + 3 x 7 Step 1 Multiply 3 x 7. Step 2 Rewrite the expression. 4 + 21 Step 3 Add 4 + 21. So, 4 + 3 x 7 = 25. Slide 19 / 191 Evaluate the expression. 25 - 4 x 5 + 4 Step 1 Multiply 4 x 5. Step 2 Rewrite the expression. 25 - 20 + 4 Step 3 S ubtract 25 - 20 Step 4 Rewrite the expression. 5 + 4 Step 5 Add 5 + 4. So, 25 - 4 x 5 + 4 = 9. Slide 20 / 191 4 Evaluate 6 + 3 x 2 + 7 =
Slide 20 (Answer) / 191 4 Evaluate 6 + 3 x 2 + 7 = Answer 19 [This object is a pull tab] Slide 21 / 191 5 Evaluate 12 + 12 ÷ 4 ÷ 3 = Slide 21 (Answer) / 191 5 Evaluate 12 + 12 ÷ 4 ÷ 3 = Answer 13 [This object is a pull tab]
Slide 22 / 191 6 Evaluate 100 - 6 x 6 + 4 x 10 = Slide 22 (Answer) / 191 6 Evaluate 100 - 6 x 6 + 4 x 10 = Answer 104 [This object is a pull tab] Slide 23 / 191 7 Evaluate 50 ÷ 10 + 15
Slide 23 (Answer) / 191 7 Evaluate 50 ÷ 10 + 15 Answer 20 [This object is a pull tab] Slide 24 / 191 Grouping Symbols Return to Table of Contents Slide 25 / 191 Sarah has 8 dollars. Jonathan has 5 dollars more than Sarah. He spends half of his money. Write an expression that represents this scenario. Sara's $ plus $5 divided in half 8 + 5 2 Think, pair, share: Is this correct? Explain your answer on your paper.
Slide 26 / 191 If we follow the order of operations, we would divide the "$5 more" before we added it to Sarah's money. plus $5 divided in half Sara's $ 8 + 5 2 So how can we represent this scenario? We can use parenthesis. Slide 27 / 191 Parentheses ( ) are used to group calculations to be sure that they are done in a certain order. When you use parentheses ( ), you are saying, "DO THIS FIRST." plus $5 divided in half Sara's $ (8 + 5) 2 The parenthesis tell us to add $5 to Sarah's money before we divide it in half. Slide 28 / 191 Sarah has 8 dollars. Jonathan has 5 dollars more than Sarah. He spends half of his money. Lets look at the results of each expression. 8 + 5 2 (8 + 5) 2 Step 1: 8 + 2.5 13 2 6.5 10.5 Step 2: John has $6.50. John has $10.50. Which makes more sense?
Slide 29 / 191 Evaluate each expression using the order of operations. Remember, to do what is inside the parenthesis first. (10 - 2) x 4 10 - 2 x 4 Step 1 click 8 x 4 10 - 8 32 click Step 2 2 What do you notice? Slide 30 / 191 Let's solve (17 - 4) x 3 The parentheses tell you to subtract 17 - 4 first. (17 - 4) x 3 Then multiply by 3. 13 x 3 The answer is 39. 39 OR Let's solve 17 - (4 x 3) The parentheses tell you to multiply 4 x 3 first. 17 - (4 x 3) Then subtract. 17 - 12 The answer is 5. 5 Slide 31 / 191 Evaluate the expression. (10 + 6 x 6) - 4 x 10 Step 1 Start with computations inside the parentheses. Using the Order of Operations, multiply first and then add. (10 + 6 x 6) (10 + 36) 46 Step 2 Rewrite the expression with parentheses evaluated. 46 - 4 x 10 Step 3 Multiply 4 x 10. Step 4 Rewrite the expression. 46 - 40 Step 5 Subtract. So, (10 + 6 x 6) - 4 x 10 = 6.
Slide 32 / 191 8 What is the value of this expression? 5 + 3 x (7 - 1) Remember to do inside the parentheses( ) first. 23 A B 25 48 C D 64 Slide 32 (Answer) / 191 8 What is the value of this expression? 5 + 3 x (7 - 1) Remember to do inside the parentheses( ) first. A 23 B 25 Answer C 48 A 64 D [This object is a pull tab] Slide 33 / 191 9 What is the value of this expression? (8 + 4) ÷ 3 x 6 A 6 B 9 C 24
Slide 33 (Answer) / 191 9 What is the value of this expression? (8 + 4) ÷ 3 x 6 A 6 B 9 Answer C 24 C [This object is a pull tab] Slide 34 / 191 10 Use the Order of Operations. Write each step and evaluate the expression. 5 x (12 - 5) + 7 Slide 35 / 191 11 Evaluate (14 - 5) + ( 10 ÷ 2)
Slide 36 / 191 12 Which expression equals 72? A 36 ÷ 4 - 3 x 2 B (36 ÷ 4 - 3) x 2 C 36 ÷ (4 - 3 x 2) D 36 ÷ (4 - 3) x 2 Slide 37 / 191 13 Enter your answer. From PARCC sample test Slide 38 / 191 14 Evaluate (8 x 9) - (6 x 7)
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