Math Journal 8-20 I make 3 pizzas for my family for dinner. Each pizza is cut into 8 slices. They eat ¾ of all of them. How many slices did they eat? How many slices of left over pizza do I have left? UNIT 1 DAY 8: VERBAL MODELING Essential Questions: How do we translate between words and algebra? Vocabulary Numerical Expression: may contain only constants and/or operations. Algebraic Expression: may contain variables, constants, and/or operations. Math Keywords + Minus, difference, less Plus, sum, increased than, decreased, take by, total, more than, away (from), how many combine, altogether more Times, product, multiplied by, by, of, twice, doubled x Divided by, quotient, separate, go into, half, equal parts Example 1 Give two ways to write each algebraic expression in words. 1) x+3 the sum of x and 3 x increased by 3 2) m-7 the difference of m and 7 7 less than m Example 2 Give two ways to write each algebraic expression in words. 1) 2•y 2 times y the product of 2 and y 2) k÷5 k divided by 5 the quotient of k and 5 Check for Understanding 1. Give two ways to write the algebraic expression 4 - n in words. a 4 divided by n the quotient of 4 and n b the sum of 4 and n 4 increased by n c n decreased by 4 4 less than n d 4 decreased by n n less than 4 Check for Understanding t 2. Give two ways to write the algebraic expression in words. 5 a t is subtracted from 5 t less than 5 b the quotient of t and 5 t divided by 5 c the quotient of 5 and t 5 divided by t d the product of t and 5 t times 5 Check for Understanding 3. Give two ways to write the algebraic expression 9 + q in words. a the sum of 9 and q q added to 9 b 9 decreased by q q less than 9 c 9 times q the product of 9 and q d 9 divided by q the quotient of 9 and q Check for Understanding 4. Give two ways to write the algebraic expression 3(h) in words. a h subtracted from 3 h less than 3 b the product of 3 and h 3 times h c h more than 3 h added to 3 d the quotient of 3 and h 3 divided by h Example 3 Kudzu is a vine native to Japan. Kudzu can grow half a foot per day during the summer months. Write an expression that shows how much a 20-foot kudzu vine can grow in June. 1 Total Growth: d 2 1 Total Growth: (30) 2 d = 30 days The vine will grow 15 feet in June! Example 4 An Internet service provider charges $9.95/month for service and charges a one-time activation fee of $19.99. Using m for the number of months, write an expression that will give us the total cost after m months. Total Cost: 9.95m + 19.99 How much will you have spent after 6 months? m = 6 months Total Cost: 9.95(6) + 19.99 Total Cost: 59.70 + 19.99 You will have spent $79.69 after 6 months. Check for Understanding 5. Which situation is best modeled by the expression 25 - x? a George places x more video games on a shelf with 25 games. b Sarah has driven x miles of a 25-mile trip. c Amelia paid 25 dollars of an x dollar lunch that she shared with Ariel. d Jorge has 25 boxes full of x baseball cards each. Check for Understanding 6. Which numerical expression represents x? x 5 20 a 20 - 5 b 20(5) c 20 + 5 d 20 ÷ 5 Summary Essential Questions: How do we translate between words and algebra? Use 1 minute to write 2 sentences answering the essential questions.