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Announcements 3/5 • Homework – Decimals Test Corrections due Friday New late policy for 6th grade: -1 day late = -10 -after 1 day late = 50% Warm Up - Wednesday a) Every week, Hannah has to walk 0.35 miles to get to her local grocery store and back. How far does she walk to do her shopping over 15 weeks? (Answer in complete sentence) b) Lucila used a stair-climbing machine for 15.25 minutes and was able to climb set to 93 flights of stairs. How many flights did Lucila climb per minute? Round to hundredths place (Answer in complete sentence) Review • • • • • • Sum Product Factor Difference Quotient variable Manipulatives • Cut out the 30 squares and put them in your baggie • Write your name with a Sharpie on your baggie • Objective: Understand relationships of operations and use them to generate equivalent expressions Addition and Subtraction Identity Opening Exercise a. Draw a tape diagram to represent the following expression : 5 + 4 b. Write an expression for each tape diagram i. ii. Addition and Subtraction Identity Discussion • Take out 10 of your squares and place them on your desk • If each square represents 1 unit, represent the number 3 using the squares • Add two more squares to your tape diagram • Draw AND Write an expression to represent how we created a tape diagram with 5 squares Discussion • Remove two squares from your tape diagram • Alter our original expression, 3 +2, to create an expression that represents what we just did with the tape diagram • Evaluate the expression Discussion • Clear your desk • This time, create a tape diagram with six squares • Use your tiles to demonstrate 6 + 4 • Draw AND Write an expression to represent this tape diagram Discussion • Remove four squares from your tape diagram • Alter our original expression, 6 +4, to create an expression to represent the tape diagram • How many tiles are left on your desk? • Evaluate the expression • How many tiles did we start with? Discussion • What effect did adding four tiles then subtracting the four tiles have on the number of tiles? • What if I asked you to add 215 tiles to the six tiles we started with and then subtract 215 tiles? • Do you need to actually add and remove these tiles to know what the result will be? Why? Discussion • What do you notice about the expressions we created with the tape diagrams? • Write a number sentence, using variables, to represent what we just demonstrated with tape diagrams. Remember that a variable is a letter that represents a number. • Why do you think this is called an identity? Announcements 3/6 • Homework – Addition and Subtraction identity practice – Decimals Test Corrections due Friday New late policy for 6th grade: -1 day late = -10 -after 1 day late = 50% Warm Up – Thursday a) The sand pit for the long jump has a width of 2.75 meters and a length of 9.54 meters. Just in case it rains, the principal wants to cover the sand pit with a piece of plastic the night before the event. How many square meters of plastic will the principal need to cover the sand pit? b) A book is ½ of an inch thick. How many of these books will fit into a shelf that is 5 and ¾ inches wide? Discussion • Write a number sentence, using variables, to represent what we just demonstrated with tape diagrams. Remember that a variable is a letter that represents a number. • w + x – x = w AND w - x + x = w • Why do you think this is called an identity? Exercises • What if we rearrange the number sentence: x+w–x=? -x + x + w = ? x–x+w=? -x + w + x = ? Closing Discussion • In every problem we did today, why did the final value of the expression equal the initial expression? • Initially, we added an amount and then subtracted the same amount. Later in the lesson, we subtracted an amount and then added the same amount. Did this alter the outcome? • Why were we able to evaluate the final expression even when we did not know the amount we were adding and subtracting? Addition and Subtraction Identity: w+x–x=w w–x+x=w Homework Multiplication and Division Identity Opening Exercise • Draw a pictorial representation of the division and multiplication problems using a tape diagram. a. 8 ÷ 2 b. 3 · 2 Review • Variable • Number sentence Discussion • • • • Need 10 squares Build a tape diagram to represent 9 units Divide the 9 units into 3 equal groups Write an expression to represent the process you modeled • Evaluate the expression • Use your squares to demonstrate what it would look like to multiply 3 by 3 • Alter our original expression to represent what we just did Discussion • What do you notice about the expression of the tape diagram? • Write a number sentence, using variables, to represent the identities we demonstrated with the tape diagram. Discussion Create a model to represent your number sentence Exercises • With your partner come up with another number sentence to show the relationship between multiplication and division. The number sentence should include variables and an identity. • Model it in your notes Closing Discussion • What did you determine about the relationship between multiplication and division? Multiplication and Division Identity: a·b÷b=a a÷b·b=a Homework Announcements 3/7 • Homework – */+ and ÷/- identity practice – Study for Identity quiz on Monday New late policy for 6th grade: -1 day late = -10 -after 1 day late = 50% Warm Up - Friday a) Matt is running for student council. His friends are going to help him give out 15 posters and 6 banners. Matthew plans to pack all of the posters and the same number of banners in each box. What is the greatest number of boxes Matthew can pack? b) A pie recipe requires 2/3 lbs of apples. How many apples are needed for 4 whole pies and a mini pie (1/2 of whole pie) **Have homework on desk Review Homework Review Homework Multiplication and Addition Identity Opening Exercise • Write two different expressions that can be depicted by the tape diagram shown. One expression should include addition, the other multiplication Discussion • Need 20 squares • Partner 1 : build a tape diagram to represent the expression 2 + 2 + 2 + 2 • Partner 2 : build a tape diagram to represent the expression 4 x 2 • What do you notice about the 2 tape diagrams? • Why are they the same? • What does the say about the value of the expressions? (use your elevated diction) • 2+2+2+2=4x2 • Is there an advantage to using one over the other? Discussion • Partner 1 : Represent 3 x 4 • Partner 2 : Represent 4 + 4 + 4 • Are they equivalent? Discussion • Use variables to create a number sentence to show the relationship between addition and multiplication • g + g + g = 3·g or 3g (multiplication implied) • Is this an identity? Exercises Multiplication and Addition Identity: 3·g=g+g+g Homework Division and Subtraction Identity Discussion • • • • • Need 30 squares Build a tape diagram with 20 units Divide it into 4 equal sections How many squares are in each section? Write a number sentence to demonstrate what happened. • • • • • • • • • • • Discussion Build your tape diagram with 20 units again Subtract 4 units from your tape diagram Write an expression to demonstrate what happened. Subtract 4 more units from your tape diagram Add to your previous expression to demonstrate what happened. Subtract 4 more units from your tape diagram Add to your previous expression to demonstrate what happened. Subtract 4 more units from your tape diagram Add to your previous expression to demonstrate what happened. Subtract 4 more units from your tape diagram Add to your previous expression to demonstrate what happened. Discussion • Evaluate your expression • What is the relationship between 20 ÷ 4 = 5 and 20 – 4 – 4 – 4 – 4 – 4 = 0? Discussion • Let’s switch the quotient and the divisor: • 20 ÷ 5 = 4 • 20 ÷ x = 5 Announcements 3/10 • Homework – Weekly math Corrections – Properties worksheets New late policy for 6th grade: -1 day late = -10 -after 1 day late = 50% Warm Up – Monday a) Alisha is putting cheese cubes and crackers onto small plates. She has 24 cubes of cheese and 40 crackers. She wants both cheese and crackers on each plate and each plate must have the same number of cheese cubes and the same number of crackers. What is the greatest number of plates she can make using all the cheese and crackers? b) Create the number line below, fill in the boxes, and draw lines to 3 opposites: -7 -4 0 3 6 7 Review • • • • • • • Variable Number sentence Identity Addition and subtraction Multiplication and division Multiplication and addition Division and subtraction Review Homework Exercises Division and Subtraction Identity: 12 ÷ x = 4 means 12 – x – x – x – x = 0 Closing Discussion Properties Homework • 3 worksheets over Commutative and Associative Properties of Addition Announcements • Homework – Weekly math Corrections – Properties worksheets New late policy for 6th grade: -1 day late = -10 -after 1 day late = 50% Identities Quiz Warm Up - Tuesday