Bell Work/CRONNELLY -2 2/5  1/3 Use any strategy you choose, (diagram, finding a common denominator, or the Super Giant One), to solve the problem above. 19.32 – 13.76 – 8.25 = Convert (fraction, decimal, percent) 7/8-3/16-2/8=

Bell Work/CRONNELLY -2 2/5  1/3 -31/15; -2 1/15 -2 2/5  1/3 -31/15; -2 1/15 Use any strategy you choose, (diagram, finding a common denominator, or the Super Giant One), to solve the problem above. 19.32 – 13.76 – 8.25 = -2.69 7/8-3/16-2/8= 7/16, .4375; 43.75%

In previous lessons you have worked with expressions, combinations of numbers, variables, and operation symbols, that involve either adding integers or multiplying integers.  Today you will examine expressions that involve both operations.  By the end of this lesson, you will be expected to be able to answer these target questions: -How can expressions with the same numbers and operations have different meanings? -Does the order in which we do each operation matter?

3-1. Katrina wrote the following set of instructions for Cecil: 4 · 2 a. If Cecil the acrobat follows Katrina’s instructions, how far will he go?  Draw a diagram of Cecil’s movements and show how far he will move.    b. Katrina drew the diagram below: How was she thinking about Cecil’s moves?  Write an expression to represent Katrina’s diagram. 

3-1 Continued: c. Explain why Katrina’s diagram in part (b) will not give her the correct length for 4 · 2.5 + 1. d. Cecil changed Katrina’s set of instructions so that the length of 1 foot came first, as shown in the diagram below:   Write an expression to represent this new diagram.  How far does Cecil move here?  Does this give the same length as 4 · 2.5 + 1?

3-2. Cecil’s trainers proposed each of the following movements  3-2. Cecil’s trainers proposed each of the following movements.  Which one requires the longest rope?  Draw diagrams to justify your answer. a. 8 + 2(6.48) feet b. 2 + 8(6.48) feet c. (8 + 2)6.48 feet

3-3. The expression 5 + 3 · 4 + 2 can be used to represent the group of  +  tiles shown here: Work with your team to explain how each part of the expression connects with the groups of  +  tiles.  How many tiles are there? 

b. Each group of  +  tiles is represented by a different part of the expression, also called a numerical term.  Numerical terms are single numbers or products of numbers.  It is often useful to circle terms in an expression to keep track of separate calculations.  For example, each term circled in the expression below represents a separate part of the collection of  +  tiles above. Circle the terms in the expression shown below.  Then explain what each term could describe about collections of  +  or  –  tiles.  4 · 5 + 1 + 3(–2) + 6

3-4. Circle the terms and simplify each expression shown below 3-4. Circle the terms and simplify each expression shown below.  Simplify means to write an expression in its simplest form.  In the case of numerical expressions, the simplest form is a single number. 7.08 + 2.51 + (−3.84) b. 7.8 + 2.1(−3) c. 5(- 3 5 ) + 2 ( 1.5) d. 4.35 · 2 + 5 +(3 1 4 ) (−1) + (−10)

Practice 1. −28 ÷7+35÷2 1 3 5. 3∙2[4+ 9÷3 ] 2. 1 4 20+72 ÷−9 6. 1 2 (−16−4) 3. −9 ÷−3+4∙− 1 4 −20÷5 7. 19−24÷3+4 4. 8 1 3 +3 2 3 ÷4 −−16 8.21−7∙4+25

Practice 1. −28 ÷7+35÷2 1 3 5. 3∙2[4+ 9÷3 ] 2. 1 4 20+72 ÷−9 6. 1 2 (−16−4) 3. −9 ÷−3+4∙− 1 4 −20÷5 7. 19−24÷3+4 4. 8 1 3 +3 2 3 ÷4 −−16 8.21−7∙4+25 11 42 -10 3 15 -2 18 19

Exit Ticket 3-7. Consider the expression 7 + 3 · 4 + 2.   What movements does this represent for Cecil walking on his tightrope?  Draw a diagram to show his movements and the length of his walk.    How many different answers can you get by grouping differently?  Add parentheses to the expression  7 + 3 · 4 + 2 to create new expressions with as many different values as possible. 

Exit Ticket 3-7. Consider the expression 7 + 3 · 4 + 2.   What movements does this represent for Cecil walking on his tightrope?  Draw a diagram to show his movements and the length of his walk.    How many different answers can you get by grouping differently?  Add parentheses to the expression  7 + 3 · 4 + 2 to create new expressions with as many different values as possible.  See diagram below.  21   7 + 3(4 + 2) = 25,  (7 + 3)4 + 2 = 42, (7 + 3)(4 + 2) = 60