Please Excuse My Dear Aunt Sally

Transcription

1 Instructional strategies - math Math Hierarchy - Order of Operations PEMDAS P E M/D A/S Parenthesis first Exponents, square roots Multiplication and Division (left to right) Addition and Subtraction (left to right) Please Excuse My Dear Aunt Sally 1. Do what is within the parenthesis first 5 x (3 + 2) = 5 x 5 = Solve exponents, square roots 5 x 3 2 = 5 x (3 x 3) = 5 x 9 = Multiply and divide left to right before addition and subtraction x 2 = = Solve left to right 45 5 x 2 = 9 x 2 = 18 Examples: x 3 = = 14 multiplication before addition (3 + 3) x 5 = 9 x 5 = 45 parenthesis first = 7 4 = 3 work left to right 12 (5 4) = 12 1 = 11 parenthesis changes the answer = = 5 division comes before addition 12 (4 + 2) = 12 6 = 2 parenthesis first 2 3 x 3 = (2 x 2 x 2) x 3 = 24 exponents first 2 x 3 3 = 2 x (3 x 3 x 3) = 54 exponents first 2 (3 x 3) = 2 9 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 512 parenthesis first 12 3 x 2 = 4 x 2 = 12 work left to right = 4 2 = 2 work left to right = 18 9 = 2 exponent first (18 3) 2 = 6 2 = 36 parenthesis before exponents 12-(6-(4-2)) = 12 - (6-2) = 12-4 = 8 Parentheses can be nested - pairs of matching parentheses can be contained within other pairs of parentheses.

2 For instructional purposes, teach: 1 st - left to right for addition and subtraction 2 nd - multiplication and division left to right 3 rd combine all four operations using ( ) to designate either multiplication or division before addition and subtraction. This reinforces the concept of parenthesis first. 4 th add exponents and square roots once taught Instructional strategies: GEMS 1. GEMS for younger children use Grouping instead of parenthesis to emphasis what they are to do within the brackets. G grouping, E exponent, M multiply or divide, S subtract or add 2. Color coding and vertical solving Use different colors to denote operations and use arrow to indicate product of the operation. Complete each step under the preceding to show order of operation 3. Bingo Instead of calling numbers to play Bingo, call (and write) expressions to be evaluated for the numbers on the Bingo cards. 5 2 (2-1) 4. Dominoes Draw attention to doing operation within parenthesis by using dominoes to visualize numbers within parenthesis. State what the operation is within the parenthesis. 2 x = 24 2 x (8 + 4) = 24 x 2 = 12 (3 + 3) x 2 = True or false? Practice impact of parenthesis by giving a set of numbers with different answers. Ask students to insert parentheses to make each answer true. 4 x = 27 answer (4x6) +3 = 27 4 x = 36 answer 4 x (6 + 3) = 36 Connection to Common Core Grade 1 & 2- Add and subtract within 20 Work with addition and subtraction equations. Determine if equations involving addition and subtraction are true or false. Grade 3 - Multiply and divide within 100 Grade 5 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

3 Visualize Parenthesis Look at these number sentences. Draw ( and ) around the groups. Then write the equation = (apples) + (bananas) = fruit ( ) + ( ) = = 10 ************************************************************************************************* = ( 4 green circles + 1 blue circle) + ( 3 red squares + 2 purple squares) = colored shapes 2. ( + ) + ( + ) = shapes ************************************************************************************************** 3. ( + ) + ( + ) = 3 dimensional shapes

4 Now, draw your own number picture ( lions + bears) + ( cows + chickens) = animals zoo animals farm animals 6. ( cars + trucks) + ( airplanes + drones) = vehicles road vehicles air vehicles ( pencils + pens) + ( spoons + forks) = utensils writing utensils eating utensils 7. ( beds + dressers) + ( chairs + table) = furniture bedroom furniture dining room furniture 8. (create your own) ( + ) + ( + ) = food

5 Word Problems with Order of Operations Choose the correct equation for each word problem. Circle the answer. Example: You clean up the yard for 3 hours. You get paid $4 an hour. You get a tip of $2. How much did you earn? = 9 (3 x 4) x 2 = 12 x 2 = 24 (3 x 4) + 2 = = 14 1 st write the numbers 3 4 2, then add the operations 3 x 4 + 2, then add the parenthesis (3x4)+2 = You and 2 of your friends go to the movie. You each buy a ticket for $7 and a box of candy for $2. How much did it cost all together? 3 x (7 + 2) = $30 (3 + 7) x 2 = $20 (3 x 7) + 2 = $23 2. Sara and Mona like to walk. They walked 1 mile on Tuesday and 3 miles on Wednesday. How many miles did the walk together? = 6 (2 + 1) x 3 = 9 2 x (1 + 3 ) = 8 3. Omar and Scott and Donald went fishing. Each caught 5 fish and 2 crabs. What was their total catch? (3 + 5) + 2 = 10 3 x ( 5 + 2) = 21 (3 x 5) x 2 = The class went to the zoo on a field trip. The 6 boys each saw 3 lions and 2 tigers. The 4 girls each saw 2 seals and 3 penguins. What was the total number of animals seen that day? 6 x (3 + 2) + 4 x (2 + 3) = 50 (6 + 3) (4 + 2) + 3 = (3 x 2) (2 x 3) = There are 30 days in this month. Bob will spend 20 days at work and 6 days studying. How many days will he have for free time and fun? 30 ( 20 6) = ( ) = (20 6) = The weather was bad this month. Out of 30 days, it rained 14 and snowed 8. How many days were sunny? 30 ( ) = 8 (30 14) + 8 = 24 ( ) 8 = You decided to eat more fruit. On Monday you ate 2 bananas and 3 pears. On Tuesday you ate an apple and abowl of 23 cherries. On Wednesday, you ate 3 oranges and a cantalope. How many pieces of fruit did you eat all together. Write the equation. ( + ) + ( + ) + ( + ) = How many more pieces of fruit did you eat on Monday and Tuesday than on Wednsday?( + ) - = How many more pieces on Tuesday than Monday and Wednesday together? - ( + ) =