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Understanding the Properties SD Counts

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Ground Rules Honor private think time Be prepared for sessions, everyone should have something to contribute Listen carefully to take in another participant’s ideas Cell phones off or on vibrate Start and end each session on time Take care of your needs

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Problem-solving Activity Pattern Block Equations First do this individually Then share with a partner Large group sharing

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Understanding the Properties of Arithmetic In order to understand relational thinking and how students are thinking about and using number relationships, it is necessary for students to have a good understanding of the basic properties of number operations.

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Article job descriptions Choose a card at your table. This will be your assigned task. Good way to have a different person do different work 1 recorder 2 reporter 3 time keeper and material person

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Take out the article “Understanding the Properties of Arithmetic” With your group of three, reflect on the parts that you highlighted as you read. This should be information that either you didn’t know or information that reinforced what you did know At the end of the 20 minutes discuss key ideas with the large group

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Create a poster of the property that you were given Each poster will have Kid friendly definition Visual model Number statement Variable statement Use the article to help you complete your poster Your group will have 35 minutes to complete Gallery Walk to see the different representations NEED TO GET GRAPHIC ORGANIZER

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Please Remember It is not necessarily important that the students know the property names, but more important that they understand each one of them.

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Properties Matching Game In your group of three take turns matching the number sentences to the properties. Great way to individually access as you are walking around. You can see instantly which properties the students are struggling with 10 minutes

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View DVD 2.9 Distributive Property 8 x 6 = (6 x 6) + (2 x 6) We will stop after the child solves the first two problems. What problem might you pose next to this child? What benefits were there to using such large numbers in these problems? 15 minutes

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Let’s talk about the order of operations Mathematical Convention This is information that you just TELL your students, as they will never explore and discover this process Please (parenthesis) excuse (exponent) my (multiplication OR division from left to right) Dear Aunt Sally (add or subtract from left to right) Good idea to write in your math journal

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Do this activity individually at your table 1 + 20 x (6 + 2) / 2 = 1 + 20 x 8 / 2 = 1 + 160 / 2 = 1 + 80 = What was the common answer 5 minutes

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Order of Operations Square Puzzle With your group of three solve this puzzle Again, another assessment you can use to see what they understand after you have worked with order of operations 10 minutes

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Accountability Piece Read “Motivating Activities That Lead to Algebra” -be prepared to share activity with the rest of the group *Group 1 The Constant Sum Grid *Group 2 Fibonacci Sequence *Group 3 Predict Your Age *Group 4 Target 21 -prepare and teach games to rest of class

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Stop If time is short stop here and have them read the article for the accountability piece.

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Early Algebra Participants will explore introducing children to algebraic notation and procedures for enriching student understanding of important mathematical ideas

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Big Ideas of Early Algebra Concepts Take out the handout “Big Ideas of Algebra Concepts” Will read and discuss

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Early Algebra In Grades K-3, the following concepts of Algebra must be covered and covered well Equality Relational thinking Basic number properties

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Caged Mice Work with your table Choose a different job Identify all of the combination of mice in a cage that you would find Be ready to prove to me how you know you have found all of the combinations Be ready to discuss the different ways to record your answers

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The Caged Mice Problem Ricky has 7 pet mice. He keeps them in two cages. One cage is red and the other is blue. Show all the ways that 7 mice can be in two cages.

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What are you looking for when students do this problem? Do they have an organized way to make sure they have all of the combinations? Does anyone know the number of combinations there would be for “n” mice and how do you know? What would the number sentence look like for this combination? www.pasd.wednet.edu-good website to find early algebra problems in context www.pasd.wednet.edu-good

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Early Algebra Number Sentences Solve the problems using ONLY your understanding of equality, relational thinking, basic number properties and mathematician’s rules. NO FORMAL ALGEBRA Solve the way your 2 nd -5 th grade students would solve

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Number Sentence What can we put in for s and t so that this number sentence is true? S + t = 8 Read page 70-71 Teachers must work with a lot of sentences helping students understand letters as variables

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Number Sentence What if I have 2 letters that are the same? S + S = 10 Read page 72 Mathematicians Rule-If variables are the same the number’s used are the same.

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Solving Equations Once students have learned the rule for dealing with number sentences with repeated variables, they can attempt to solve number sentences that challenge their mathematical thinking. d + d – 5 = 13 Read Page 73 The goal is giving students these types of number sentences is not to teach student efficient ways to solve algebra equations; it is to engage them in thinking flexibly about number operations and relations Watch video clip 4.1

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Watch video clip 4.2 K + K + 13 = k + 20

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Watch video clip 4.3 E + e + e = e + 24

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Watch video clip 4.4 4 x 48 = p + p

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Accountability Piece Work with properties in your classroom-student example Play Operations Game in classroom Operations Square Game Article-”Algebraic Problem Solving in the Primary Grades”

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