Math for El Ed Exam #2 Flashcards
Define and give a number sentence to illustrate each of the following properties: Commutative property of addition, commutative property of multiplication, associative property of addition, associative property of multiplication
Commutative property of addition: Changing the order of the addenda does not affect the sum (6+4=10 = 4+6=10)
Commutative property of multiplication: Changing the order of factors does not affect the product (4x6=24 = 6x4=24)
Associative property of addition: When adding 3 or more numbers, the number that the equation starts with does not matter ((2+3)+1=6 = (3+1)+2=6))
Associative property of multiplication: When multiplying 3 or more numbers the number that the problem starts with does not matter ((2x3)x4=24 = 2x(3x4))
Identify elements of addition/ multiplication/ subtraction/ division distributive property of multiplication over addition
Distributive property of multiplication over addition because multiplication is simply repeated addition number sentences can occur
The text identifies 4 prerequisites for children engaging in formal work with operations. What are these prerequisites and how could you develop each one with your students?
- Facility with counting
- Experience with a variety of concrete situations
- Familiarity with many problem-solving contexts
- Experience using language to communicate mathematical ideas
Discuss the general sequence of activities that help children develop meaning for the 4 basic operations. Be able to define and give examples of concrete, semi concrete, and abstract representations.
concrete- modeling with material (representation with manipulatives)
Semiconcrete- representing with pictures (drawings, diagrams)
Abstract- representing with symbols (numeric expression, number sentences to illustrate the operation)
Define each of the 4 basic operations
Addition: Finding how many in all
Subtraction: Finding how many are left
Multiplication: Repeated addition, inverse of division
Division: Repeated subtraction, inverse of multiplication
Recognize different forms of joining and separating problems. Give examples of how you would support students in developing meaningful conceptual understanding of these forms of problems
Joining problems are addition and multiplication problems that push students to find out how much they have in all.
Separating problems are subtraction and division problems that push students to find out how much is left.
Describe different structures of multiplication problems. Recognize and give an example of each of the following:
-Equal-group or sharing problems
-Comparison problems
-Combination or Cartesian product problems
-Area and array problems
Equal-groups problems: When both of the amounts that are being used are known but the overall total is unknown (Noah and Pete each have $12 in their wallets, how much do they have in total? (12x2))
Comparison problems: Involve 2 different sets that are being compared (Ruben spent $20 on groceries but Judy spent 3 times as much. How much did Judy spend?)
Combination problems: Two factors are being represented in 2 sizes of 2 different sets. (What are all the possible combinations of children’s genders parents can have if they have a total of 3 kids?)
Area and array problems: Finding the area of shapes (The classroom is set up in rows of 3 and there are 5 columns how many desks are there?)
Distinguish between division as measurement and division as partitioning. Give examples and illustrate each type.
Division as a measurement shows how many objects are in a group whereas division is used to evenly distribute objects.
Describe and apply thinking strategies that you would use with children in learning the basic facts of addition, subtraction, multiplication and division. Be able to recognize common strategies and give examples of strategies you would use with children.
Basic addition: Involves two one-digit addenda and their sum
-Encourage students to look for patterns and identify them
-Use a variety of combinations
Describe current curricular recommendations regarding the teaching of computation. What is your personal position on computational instruction? What are implications of your position for classroom instruction? Discuss Mental computation , written computation, computational estimation, computation with calculators
I think that computational thinking is a great way to teach content because it pushes students to think more critically and abstractly. When an educator is using computational instruction it focuses on having students think about what they would do before solid understanding through asking the students questions.
Describe how you would build a bridge between conceptual understanding and algorithmic proficiency when teaching a new algorithm? Be able to describe appropriate methods and materials to use in this process
For any standard algorithm start with manipulatives and give students the opportunity to explore and learn the concept using these manipulatives. Students must have knowledge on the 4 basic operations.
Describe the important relationships children should recognize between the various operations (their concepts and algorithms). How can these relationships be developed?
It is important for students to recognize the operations that they are using for full conceptual understanding. An example would be base ten blocks and explaining to students how each place value holds a different value then model how to use the base ten blocks to visualize more clearly.
Describe appropriate uses of alternative algorithms. Be able to illustrate your discussion with specific examples of alternative algorithms.
Low stress column addition. Alternative algorithms help students who easily feel overwhelmed with standard algorithms and need a better visual representation of how to organize their mathematical thinking.
Diagnose algorithmic difficulties that children may encounter in performing whole number operations and recommend appropriate intervention.
Difficulties: Keeping the problem organized
Regrouping:confusion of place value; incorrect distribution
Solutions: partial products; lattice; using graph paper
Describe each of the following forms of estimation and given an example of how each one might be used in mathematics instruction.
-Adjusting and compensating
-Flexible rounding
-Front-end estimation
-Compatible number
-Clustering
Front-end-estimation: Involves checking the leading or front-end digit of the number, placing the value of that digit (uses the most important digits)
Clustering (averaging): 1. Estimate the average value 2. Multiply by that number
Flexible rounding: rounding to get numbers that are easier to work with
