Download presentation
Presentation is loading. Please wait.
Published byErica Bryan Modified over 8 years ago
1
Rectangles as Problem- Solving Tools Use Area Models to Teach Math Concepts at All Levels www.elevatingadulteducation.com1
2
Introductions Amy Vickers www.elevatingadulteducation.com amyjvickers@gmail.com In what areas do you teach? Are you familiar with area models? www.elevatingadulteducation.com2
3
Objectives Participants will be able to… Gain an understanding of the value of area models Build area models and discuss their components Use area models to teach relevant mathematical concepts Today we will…. Become familiar with area models and how they work. Consider area models as tools for teaching conceptual understanding. Use area models as tools for exploring various topics. www.elevatingadulteducation.com3
4
Why this topic? COABE 2013 ANN pre-conference Math 140 Rigor www.elevatingadulteducation.com4
5
Levels of Knowing Math Mahesh Sharma www.elevatingadulteducation.com5 Communication Application Abstract Pictorial Concrete Intuitive
6
Numeracy vocabulary gives learners the tools to make math their own www.elevatingadulteducation.com6
7
How many eggs? www.elevatingadulteducation.com7
8
How many eggs? How did you know? www.elevatingadulteducation.com8
9
How many muffins are in this pan? www.elevatingadulteducation.com9
10
How many muffins? How did you know? www.elevatingadulteducation.com10
11
Rectangular arrays www.elevatingadulteducation.com11
12
How many rectangular arrays do you see in this photo? Envision Plans to Install 2,300 Rotating Solar Tree Car Shelters in South Carolina www.elevatingadulteducation.com12
13
What is a rectangular array? How can we use them for teaching math? www.elevatingadulteducation.com13
14
Directions Clear a work space at your table. You will need one bag of tiles, a sheet of paper, and a writing utensil. Count your tiles. Let me know if you do not have 25 tiles. Arrange the tiles in a rectangular array to demonstrate 8 x 3 = 24. Look around the table and help others as needed. www.elevatingadulteducation.com14
15
Discuss at your table: Describe your array. Do you see an array that is different than yours? How is it different? What equations can you write to describe the array that use multiplication? What equations can you write to describe the array that use division? What is the relationship between multiplication and division? What shape is your array? What are the properties of that shape? www.elevatingadulteducation.com15
16
What are the factors of 12? Show us that they are factors by using rectangular arrays. www.elevatingadulteducation.com16
17
Discuss at your table: What is a factor? How would you explain a factor in the context of rectangular arrays? What are the factors of 12? What are a few examples of numbers that are not factors of 12? How would this look in a rectangular array? What equations can you write to describe the arrays that use multiplication? What equations can you write to describe the arrays that use division? What is the relationship between multiplication and division? For what other math topics is an understanding of factors essential? www.elevatingadulteducation.com17
18
A measured area model is a type of rectangular array www.elevatingadulteducation.com18
19
Practice with area models Put the tiles back in the bag and take out a piece of graph paper. On a piece of graph paper, use an area model to multiply 9 x 4. Write 2 multiplication and 2 division equations to describe the model. On a piece of graph paper, use an area model to multiply 14 x 25. Now multiply 135 x 29. Try 14 x 25 using an abstract area model. www.elevatingadulteducation.com19
20
Got it? Or should we do more examples? www.elevatingadulteducation.com20
21
What is an abstract area model? When is it useful? www.elevatingadulteducation.com21
22
As you share this with learners, do not skip steps in conceptual understanding! Rectangular array Measured area model Abstract area model www.elevatingadulteducation.com22
23
Levels of Knowing Math Mahesh Sharma www.elevatingadulteducation.com23 Communication Application Abstract Pictorial Concrete Intuitive
24
Activities with area models will give opportunities for … Thinking about math Reasoning through problems using mathematical thinking Hearing math vocabulary Using math vocabulary Explaining the process Examining various solutions Asking and answering clarifying questions Asking and answering follow-up questions www.elevatingadulteducation.com24
25
The purpose of using area models… Is to add a layer of conceptual understanding to the learner’s experience… Not to replace all computation methods. www.elevatingadulteducation.com25
26
What does this have to do with math anxiety? Math has structure. Math fits with what I understand. Math is predictable. I can trust it. I don’t always need to memorize steps. Important ideas work at all levels. www.elevatingadulteducation.com26
27
CCRS Connections Level B: Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. Level B: Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning. Level C: Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Level C: Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. www.elevatingadulteducation.com27
28
Using area models in various settings How can this work for me? www.elevatingadulteducation.com28
29
Multiplying Fractions Multiply 2/3 by 3/5. www.elevatingadulteducation.com29
30
Multiplying Fractions Multiply 1/4 by 4/5. www.elevatingadulteducation.com30
31
Division Divide 529 by 7. Write an equation that shows how to check your answer. www.elevatingadulteducation.com31
32
Division Divide 816 by 5. Write an equation that shows how to check your answer. www.elevatingadulteducation.com32
33
Examining properties Evaluate 4(3 + 2) by using an area model. What property does this illustrate? www.elevatingadulteducation.com33
34
Examining properties Evaluate x(y + 4) by using an area model. What property does this illustrate? www.elevatingadulteducation.com34
35
Examining properties Use an area model to illustrate the commutative property of multiplication. www.elevatingadulteducation.com35
36
Multiplying polynomials Find the product of (x+3) and (x-5). www.elevatingadulteducation.com36
37
www.elevatingadulteducation.com37
38
www.elevatingadulteducation.com38
39
Objectives Participants will be able to… Gain an understanding of the value of area models Build area models and discuss their components Use area models to teach relevant mathematical concepts To take with you… Set of 25 tiles Sample facilitation questions to use with tiles www.elevatingadulteducation.com39
40
Thank you! www.elevatingadulteducation.com40
Similar presentations
© 2024 SlidePlayer.com. Inc.
All rights reserved.