Unit : Area Model Factoring
Area Model Factoring;presents factoring as one kind of unmultiplying, using the ideas of Unit 4: Area and Multiplication, which introduced the area model as a tool for organizing multiplication of numbers and polynomials. In this unit, students first divide with area models, working with a given area and one dimension or length of the area model rectangle to find the other length . Students connect the models to multiplication and division equations that express the same relationship and explore area model puzzles which provide enough information about the factors and product to find the missing terms. This supports students in understanding the roles of and relationships between the pieces of the area model and their corresponding equations and in thinking flexibly with the model in preparation for factoring. The factoring problems in this unit focus primarily on expressing trinomial products as two binomial factors. Students use tables to organize possible sums for pairs of numbers with a given product and build logic about the zero product property and its role in solving equations by factoring.
Unit : Language Of Algebra
Language of Algebra presents algebra as a language for expressing patterns and relationships. Starting with a pictorial notation for the results of number tricks, students build intuition about algebraic solving processes. They develop algebraic language to describe these tricks as they move from pictures, to words, and finally to algebraic notation in order to track the transformations of an unknown starting number. Students also use the logic of mobile puzzles to learn about equivalence and to visualize the common sense behind algebraic solving steps.
Transition To Algebra Curriculum
Transition to Algebra is an initiative of the Learning and Teaching Division at Education Development Center, Inc. . Supported by;the;National Science Foundation, TTA seeks to quickly give students the mathematical knowledge, skills, and confidence to succeed in a standard firstyear algebra class and to show;them that they can explore mathematics and actually enjoy it.
TTA is a fullyear algebra support curriculum, published by;Heinemann;and distributed by their parent company Houghton Mifflin Harcourt,;designed to:
 run concurrently with firstyear algebra ; and
 raise the competence and confidence of students who may benefit from supports for algebra success.
Please visit the;transitiontoalgebra.com;for sample materials and purchasing options.
TTA is designed to build students’ algebraic habits of mind, key mathematical ways of thinking aligned with the Common Core Standards for Mathematical Practice. Students explore algebraic logic puzzles that connect to and extend algebra course topics and learn broadlyapplicable tools and strategies to help them make sense of what they are learning in;algebra. Students discuss and refine their ideas as they work through mental mathematics activities, written puzzles, spoken dialogues, and handson explorations that engage them in cultivating mathematical knowledge, intuition, and skills.
You May Like: Math Caching Algebra 1 Answers
Unit : Points Slopes And Lines
Points, Slopes, and Lines;aims to help students understand that graphs and equations help to visualize and describe a collection of points. Building on the ideas from Unit 6: Geography of the Coordinate Plane, students think about two relationships between any two points: distance and slope. They will compare points by describing the horizontal and vertical distances between them and will use these measurements to find the length of the straightline path between any two points. They will also use the ratio of vertical to horizontal distance to quantify the slope of that straightline path. They will use slope to determine collinearity, test whether points are on a line, generate new points along a line, and create an equation to describe the location of all points on a line.
Unit 1: Algebraic Habits Of Mind
Algebraic Habits of Mind;reviews, consolidates, and extends several of the overarching themes of the year: building equations and expressions, distance and area modeling, and solving problems carefully with logic, persistence, and strategy. Lesson 1 reviews the use of variables and expressions as well as the kinds of manipulations that preserve balance. Lesson 2 revisits the use of the number line as a tool for reasoning about location, order, and basic operations. Lesson 3 reviews the area model and its use for multiplying, dividing, and factoring polynomial expressions. Lesson 4 distinguishes two types of measurement on the plane: distance and slope. Lesson 5 reviews the concept of solving and what a solution looks like in various contexts.
The contents of this website are the results of work supported by the National Science Foundation under Grants No. 0917958 and 1621011. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation. The text, images, and resources on this website, unless marked otherwise, are developed at EDC . EDC owns the copyright © 20112019.
Read Also: Abiotic Definition Science
Unit : Geography Of The Coordinate Plane
Geography of the Coordinate Plane;builds familiarity and facility with the conventions of the coordinate plane, graphs, and equation graphing. Students explore coordinated data to understand how a single point can represent more than one piece of information. This understanding is furthered when students use transformations to affect a shapes xcoordinates, ycoordinates, or both. By the end of the unit, students graph equations using the idea that every point on a graph represents a particular x and y pair whose values are related by the equation. As students use equations to test arbitrary points to see whether they are on the graph of an equation , they come to understand graphs as a collection of solution points, which will support future work in Unit 9: Points, Slopes, and Lines.
Unit : Logic Of Algebra
Logic of Algebra builds facility with manipulating expressions and equations thoughtfully, logically, and accurately. Students use the commonsense logic they have developed in the Think of a Number tricks and mobile puzzles to make sense of the rules for solving equations. Solving for unknown weights in puzzles about balance builds the same logic as is required in solving equations and systems of equations: seeking every unknown value by performing only operations that preserve balance and substituting equivalent values or shapes as needed.;;
Read Also: Road Trip Project Answer Key
Algebraic Habits Of Mind
One important purpose of learning mathematics is to develop useful, analytic, quantitative, logical ways of looking at the world and thinking about things. When mathematical ways of thinking begin to become automaticnot just ways one can use, but ways one is likely to useit is reasonable to call them habits: mathematical habits of mind.
The Standards for Mathematical Practice listed in the Common Core State Standards are one way of organizing and presenting a subset of mathematical habits of mind that are essential for mathematical proficiency. Transition to Algebra focuses on algebraic aspects of five of these: puzzling and persevering, seeking and using structure, using tools strategically, describing repeated reasoning, and communicating with precision. Transition to Algebra is designed to develop these algebraic habits by fostering and building on the commonsense logic that students bring.
Unit : Thinking Things Through Thoroughly
Thinking Things Through Thoroughly is designed to stimulate mathematical thinking and to offer more practice solving problems, skills that take time and experience to develop. Problem solving requires a kind of thinking that cannot quite be captured in steps. Students must look for what is familiar and unfamiliar in the problem, look for entry points, poke around a bit, pay attention to hunches and intuitions, and assess whether their trials and experiments move them closer to an insight or a solution. Unit 7 invites students to consider what they can determine from a context and what possibilities there are before focusing on the answer requested. Students use tables and diagrams to organize information, and learn to repeat and generalize calculations to produce algebraic equations to describe problem contexts.
Recommended Reading: Algebra Age Word Problems
Teaching Guide Area And Multiplication Transition To Algebra Unit 4 Teaching Guide Unit
 Views:
Transcription
1 4 Unit TEACHING GUIDE Area and Multiplication Transition To Algebra Unit 4 Teaching Guide June Mark E. Paul Goldenberg Mary Fries Jane M. Kang Tracy Cordner Unit Area and Multiplication 4 HEINEMANN Portsmouth, NH Researchbased National Science Foundationfunded Learning transforms lives.
3 Unit 4 Area and Multiplication CONTENTS T4 Unit Introduction T7 Lesson 1: MysteryGrid Puzzles T11 Lesson 2: Multiplication Patterns T15 Lesson 3: Measuring Area T20 Lesson 4: Area Models T22 Student Reflections & Snapshot Checkin T23 Lesson 5: Area Models with Algebra T26 Lesson 6: Signs and Terms T28 Lesson 7: Squares and Like Terms T30 Lesson 8: Equivalent Expressions T32 Student Reflections & Unit Assessment T33 Exploration: Trains T35 Exploration: Building Squares T38 Game: Greatest Product Challenge RESOURCES T39 Latin Square Puzzles T40 MysteryGrid Puzzles T41 Multiplication Table T42 Areas to Calculate T43 Matching Cards Cutouts T44 Snapshot Checkin T45 Snapshot Checkin Answer Key T46 Unit Assessment T48 Unit Assessment Answer Key T50 MENTAL MATHEMATICS Base 10 structure: place value T51 Multiplying by 10 and 100 T52 Dividing by 10 and 100 T53 Dividing 2digit numbers by 10 T54 Dividing by 10 repeatedly T55 Multiplying decimal numbers by 10 T56 Multiplication table with multiples of 10 T58 How many zeros? T60 Multiplying by 2 and 3 with area model thinking T61 Squaring T62 Squaring multiples of 10 T63 Square roots
Geo1 Constructions And Rigid Transformations
In this unit, students first informally explore;geometric properties using straightedge and compass constructions. This allows them to build conjectures and observations before formally defining rotations, reflections, and translations. In middle school, students studied;transformations of figures in the coordinate plane. In this unit, they transition to more formal definitions;that don’t rely on the coordinate plane, and the focus shifts from transforming whole figures towards a more pointbypoint analysis. Students then begin to use the rigorous definitions they developed to prove statements involving angles and distances, preparing them for congruence proofs in the next unit.
A blank reference chart is provided for students, and a completed reference chart for teachers.;The purpose of the reference chart is to be a resource for students to reference as they make formal arguments. Students will continue adding to it throughout the course. Refer to About These Materials;in the Geometry course for more information.
Don’t Miss: Who Are Paris Jackson’s Biological Parents
Unit : Area And Multiplication
Area and Multiplication;builds a commonsense foundation for multiplying algebraic expressions by examining multiplication in the context of area. Students use area models to multiply integers and numerical expressions in order to support understanding the logic of the distributive property. They then extend their understanding of this model to multiplying algebraic expressions and identifying equivalent expressions. Students will revisit area models extensively in Unit 10: Area Model Factoring.
Seeking And Using Structure:
Mathematically proficient students look closely to discern a pattern or structure… They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects…
Students in beginning algebra are often taught to solve equations like 2 + 4 = 24 by going through a particular set of steps written in a particular way. On successive lines, they write the original equation, 4 below each side, a new equation, ÷2 below each side, a new equation, and so on. That method works for all firstyear algebra cases and helps students see the steps. But it doesnt encourage students to see beyond the trees and perceive the overall structure. Both are necessary. Seeing the structure helps students see the logic of algebra; it often also makes calculation much easier.
Consider the example to the right. Proceeding in the conventional way is much, much harder than seeing the equation as 11 minus something is 6 and concluding that the something equals 5. We can read that as fifty divided by something is 5. So, that something ;is 10. That leaves 3x 2 = 10, which is easier to solve.
Don’t Miss: Eoc Fsa Warm Ups Algebra 1 Answers
Unit : Geography Of The Number Line
Geography of the Number Line presents the number line as a tool for reasoning about integers and the relationships between integers, including order and distance. The number line is also used as a tool for making sense of the operations of addition and subtraction, first with numbers and then generalized to variables.
Unit : Logic Of Fractions
Logic of Fractions;builds on tools and strategies developed in earlier units, focusing on basic operations with rational numbers and rational expressions. Number lines and area models are used to help students make sense of additive and multiplicative operations with fractions. Mobile puzzles are used to build students intuition about proportional reasoning. In the last lesson, students see how graphs can be used to depict proportional relationships. Throughout the unit, students make connections between numerical quantities and algebraic expressions in ways that extend their understanding of the logic of fractions.
You May Like: How Did Geography Discourage Greek Unity
Unit 5 Logic Of Algebra
 Page 50 and 51: Additional Practice ProblemsSelect
 Page 52 and 53:
Lesson 8: Solving with SystemsWhy T
 Page 54 and 55:

Review for Unit AssessmentTeacher N
 Page 60 and 61:
Solve these equations. Show your pr
 Page 62 and 63:
Mental Mathematics Activity 1: Who
 Page 64 and 65:
Mental Mathematics Activity 1: Who
 Page 66 and 67:
Mental Mathematics Activity 1: Who
 Page 68 and 69:
Mental Mathematics Activity 1: Who
 Page 70 and 71:
Mental Mathematics Activity 1: Who
 Page 72 and 73:
Mental Mathematics Activity 7: Sile
 Page 74 and 75:
Four Corners Mobile61416NUnit 5: Lo
 Page 76 and 77:
Four Corners – Corner OptionsStep 1
 Page 78 and 79:
Lena & Jays ThinkofaNumber Ta
 Page 80 and 81: