Mathematics – Algebra 1
Unit 0: Calculator
First Grading Period - Weeks 1- 2 (6 days) CURRICULUM OVERVIEW
Big Idea / Unit RationaleA graphing calculator is a tool to be used not only for calculating but also for exploring and learning mathematics.
Algebra newcomers will be lead through the graphing calculator basics during their first few days of high school math after reviewing the key aspects of Descartes’ coordinate plane. / The student should understand:
· the importance of locating, translating and naming points on a coordinate plane using ordered pairs of rational numbers.
· the importance of using the graphing calculator as both a calculating and a learning tool.
TEKS / TEKS Specificity - Intended Outcome
Concepts / 8.6 Geometry and spatial reasoning. The student uses transformational geometry to develop spatial sense.
8.6(B) graph dilations, reflections, and translations on a coordinate plane.
8.7 Geometry and spatial reasoning. The student uses geometry to model and describe the physical world. The student is expected to:
8.7(D) locate and name points on a coordinate plane using ordered pairs of rational numbers.
(a.5)Tools for algebraic thinking. Techniques for working with functions and equations are essential in understanding underlying relationships. Students use a variety of representations (concrete, pictorial, numerical, symbolic, graphical, and verbal), tools, and technology (including, but not limited to, calculators with graphing capabilities, data collection devices, and computers) to model mathematical situations to solve meaningful problems.
(a.6) Underlying mathematical processes.
Makes connections; uses multiple representations, technology, applications and modeling, and numerical fluency in problem-solving contexts. / ” I CAN” statements highlighted in yellow and italicized should be displayed for students.
I can:
· locate and name ordered pairs on a coordinate plane. (8.7D)
· translate points on a coordinate plane. (8.6B)
· use a graphing calculator to model mathematical situations to solve meaningful problems. (a5)
· use a calculator to improve numerical fluency in problem solving situations(a.6)
Evidence of Learning
1. Given a set of coordinate points the student will be able to graph them at least 80% of the time.
2. Given a set of order of operations problems, using the graphing calculator, the student will be able to solve the problems at least 80% of the time.
Mathematics – Algebra 1
Unit 0: Calculator
First Grading Period - Weeks 1- 2 (6 days) CURRICULUM GUIDE
Essential Questions / Essential Pre-requisite Skills· What is the significance in the sign of the coordinate (ordered pair) in
· plotting a point?
· How do the quadrants relate to the ordered pairs?
· How does a graphing calculator help you solve complex problems? / Students should know how to:
· locate and name points on a coordinate plane using ordered pairs of integers (7.7A)
· graph dilations, reflections, and translations on a coordinate plane (8.6B)
· simplify numerical expressions involving order of operations and exponents (7.2E)
The Teaching and Learning Plan
Instructional Model & Teacher Directions
The teacher will… / So students can …
Ice Breaker Activity (1 day)
· Establish a student centered culture by engaging students in one of the nine icebreaker activities.
· Discover interesting things about their students.
· Incorporate student expectations, social skills, classroom rules and procedures at this time.
Engage:
· Chose one of the 9 activities to get to know the students. The activity chosen will allow students to learn something interesting about their classmates. Elicit responses to discover whether students already know each other.
Explore:
· Read the rules for the activity and pass out materials to play the game
· Establish expected social skills, classroom rules and procedures.
Explain:
· Lead the class presentation of what they have learned about another classmate.
Elaborate:
· Ask for volunteers to see who can name everyone in class.
Evaluate:
· Restate interesting information about others.
· Restate social skills, classroom rules, and procedures / · develop a positive learning environment
· learn something new about each student
· interact in cooperative learning
· develop a clear understanding of social skills, classroom rules and procedures.
Engage:
· participate in an activity where they will learn something new about their classmates.
Explore:
· listen to the rules in order to play the game and then begin the activity.
· demonstrate social skills, classroom rules and procedures
Explain:
· share information about their classmates.
Elaborate:
· name everyone in class.
Evaluate:
· provide definitive answers.
Coordinate Plane Activity “Buried Treasure” (1 day)
Engage:
· Conduct a brief discussion about pirates.
· Show a small clip of the Pirates of the Caribbean, or bring in pictures of pirates and talk about buried treasure.
· Pair up students, using the Think-Pair-Share Strategy, to discuss their knowledge of pirates. (5 min)
Explore:
· Pass out worksheets, introduce, facilitate and monitor student work in the “Buried Treasure” activity.
Explain/Elaborate:
· Facilitate a class discussion by asking the following questions:
What were your strategies in finding the buried treasures?
How did you use the clues to answer the questions?
What did you remember about plotting points from 8th grade?
Evaluate:
· Elicit vocabulary during the discussion.
y-axis x-axis
coordinate plane coordinate point
quadrants origin
ordered pair
· Place vocabulary words on the word wall as students recall words used in the activity. / Engage:
· work in pairs to share knowledge of pirates.
Explore:
· read the instructions to “The Buried Treasure Activity”.
· work with your partner to follow a logical sequence of events using the clues to find the buried treasure. (8.6B, 8.7D)
Explain/Elaborate:
· respond to the teachers’ questions as a class.
· share strategies in finding the buried treasure. (8.6B)
· explain how they used the clues to answer the questions.
· recall vocabulary used to plot points in 8th grade
Evaluate:
· recall vocabulary as they discover the coordinates of the missing treasure.
Calculator Skills Activity “Calculator Power Point with Activity Sheet” (4 days)
Day 1
Engage:
· Demonstrate the graphing calculator using the calculator power point presentation and work the first 3 pages of “Calculator Introduction” Activity worksheet as a class.
Explore:
· Monitor students as they work the “Arithmetic Keys” (page 4 of calculator introduction) worksheet independently and explore the functions of a calculator.
· Go over the problems as a class.
Days 2 and 3
Explain:
· Materials: a deck of cards
· Pair up students by passing out matching faces or number cards. Students who have the same face or number card will partner.
· Review the rules for “order of operation”.
· Use the “Calculator Cross-Word Puzzle” activity to monitor student understanding of calculator skills as they solve order of operation problems.
Elaborate:
· Pass out copies of “ What do you know?” to each student.
· Identify prior knowledge, incorporate calculator, work independently.
Day 4
Evaluate:
· Prepare the power point activity “Who Wants to be a Millionaire?”
· Explain the rules and inform students that the problems on the game are 8th grade TAKS problems. / Day 1
Engage:
· work the first 3 pages of the calculator worksheets simultaneously with the teacher as the teacher explains calculator keys, keystrokes and their function. (a6)
Explore:
· work “Arithmetic Keys” independently to further explore the functions of a calculator. (a6)
Days 2 and 3
Explain:
· pair up according to matching cards.
· complete the Calculator Crossword Puzzle with a partner and practice the rules for the order of operations to solve problems. (a5, a6)
Elaborate:
· demonstrate understanding of calculator, complete the “What Do You Know?” worksheets. (a6)
· work independently and ask questions as needed.
Day 4
Evaluate:
· prepare to answer questions according to the teachers’ guidelines.
· use the graphing calculator to answer 8th grade TAKS questions (a6)
Vocabulary:
· Coordinate plane
· Coordinate Point
· X-axis
· Quadrants / Order of Operations
Ordered pair
Y-axis
Origin / Resources for Instruction:
Algebra 1 Curriculum Binder
Unit 0 Calculator
Calculator Skills:
· Ice Breaker Activity (1 day)
· Blanca Oropez’s People Bingo Icebreaker
· Coordinate Plane Activity “Buried Treasure” (1 day)
· Calculator Intro. Skills. (4 days)
Activity worksheet
Calculator-power point
Cross-Word Puzzle
What do you know?
Strategies for using Millionaire game
Who wants to be a Millionaire?
Power point
Additional calculator resource
For teachers
Evidence of Learning
Differentiation / Interims/TAKS/Benchmarks / College-Readiness i.e.,
Anticipated Skills for SAT/ACT/College Board/Career/Life
What do you do for students who need additional support?
Teacher can use the:
· Coordinate Drawing Activity:
Students will connect the points in consecutive order, noting the line ends and begins to create a drawing.
· Battleship Activity:
Students will work with a partner to play Battleship. Make up coordinate points that are the length of the battleship in order to hide their battleships. Place the ships either horizontally or vertically throughout the coordinate plane. (This is done before the game begins.) Take turns guessing the location of one of the ships hoping to hit or miss a battleship. If the student hits their opponents ships they get to guess again. The game ends when one player “sinks” all of their opponents ships.
The teacher can visit:
· Grade 9 TAKS Study Guide: Mathematics
Interactive TEA website
Specific TEKS: 8.7D
What do you do for students who master the learning quickly?
Enrichment:
· Students will create their own buried treasure map. /
(from the April 2004 TAKS Test, TEKS 8.7D #52)
(from the 2003 9th grade TAKS Test, TEKS 8.7D #43) / In the xy-plane, the points with coordinates (0,-5) and (6,-2) lie on line l. Line p contains the point with coordinates (-5,0) and is perpendicular to line l. What is the x-coordinate of the point where lines l and p intersect?
/ (A) / -6
/ (B) / -5
/ (C) / -4
/ (D) / -3
/ (E) / -2
Evidence of Learning
Formative Mini Assessment / TAKS Benchmarks / College-Readiness
Anticipated Skills for SAT/ACT/College Board
Mathematics – Algebra 1
Unit I: Foundation of Functions
First Grading Period – Weeks 3 - 4 (10 days) CURRICULUM OVERVIEW
Big Idea / Unit RationaleUnderstand relations and functions and select, convert flexibly among, and use various representations for them. In addition, interpret representations of functions of two variables. NCTM / The students should understand:
· a function represents a dependence of one quantity on another and can be described in a variety of ways.
· the properties and attributes of a function.
· special kinds of relationships between two quantities.
TEKS / TEKS Specificity - Intended Outcome
Concepts / (A.1)Foundations for functions. The student understands that a function represents a dependence of one quantity on another and can be described in a variety of ways. The student is expected to:
A.1(A)describe independent and dependent quantities in functional relationships;
A.1(B)gather and record data and use data sets to determine functional relationships between quantities;
A.1(D)represent relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities; and
A.1(E)interpret and make decisions, predictions, and critical judgments from functional relationships.
(A.2)Foundations for functions. The student uses the properties and attributes of functions. The student is expected to:
A.2(B)identify mathematical domains and ranges and determine reasonable domain and range values for given situations, both continuous and discrete;
A.2(C)interpret situations in terms of given graphs or create situations that fit given graphs; and
A.2(D)collect and organize data, make and interpret scatterplots (including recognizing positive, negative, or no correlation for data approximating linear situations), and model, predict, and make decisions and critical judgments in problem situations.
(a.3) Functions concepts. A function is a fundamental mathematical concept; it expresses a special kind of relationship between two quantities. Students use functions to determine one quantity from another, to represent and model problem situations, and to analyze and interpret relationships / ” I CAN” statements highlighted in yellow and italicized should be displayed for students.
I can:
· describe independent and dependent quantities (A.1A)
· gather and record data (A.1B)
· illustrate various representations of functions using the 4 corner method (A.1D)
· make decisions, predictions and critical judgments from functional relationships
(A.1E)
· identify the properties and attributes of domain and range (A.2B)
· interpret situations in terms of given graphs(A.2C)
· collect and organize data, make and interpret scatter plots and model, predict,
and make decisions and critical judgments in problem situations (A.2D)
· determine the relationship between two quantities (a.3)
Evidence of Learning
1. Given a verbal or numerical form of a function, the student will be able to describe independent and dependent quantities at least 80% of the time.
2. Given a verbal or numerical situation, the student will be able to determine whether or not a relation is a function at least 80% of the time.
3. Given a real world situation, the student will be able to gather, organize, record and make critical judgments in problem situations at least 80% of the time.
4. Given various representations of functions, the student will be able to identify the properties and attributes of domain and range at least 80% of the time.
5. Given two quantities, the student will be able to determine their relationship at least 80% of the time.
Mathematics – Algebra 1
Unit I: Foundation of Functions
First Grading Period – Weeks 3 - 4 (10 days) CURRICULUM GUIDE
Essential Questions / Essential Pre-requisite Skills· How are variables used to evaluate algebraic expressions?
· What are the properties and attributes of a function?
· What strategies are helpful in determining if a relation is a function?
· What are the 4 ways that a function can be represented?
· What are the different types of correlations modeled when collecting data? / Students should know how to:
· locate and name points on a coordinate plane using ordered pairs of rational numbers (8.7D)
· make connections among various representations (such as a table, graph, equation, or