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Patterns, Algebra, and Functions
Green text represents Arizona Standard matched.
Maroon text represents NWEA Learning Continuum Goal matched.
MAP Learning Continuum--Mathematics Algebraic Concepts
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Concept 1 |
Making Patterns - (PRI/INT) This interactive lesson allows students to use an online tool to create and explore patterns. The link opens the
teacher page. There is a stand-alone applet that the students will use in the classroom or lab while the teacher directs the lesson. (Strand 3: Patterns, Algebra, and Functions, Concept 1: Patterns)
People Patterns - (PRI/INT) This interactive lesson allows students to use an online tool to explore patterns about people. Students are able to pick a level and then look at a line of people to determine who should come next. (Strand 3: Patterns, Algebra, and Functions, Concept 1: Patterns)
Creating, Describing, and Analyzing Patterns to Recognize Relationships and Make Predictions: Making Patterns - (PRI/INT) This three-part example highlights different aspects of students' understanding and use of patterns as they analyze relationships and make predictions. (Strand 3: Patterns, Algebra, and Functions, Concept 1: Patterns)
Math Cats: Polygon Playhouse -Students are given a workspace and sets of several different polygons of different sizes and colors. Students can create patterns using the shapes. (Standard 3: Patterns, Algebra, and Functions, Concept 1: Patterns)
Number Patterns - (INT/HS) Uses Pascal's Triangle to show how a variety of different number patterns are found. (Strand 3: Patterns, Algebra, and Functions, Concept 1: Patterns, PO 1 && 2)
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Concept 2 |
Function Machine/Number Cruncher - (INT/MS) A simple function machine that allows students to figure out the function represented by a function machine by inputting several numbers into the machine. (Strand 3: Patterns, Algebra, and Functions, Concept 2: Functions and Relationships)
Graphing Complex Functions - (HS+) This site provides a graphing tool to enable students to quickly graph and compare changes in complex functions. It teaches principles such as variable substitution and composition of functions by allowing the students to test variables in a variety of situations. (Strand 3: Patterns, Algebra, and Functions, Concept 2: Functions and Relationships PO 1, 5)
Equation Grapher - (MS-HS) This interactive activity lets students plug in a wide variety of equations [y=f(x)] and it instantly graphs them. Distinguish linear & nonlinear functions at a glance. (Strand 3: Patterns, Algebra, and Functions, Concept 2: Functions and Relationships, PO 1 & 2)
Investigating Functions Using Spreadsheets - (HS) This site has Excel spreadsheet templates that students can use as they explore functions. (Strand 3: Patterns, Algebra, and Functions, Concept 2: Functions and Relationships, PO 1 & 2)
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Concept 3 |
Trigonometric Functions - (HS) This site allows students to examine the 6 trigonometric functions with a click of the mouse. Students are able to move the points on the graph to demonstrate trig values of various right triangles. (Strand 3: Patterns, Algebra, and Functions, Concept 3: Algebraic Representations, PO 18)
Evaluating a 1 Variable Expression - (INT) Students solve expressions with one variable by substituting a given whole number for the variable. Students may choose to complete problems in 60 seconds, receive extended time for correct answers, or see how quickly they can get 20 more answers correct than incorrect. The best scores for each category are recorded on the screen as the students play each round. (Strand 3: Patterns, Algebra, and Functions, Concept 3: Algebraic Representations, PO 1 and 2)
Quick Math: Automatic Math Solutions - (MS and HS) Quick Math allows the students test solutions to algebra problems. While working on this site, the students would enter an equation (from basic algebra to calculus) and click on results to find the answer. (Strand 3: Patterns, Algebra, and Functions, Concept 3 Algebraic Representations, POs: a variety)
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Concept 4 |
Understanding Distance, Speed, and Time Relationships - (INT) In this activity, students use a software simulation of one runner along a track. Students control the speed and starting point of the runner, watch the race, examine a graph, and analyze the time-versus-distance relationship. This activity helps students understand, describe, and compare situations involving constant rates of change. (Strand 3: Patterns, Algebra, and Functions, Concept 4: Analysis of Change)
Understanding Distance, Speed, and Time Relationships with 2 Runners - (INT) In this activity, students use a software simulation of two runners along a track. Students control the speed and starting point of the runners, watch the race, examine the graphs, and analyze the time-versus-distance relationships. This activity helps students understand, describe, and compare situations involving constant rates of change. (Strand 3: Patterns, Algebra, and Functions, Concept 4: Analysis of Change)
Population Changes in a Trout Pond - (HS) This investigation illustrates the use of iteration, recursion and algebra to model and analyze a changing fish population. Graphs, equations, tables, and technological tools are used to investigate the effect of varying parameters on the long-term population. (Strand 3: Patterns, Algebra, and Functions, Concept 4: Analysis of Change) |
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