Element Cards Mathematics Patterns, Relations, and Functions
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* Interactive whiteboard or other technology to model AB patterns | * Interactive whiteboard or other technology to model AB patterns | ||
* Use of graphic organizers to illustrate a pattern of sets in which the student places 2D or 3D shapes or colors showing an A B pattern | * Use of graphic organizers to illustrate a pattern of sets in which the student places 2D or 3D shapes or colors showing an A B pattern | ||
− | :[[Image:Squarescircles.JPG|159px]] | + | :[[Image:Squarescircles.JPG|159px|A set of a square and circle on first line followed by 3 more sets on the second line]] |
|- | |- | ||
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* T-Charts for growing patterns | * T-Charts for growing patterns | ||
* Use of graphic organizers to illustrate a pattern of sets in which the student places 2D or 3D shapes or colors using addition: e.g., +2 growing pattern: | * Use of graphic organizers to illustrate a pattern of sets in which the student places 2D or 3D shapes or colors using addition: e.g., +2 growing pattern: | ||
− | :[[Image:Squarestack.JPG|98px]] | + | :[[Image:Squarestack.JPG|98px|1 square, 3 squares, 5 squares. Pattern add 2 to previous amount]] |
* Interactive whiteboard or other technology to model growing patterns | * Interactive whiteboard or other technology to model growing patterns | ||
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* Teach/model a growing addition patterns using 2D shapes or 3D objects as a pattern that increases by the same number in each row of the pattern (e.g., a pattern that grows by +3 would have 1 in the first row, 4 in the second row, 7 in the third row) | * Teach/model a growing addition patterns using 2D shapes or 3D objects as a pattern that increases by the same number in each row of the pattern (e.g., a pattern that grows by +3 would have 1 in the first row, 4 in the second row, 7 in the third row) | ||
* Model a growing pattern using a T-chart: | * Model a growing pattern using a T-chart: | ||
− | ::[[Image:Tchartoranges.JPG|258px]] | + | ::[[Image:Tchartoranges.JPG|258px|two column table with the picture pattern in the second column and the rule "plus 3" in the first column|]] |
* Using a T-chart, provide the first two rows of the growing pattern and ask the student to create the third row of the growing pattern | * Using a T-chart, provide the first two rows of the growing pattern and ask the student to create the third row of the growing pattern | ||
* Model- Lead-Test | * Model- Lead-Test | ||
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* Examples of repeating patterns in a real-world setting (e.g., in the environment and art) | * Examples of repeating patterns in a real-world setting (e.g., in the environment and art) | ||
* T-Charts for growing patterns | * T-Charts for growing patterns | ||
− | * Use of graphic organizers to illustrate a pattern of sets in which the student places 2D or 3D shapes or colors using addition or multiplication (e.g., | + | * Use of graphic organizers to illustrate a pattern of sets in which the student places 2D or 3D shapes or colors using addition or multiplication (e.g., +3 growing pattern) |
− | :[[Image:Squarestack2.JPG|221px]] | + | :[[Image:Squarestack2.JPG|221px|Shows a "plus 3" pattern. 3 squares, 6 squares, 9 squares]] |
* Counters | * Counters | ||
* 2D and 3D shapes, objects, or pictures | * 2D and 3D shapes, objects, or pictures | ||
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** e.g., Show 6 ÷ 2: | ** e.g., Show 6 ÷ 2: | ||
− | ::[[Image:Circlesinovals.JPG|272px]] | + | ::[[Image:Circlesinovals.JPG|272px|6 circles divided in two equal groups of 3]] |
* Trial and error to form equal sets of objects to make the arrays | * Trial and error to form equal sets of objects to make the arrays | ||
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** Use the information in the problem/situation to fill in the number of books. | ** Use the information in the problem/situation to fill in the number of books. | ||
− | [[Image:Ratiotable.JPG|490px]] | + | [[Image:Ratiotable.JPG|490px|Shows the ratio between days and total books read]] |
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* Ratio: Here is the ratio 3: 1. This picture shows the ratio. | * Ratio: Here is the ratio 3: 1. This picture shows the ratio. | ||
− | [[Image:4squareratio.JPG|100px]] | + | [[Image:4squareratio.JPG|100px|3 to 1 ratio]] |
− | * This picture shows the ratio.[[Image:4squareratio.JPG|100px]] | + | * This picture shows the ratio.[[Image:4squareratio.JPG|100px|3 to 1 ratio]] |
* This does not show the ratio. | * This does not show the ratio. | ||
− | [[Image:4squareratio.JPG|100px]] | + | [[Image:4squareratio.JPG|100px| 3 to 1 ratio]] |
* Show me a picture that shows the ratio 3:1. | * Show me a picture that shows the ratio 3:1. | ||
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## The percent is unknown or '''x'''. Write '''x''' in the proportion. | ## The percent is unknown or '''x'''. Write '''x''' in the proportion. | ||
− | :::[[Image:Partpercentage.JPG|232px]] | + | :::[[Image:Partpercentage.JPG|232px|3 divided by 5 equals x divided by 100]] |
# Fill in the numbers on each side. | # Fill in the numbers on each side. | ||
− | :[[Image:Partpercentage2.JPG|383px]] | + | :[[Image:Partpercentage2.JPG|383px|5 multiplied by x equals 3 multiplied by 100]] |
# Use the calculator to multiply the numbers on each side of the equation. | # Use the calculator to multiply the numbers on each side of the equation. |
Revision as of 13:36, 29 May 2014
BACK TO Element Cards
Contents |
Teaching Patterns, Relations, and Functions
All of the CCCs in this document relate to teaching Patterns, Relations, and Functions. Below are some additional resources that may be helpful:
NCSC Curriculum Resource Guide: Ratio and Proportions
NCSC Curriculum Resource Guide: Equations
NCSC Content Module: Ratios and Proportions Content Module
NCSC Content Module: Linear Equations Content Module
NCSC Content Module: Expressions Content Module
NCSC Content Module: Functions Content Module
Websites
http://www.mathplayground.com/
Other Resources
http://www.jstor.org/stable/10.5951/teacchilmath.19.1.0050?origin=JSTOR-pdf
http://www.ncpublicschools.org/acre/standards/common-core-tools/
CCC Mathematics | Patterns, Relations, and Functions
CCSS: K.OA.2 Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. | ||
CCC: | K.PRF.1c1 | Solve one step addition and subtraction word problems, and add and subtract within 10 using objects, drawings, pictures. |
Strand: Patterns, Relations, and Functions | Family: Representing and Modeling Problems | |
Progress Indicator: E.PRF.1c Modeling problem solving situations that involve addition and subtraction of whole numbers using objects, diagrams, and symbols | ||
Essential Understandings | Concrete Understandings:
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Representation:
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Suggested Instructional Strategies:
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Suggested Supports and Scaffolds:
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- Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies
CCSS: N/A | ||
CCC: | K.PRF.2a3 | Extend a repeating numerical AB pattern. |
Strand: Patterns, Relations and Functions | Family: Describing and Extending Patterns | |
Progress Indicator: E.PRF.2a Recognizing, describing, and extending simple repeating (ABAB) and growing (A+1, A+2, A+3) patterns (e.g., colors, sounds, words, shapes, numeric – counting, odd, even) | ||
Essential Understandings | Concrete Understandings:
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Representation:
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Suggested Instructional Strategies:
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Suggested Supports and Scaffolds:
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- Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies
CCSS: 1.OA.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. | ||
CCC: | 1.PRF.1b3 | Using objects or pictures to respond appropriately to "add __" and "take away ___" |
Strand: Patterns, Relations and Functions | Family: Representing and Modeling Problems | |
Progress Indicator: E.PRF.1b Exploring and describing how addition or subtraction changes a quantity | ||
Essential Understandings | Concrete Understandings:
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Representation:
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Suggested Instructional Strategies:
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Suggested Supports and Scaffolds:
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- Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies
CCSS: N/A | ||
CCC: | 1.PRF.2b2 | Create a growing pattern using numbers or objects. |
Strand: Patterns, Relations and Functions | Family: Describing and Extending Patterns | |
Progress Indicator: E.PRF.2b creating and explaining repeating and growing patterns using objects or numbers | ||
Essential Understandings | Concrete Understandings:
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Representation:
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Suggested Instructional Strategies:
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Suggested Supports and Scaffolds:
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- Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies
CCSS: N/A | ||
CCC: | 2.PRF.2c2 | Identify the rule of arithmetic patterns that are increasing. |
Strand: Patterns, Relations and Functions | Family: Describing and Extending Patterns | |
Progress Indicator: E.PRF.2c Extending and analyzing simple numeric patterns with rules that involve addition and subtraction | ||
Essential Understandings | Concrete Understandings:
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Representation:
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Suggested Instructional Strategies:
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Suggested Supports and Scaffolds:
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- Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies
CCSS: 2.OA.1 Use addition and subtraction within 100 to solve one and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | ||
CCC: | 2.PRF.1c5 | Write or select an equation representing the problem and its solution. |
Strand: Patterns, Relations and Functions | Family: Problem Solving and Using Variables | |
Progress Indicator: E.PRF.1c Modeling problem solving situations that involve addition and subtraction of whole numbers using objects, diagrams, and symbols | ||
Essential Understandings | Concrete Understandings:
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Representation:
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Suggested Instructional Strategies:
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Suggested Supports and Scaffolds:
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- Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies
CCSS: 3.OA.9 Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends. | ||
CCC: | 3.PRF.2d1 | Identify multiplication patterns in a real-word setting. |
Strand: Patterns, Relations, and Functions | Family: Describing and Extending Patterns | |
Progress Indicator: E.PRF.2d Representing and analyzing patterns and rules (e.g. doubling, adding 3) using words, tables, graphs, and models | ||
Essential Understandings | Concrete Understandings:
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Representation:
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Suggested Instructional Strategies:
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Suggested Supports and Scaffolds:
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- Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies
CCSS: 3.OA.1 Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7. | ||
CCC: | 4.PRF.1d2 | Use objects to model multiplication and division situations involving up to 10 groups with up to 5 objects in each group and interpret the results. |
Strand: Patterns, Relations and Functions | Family: Representing and Modeling Problems | |
Progress Indicator: E.PRF.1d Describing and modeling how addition, subtraction, multiplication, or division changes a quantity, including with fractions | ||
Essential Understandings | Concrete Understandings:
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Representation:
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Suggested Instructional Strategies:
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Suggested Supports and Scaffolds:
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- Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies
CCSS: 5.NF.5 Interpret multiplication as scaling (resizing), by:
Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1. | ||
CCC: | 5.PRF.1a1 | Determine whether the product will increase or decrease based on the multiplier. |
Strand: Patterns, Relations and Functions | Family: Proportional Relationships and Graphing | |
Progress Indicator: M.PRF.1a Describing how multiplication or division changes a quantity, including with fractions or decimals | ||
Essential Understandings | Concrete Understandings:
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Representation:
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Suggested Instructional Strategies:
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Suggested Supports and Scaffolds:
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CCSS: 6.EE.7 Solve real‐world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. | ||
CCC: | 6.PRF.1d1 | Solve real-world single step linear equations. |
Strand: Patterns, Relationships and Functions | Family: Problem Solving and Using Variables | |
Progress Indicator: M.PRF.1d Using symbolic equations to summarize how the quantity of something changes | ||
Essential Understandings | Concrete Understandings:
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Representation:
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Suggested Instructional Strategies:
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Suggested Supports and Scaffolds:
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CCSS: 6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, "The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak." "For every vote candidate A received, candidate C received nearly three votes." | ||
CCC: | 6.PRF.1c1 | Describe the ratio relationship between two quantities for a given situation. |
Strand: Patterns, Relationships and Functions | Family: Proportional Relationships and Graphing | |
Progress Indicator: M.PRF.1c Comparing two rates and evaluating them for a given situation (e.g., best value) | ||
Essential Understandings | Concrete Understandings:
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Representation:
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Suggested Instructional Strategies:
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Suggested Supports and Scaffolds:
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- Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies
CCSS: 7.EE.4 Use variables to represent quantities in a real‐world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
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CCC: | 7.PRF.1g2 | Use variables to represent quantities in a real‐world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities |
Strand: Patterns, Relationships and Functions | Family: Problem Solving and Using Variables | |
Progress Indicator: M.PRF.1g Modeling, solving, and explaining contextualized problems using various representations such as graphs, tables, functions, and equations | ||
Essential Understandings | Concrete Understandings:
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Representation:
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Suggested Instructional Strategies:
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Suggested Supports and Scaffolds:
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CCSS: 7.RP.3 Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error | ||
CCC: | 7.PRF.1f1 | Use proportional relationships to solve multistep percent problems. |
Strand: Patterns, Relationships and Functions | Family: Proportional Relationships and Graphing | |
Progress Indicator: M.PRF.1f Identifying essential quantitative relationships in a situation and using symbolic expressions to represent it and draw reasonable conclusions from it | ||
Essential Understandings | Concrete Understandings:
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Representation:
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Suggested Instructional Strategies:
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Suggested Supports and Scaffolds:
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CCSS: 8.EE.7 Solve linear equations in one variable.
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CCC: | 8.PRF.1g3 | Solve linear equations with 1 variable. |
Strand: Patterns, Relationships and Functions | Family: Problem Solving and Using Variables | |
Progress Indicator: M.PRF.1g Modeling, solving, and explaining contextualized problems using various representations such as graphs, tables, functions, and equations | ||
Essential Understandings | Concrete Understandings:
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Representation:
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Suggested Instructional Strategies:
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Suggested Supports and Scaffolds:
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CCSS: 8.EE.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance‐time graph to a distance‐time equation to determine which
of two moving objects has greater speed. | ||
CCC: | 8.PRF.1e2 | Represent proportional relationships on a line graph. |
Strand: Patterns, Relationships and Functions | Family: Proportional Relationships and Graphing | |
Progress Indicator: M .PRF.1e Representing and computing unit rates associated with ratios of lengths, areas, and other quantities measured in like or different units | ||
Essential Understandings | Concrete Understandings:
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Representation:
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Suggested Instructional Strategies:
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Suggested Supports and Scaffolds:
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CCSS: 8.F.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. | ||
CCC: | 8.PRF.2e2 | Identify the rate of change (slope) and initial value (y-intercept) from graphs. |
Strand: Patterns, Relationships and Functions | Family: Proportional Relationships and Graphing | |
Progress Indicator: M.PRF.2e Using functions to describe quantitative relationships | ||
Essential Understandings | Concrete Understandings:
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Representation:
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Suggested Instructional Strategies:
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Suggested Supports and Scaffolds:
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CCSS: A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. | ||
CCC: | H.PRF.2b1 | Translate a real-world problem into a one variable linear equation. |
Strand: Patterns, Relationships and Functions | Family: Problem Solving and Using Variables | |
Progress Indicator: H.PRF.2b Creating equations and inequalities (in one or two variables) and using them to solve problems and graph solutions | ||
Essential Understandings | Concrete Understandings:
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Representation:
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Suggested Instructional Strategies:
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Suggested Supports and Scaffolds:
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CCSS: F.LE.1 Distinguish between situations that can be modeled with linear functions and with exponential functions. | ||
CCC: | H.PRF.1c1 | Select the appropriate graphical representation of a linear model based on real-world events. |
Strand: Patterns, Relationships and Functions | Family: Proportional Relationships and Graphing | |
Progress Indicator:'' H.PRF.1c Creating mathematical models, using rules and relationships to describe and predict objects and events in the real world '' | ||
Essential Understandings | Concrete Understandings:
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Representation:
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Suggested Instructional Strategies:
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Suggested Supports and Scaffolds:
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