Element Cards Mathematics Patterns, Relations, and Functions
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=Teaching Patterns, Relations, and Functions= | =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: | 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: [[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== | ==Websites== | ||
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[http://www.mathhelp.com/ http://www.mathhelp.com/] | [http://www.mathhelp.com/ http://www.mathhelp.com/] | ||
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==Other Resources== | ==Other Resources== | ||
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=CCC Mathematics | Patterns, Relations, and Functions= | =CCC Mathematics | Patterns, Relations, and Functions= | ||
{|border=1 | {|border=1 | ||
− | | | + | | colspan=3 |'''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. |
|- | |- | ||
− | | | + | | colspan=2 |'''Strand: '''Patterns, Relations, and Functions |
| style="background-color:#fde9d9;"|'''Family: '''Representing and Modeling Problems | | style="background-color:#fde9d9;"|'''Family: '''Representing and Modeling Problems | ||
|- | |- | ||
− | | | + | | colspan=3 |'''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:''' |
* Count up to 10 objects. | * Count up to 10 objects. | ||
* Make a set of up to 10 objects. | * Make a set of up to 10 objects. | ||
* Join or separate objects and recount to get a total. | * Join or separate objects and recount to get a total. | ||
− | | | + | ||'''Representation:''' |
* Select a numeral to place under each representation in a modeled equation. | * Select a numeral to place under each representation in a modeled equation. | ||
* Select a pictorial representation of an array that matches the addition or subtraction problem. | * Select a pictorial representation of an array that matches the addition or subtraction problem. | ||
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|- | |- | ||
− | | | + | | colspan=3 |'''Suggested Instructional Strategies:''' |
* Teach explicitly how to count objects in a set and that the last number said tells the number of counted objects. | * Teach explicitly how to count objects in a set and that the last number said tells the number of counted objects. | ||
** Present a set of objects for the student to count. | ** Present a set of objects for the student to count. | ||
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|- | |- | ||
− | | | + | | colspan=3 |'''Suggested Supports and Scaffolds:''' |
* Counters | * Counters | ||
* 2D and 3D shapes or objects, pictures | * 2D and 3D shapes or objects, pictures | ||
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* Interactive whiteboard or other technology to create arrays | * Interactive whiteboard or other technology to create arrays | ||
− | |||
|} | |} | ||
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{|border=1 | {|border=1 | ||
− | | | + | | colspan=3 |'''CCSS:''' N/A |
|- | |- | ||
− | | | + | ||'''CCC:''' |
− | | | + | ||K.PRF.2a3 |
− | | | + | ||Extend a repeating numerical AB pattern. |
|- | |- | ||
− | | | + | | colspan=2 |'''Strand: '''Patterns, Relations and Functions |
| style="background-color:#fbd4b4;"|'''Family: '''Describing and Extending Patterns | | style="background-color:#fbd4b4;"|'''Family: '''Describing and Extending Patterns | ||
|- | |- | ||
− | | | + | | colspan=3 |'''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:''' |
* Identify attribute (color, shape, size) of an object used in a pattern. | * Identify attribute (color, shape, size) of an object used in a pattern. | ||
− | | | + | ||'''Representation:''' |
* Recognize patterns and use words to describe the patterns they see. | * Recognize patterns and use words to describe the patterns they see. | ||
* Use colors, shapes, symbols or objects to represent an AB pattern. | * Use colors, shapes, symbols or objects to represent an AB pattern. | ||
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|- | |- | ||
− | | | + | | colspan=3 |'''Suggested Instructional Strategies:''' |
* Multiple Exemplar Training or Example/Non-Example Training:* | * Multiple Exemplar Training or Example/Non-Example Training:* | ||
− | ** AB Pattern: "Here is a pattern ([[Image:Appleoranges.JPG|120px|float]]). Here is the same pattern. Here is the same pattern. This not the same pattern. Show me a pattern that is the same as this pattern (point to the first pattern). | + | ** AB Pattern: "Here is a pattern ([[Image:Appleoranges.JPG|120px|float|Alternating pattern of apple then orange]]). Here is the same pattern. Here is the same pattern. This not the same pattern. Show me a pattern that is the same as this pattern (point to the first pattern). |
* Teach explicitly how an AB pattern has the same pattern over and over and never changes using colors, shapes, or objects. | * Teach explicitly how an AB pattern has the same pattern over and over and never changes using colors, shapes, or objects. | ||
* Model-Lead-Test* | * Model-Lead-Test* | ||
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|- | |- | ||
− | | | + | | colspan=3 |'''Suggested Supports and Scaffolds:''' |
* Examples of AB patterns in real-world setting (e.g., in the environment and art) | * Examples of AB patterns in real-world setting (e.g., in the environment and art) | ||
* Use of graphic organizers to illustrate an AB pattern in which the student places pictures, 2D or 3D shapes or colors | * Use of graphic organizers to illustrate an AB pattern in which the student places pictures, 2D or 3D shapes or colors | ||
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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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{|border=1 | {|border=1 | ||
− | | | + | | colspan=3 |'''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 ___" |
|- | |- | ||
− | | | + | | colspan=2 |'''Strand: '''Patterns, Relations and Functions |
| style="background-color:#fde9d9;"|'''Family: '''Representing and Modeling Problems | | style="background-color:#fde9d9;"|'''Family: '''Representing and Modeling Problems | ||
|- | |- | ||
− | | | + | | colspan=3 |'''Progress Indicator:'' '''E.PRF.1b''' '''Exploring and describing how addition or subtraction changes a quantity'' |
|- | |- | ||
− | | | + | ||'''Essential Understandings''' |
− | | | + | ||'''Concrete Understandings:''' |
* Show addition with objects to an existing set. | * Show addition with objects to an existing set. | ||
* Count objects. | * Count objects. | ||
* Make a set with objects or with drawings given a number. | * Make a set with objects or with drawings given a number. | ||
− | | | + | ||'''Representation:''' |
* Select a pictorial of a set that has been added or taken away from. | * Select a pictorial of a set that has been added or taken away from. | ||
* Know the following symbols and vocabulary: =, +, - , take away, add. | * Know the following symbols and vocabulary: =, +, - , take away, add. | ||
|- | |- | ||
− | | | + | | colspan=3 |'''Suggested Instructional Strategies:''' |
* Teach explicitly the meaning of "add" and "take away" by connecting the vocabulary to known language (e.g. "add" means plus, more, join; "take away" means less, fewer); | * Teach explicitly the meaning of "add" and "take away" by connecting the vocabulary to known language (e.g. "add" means plus, more, join; "take away" means less, fewer); | ||
* Teach/model "adding to" a set of object results in a larger set; teach "take away" from a set of objects results in a smaller set; | * Teach/model "adding to" a set of object results in a larger set; teach "take away" from a set of objects results in a smaller set; | ||
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|- | |- | ||
− | | | + | | colspan=3 |'''Suggested Supports and Scaffolds:''' |
* Counters (chips) | * Counters (chips) | ||
* Picture and objects | * Picture and objects | ||
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* Graphic organizers | * Graphic organizers | ||
− | |||
|} | |} | ||
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{|border=1 | {|border=1 | ||
− | | | + | | colspan=3 |'''CCSS:''' N/A |
|- | |- | ||
− | | | + | ||'''CCC:''' |
− | | | + | ||1.PRF.2b2 |
− | | | + | ||Create a growing pattern using numbers or objects. |
|- | |- | ||
− | | | + | | colspan=2 |'''Strand: '''Patterns, Relations and Functions |
| style="background-color:#fbd4b4;"|'''Family: '''Describing and Extending Patterns | | style="background-color:#fbd4b4;"|'''Family: '''Describing and Extending Patterns | ||
|- | |- | ||
− | | | + | | colspan=3 |'''Progress Indicator:''''' E.PRF.2b creating and explaining repeating and growing patterns using objects or numbers'' |
|- | |- | ||
− | | | + | ||'''Essential Understandings''' |
− | | | + | ||'''Concrete Understandings:''' |
* Recognize/identify an AB pattern as a pattern that has the same pattern over and over and never changing using colors, shapes, or objects | * Recognize/identify an AB pattern as a pattern that has the same pattern over and over and never changing using colors, shapes, or objects | ||
* Count. | * Count. | ||
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* Identify that a growing pattern increases by same amount. | * Identify that a growing pattern increases by same amount. | ||
− | | | + | ||'''Representation:''' |
* Match a pattern using symbols or objects to represent a provided growing addition pattern. | * Match a pattern using symbols or objects to represent a provided growing addition pattern. | ||
|- | |- | ||
− | | | + | | colspan=3 |'''Suggested Instructional Strategies:''' |
* Multiple Exemplar Training or Example/Non-Example Training* | * Multiple Exemplar Training or Example/Non-Example Training* | ||
** Growing Pattern: "Here is a pattern that grows by 1 ([[Image:1,2cats.JPG|74px]]). Here is that pattern that grows by one ([[Image:3cats.JPG|68px]]). Here is that pattern that grows by one ([[Image:4cats.JPG|92px]]). This pattern does not grow by one ([[Image:6cats.JPG|143px]]). Show me a pattern that grows by one. | ** Growing Pattern: "Here is a pattern that grows by 1 ([[Image:1,2cats.JPG|74px]]). Here is that pattern that grows by one ([[Image:3cats.JPG|68px]]). Here is that pattern that grows by one ([[Image:4cats.JPG|92px]]). This pattern does not grow by one ([[Image:6cats.JPG|143px]]). Show me a pattern that grows by one. | ||
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|- | |- | ||
− | | | + | | colspan=3 |'''Suggested Supports and Scaffolds:''' |
* Unit blocks of ones | * Unit blocks of ones | ||
* Colored tiles | * Colored tiles | ||
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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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{|border=1 | {|border=1 | ||
− | | | + | | colspan=3 |'''CCSS:''' N/A |
|- | |- | ||
− | | | + | ||'''CCC:''' |
− | | | + | ||2.PRF.2c2 |
− | | | + | ||Identify the rule of arithmetic patterns that are increasing. |
|- | |- | ||
− | | | + | | colspan=2 |'''Strand: '''Patterns, Relations and Functions |
| style="background-color:#fde9d9;"|'''Family: '''Describing and Extending Patterns | | style="background-color:#fde9d9;"|'''Family: '''Describing and Extending Patterns | ||
|- | |- | ||
− | | | + | | colspan=3|'''Progress Indicator:'' '''E.PRF.2c Extending and analyzing simple numeric patterns with rules that involve addition and subtraction'' |
|- | |- | ||
− | | | + | ||'''Essential Understandings''' |
− | | | + | ||'''Concrete Understandings:''' |
* Recognize/identify a growing pattern with a single element (i.e., apple) that has one more member at each successive step using colors, shapes, or objects. | * Recognize/identify a growing pattern with a single element (i.e., apple) that has one more member at each successive step using colors, shapes, or objects. | ||
* Count. | * Count. | ||
* Join objects to represent addition. | * Join objects to represent addition. | ||
− | | | + | ||'''Representation:''' |
* Match a pattern using symbols or objects to represent a provided growing addition pattern. | * Match a pattern using symbols or objects to represent a provided growing addition pattern. | ||
* Recognize patterns and describe the patterns. | * Recognize patterns and describe the patterns. | ||
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|- | |- | ||
− | | | + | | colspan=3 |'''Suggested Instructional Strategies:''' |
* Multiple Exemplar Training or Example/Non-Example Training* | * Multiple Exemplar Training or Example/Non-Example Training* | ||
** Growing Pattern: "Here is a pattern that grows by two. Here is that pattern growing by two. Here is that pattern that is growing by two more. This pattern does not grow by two. Show me a pattern that grows by two." | ** Growing Pattern: "Here is a pattern that grows by two. Here is that pattern growing by two. Here is that pattern that is growing by two more. This pattern does not grow by two. Show me a pattern that grows by two." | ||
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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: | + | ::[[Image:Tchart.PNG|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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|- | |- | ||
− | | | + | | colspan=3 |'''Suggested Supports and Scaffolds:''' |
* Counters, shapes, and objects | * Counters, shapes, and objects | ||
* Examples of growing patterns in real-world settings (e.g., in the environment and art) | * Examples of growing patterns in real-world settings (e.g., in the environment and art) | ||
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* Use of graphic organizers to illustrate a pattern of sets in which the student places 2D or 3D shapes or colors showing a growing pattern | * Use of graphic organizers to illustrate a pattern of sets in which the student places 2D or 3D shapes or colors showing a growing pattern | ||
− | |||
|} | |} | ||
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{|border=1 | {|border=1 | ||
− | | | + | | colspan=3 |'''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. |
|- | |- | ||
− | | | + | | colspan=2 |'''Strand:''' Patterns, Relations and Functions |
| style="background-color:#fabf8f;"|'''Family: '''Problem Solving and Using Variables | | style="background-color:#fabf8f;"|'''Family: '''Problem Solving and Using Variables | ||
|- | |- | ||
− | | | + | | colspan=3 |'''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:''' |
* Match the action of combining with vocabulary (i.e., in all; altogether) or the action of decomposing with vocabulary (i.e., have left; take away) in a word problem. | * Match the action of combining with vocabulary (i.e., in all; altogether) or the action of decomposing with vocabulary (i.e., have left; take away) in a word problem. | ||
* Count up to __ objects. | * Count up to __ objects. | ||
− | | | + | ||'''Representation:''' |
* Identify a representation of an array that matches the problem. | * Identify a representation of an array that matches the problem. | ||
* State what the numbers represent. | * State what the numbers represent. | ||
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|- | |- | ||
− | | | + | | colspan=3 |'''Suggested Instructional Strategies:''' |
* Teach explicitly the meaning of "add" and "take away" by connecting the vocabulary to known language (e.g., "add" means plus, more, join; "take away" means less, fewer). | * Teach explicitly the meaning of "add" and "take away" by connecting the vocabulary to known language (e.g., "add" means plus, more, join; "take away" means less, fewer). | ||
* Teach/model "adding to" a set of object results in a larger set; teach "take away" from a set of objects results in a smaller set; teach "adding" means joining and "take away" means removing. | * Teach/model "adding to" a set of object results in a larger set; teach "take away" from a set of objects results in a smaller set; teach "adding" means joining and "take away" means removing. | ||
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|- | |- | ||
− | | | + | | colspan=3 |'''Suggested Supports and Scaffolds:''' |
* Pictures and manipulatives | * Pictures and manipulatives | ||
* Template for solving an equation | * Template for solving an equation | ||
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* Calculator | * Calculator | ||
− | |||
|} | |} | ||
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{|border=1 | {|border=1 | ||
− | | | + | | colspan=3 |'''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. |
|- | |- | ||
− | | | + | | colspan=2 |'''Strand: '''Patterns, Relations, and Functions |
| style="background-color:#fde9d9;"|'''Family: '''Describing and Extending Patterns | | style="background-color:#fde9d9;"|'''Family: '''Describing and Extending Patterns | ||
|- | |- | ||
− | | | + | | colspan=3 |'''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:''' |
* Identify that a pattern is formed by repeatedly adding the same number to a set. | * Identify that a pattern is formed by repeatedly adding the same number to a set. | ||
* Add within 100 with calculator and/or manipulatives. | * Add within 100 with calculator and/or manipulatives. | ||
− | | | + | ||'''Representation:''' |
* Match a pattern using symbols or objects to represent a provided growing multiplication pattern in a real-word setting. | * Match a pattern using symbols or objects to represent a provided growing multiplication pattern in a real-word setting. | ||
* Recognize patterns and use words to describe the patterns they see. | * Recognize patterns and use words to describe the patterns they see. | ||
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|- | |- | ||
− | | | + | | colspan=3 |'''Suggested Instructional Strategies:''' |
* Multiple Exemplar Training or Example/Non-Example Training* | * Multiple Exemplar Training or Example/Non-Example Training* | ||
** Growing Pattern: "Here is a growing pattern. Here is a growing pattern. Here is growing pattern. This not a growing pattern. Show me a growing pattern." | ** Growing Pattern: "Here is a growing pattern. Here is a growing pattern. Here is growing pattern. This not a growing pattern. Show me a growing pattern." | ||
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|- | |- | ||
− | | | + | | colspan=3 |'''Suggested Supports and Scaffolds:''' |
* 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 | ||
* Interactive whiteboard or other technology to model growing patterns | * Interactive whiteboard or other technology to model growing patterns | ||
− | |||
|} | |} | ||
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{|border=1 | {|border=1 | ||
− | | | + | | colspan=3 |'''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. |
|- | |- | ||
− | |colspan=2 | + | |colspan=2|'''Strand: '''Patterns, Relations and Functions |
| style="background-color:#fbd4b4;"|'''Family: '''Representing and Modeling Problems | | style="background-color:#fbd4b4;"|'''Family: '''Representing and Modeling Problems | ||
|- | |- | ||
− | | | + | | colspan=3 |'''Progress Indicator:'' '''E.PRF.1d''' '''Describing and modeling how addition, subtraction, multiplication, or division changes a quantity, including with fractions '' |
|- | |- | ||
− | | | + | ||'''Essential Understandings''' |
− | | | + | ||'''Concrete Understandings:''' |
* Create an array (e.g., show me 2 groups/rows of 3; or 2X3). | * Create an array (e.g., show me 2 groups/rows of 3; or 2X3). | ||
* Use calculator and/or manipulatives to add and subtract within 50. | * Use calculator and/or manipulatives to add and subtract within 50. | ||
− | | | + | ||'''Representation:''' |
* Use an array to represent a multiplication or division problem. | * Use an array to represent a multiplication or division problem. | ||
* Select a numeral to place under each representation in the modeled equation. | * Select a numeral to place under each representation in the modeled equation. | ||
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|- | |- | ||
− | | | + | | colspan=3 |'''Suggested Instructional Strategies:''' |
* Multiple Exemplar Training* | * Multiple Exemplar Training* | ||
** Equal sets: "This is a set. This is an equal set. This is an equal set. This is not an equal set. Show me an equal set." | ** Equal sets: "This is a set. This is an equal set. This is an equal set. This is not an equal set. Show me an equal set." | ||
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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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|- | |- | ||
− | | | + | | colspan=3 |'''Suggested Supports and Scaffolds:''' |
* Counters | * Counters | ||
* Number lines | * Number lines | ||
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* Interactive whiteboard or other technology to create arrays | * Interactive whiteboard or other technology to create arrays | ||
− | |||
|} | |} | ||
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{|border=1 | {|border=1 | ||
− | | | + | | colspan=3 |'''CCSS:''' 5.NF.5 Interpret multiplication as scaling (resizing), by: |
:a Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. | :a Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. | ||
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. | 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. |
|- | |- | ||
− | | | + | | colspan=2 |'''Strand: '''Patterns, Relations and Functions |
| style="background-color:#e36c0a;"|'''Family: '''Proportional Relationships and Graphing''' ''' | | style="background-color:#e36c0a;"|'''Family: '''Proportional Relationships and Graphing''' ''' | ||
|- | |- | ||
− | | | + | | colspan=3 |'''Progress Indicator:'' '''M.PRF.1a''' '''Describing how multiplication or division changes a quantity, including with fractions or decimals '' |
|- | |- | ||
− | | | + | ||'''Essential Understandings''' |
− | | | + | ||'''Concrete Understandings:''' |
* Show what happens to a set when it's multiplied by 1(1X) or some other whole number (2X). | * Show what happens to a set when it's multiplied by 1(1X) or some other whole number (2X). | ||
** Example: I have 3 chips; which is one set of 3 chips…Now show me 2 sets of 3 chips. …Which is more? | ** Example: I have 3 chips; which is one set of 3 chips…Now show me 2 sets of 3 chips. …Which is more? | ||
* Use whole numbers. | * Use whole numbers. | ||
− | | | + | ||'''Representation:''' |
* Select a pictorial representation that matches the multiplication problem. | * Select a pictorial representation that matches the multiplication problem. | ||
* Recognize that when a number is multiplied by a fraction or decimal, the product will decrease. | * Recognize that when a number is multiplied by a fraction or decimal, the product will decrease. | ||
Line 591: | Line 584: | ||
|- | |- | ||
− | | | + | | colspan=3 |'''Suggested Instructional Strategies:''' |
* Explicitly teach that a multiplicand multiplied by a whole number multiplier increases the product and a fraction/decimal multiplier decreases the product; demonstrate a strategy for self-checking the answer. | * Explicitly teach that a multiplicand multiplied by a whole number multiplier increases the product and a fraction/decimal multiplier decreases the product; demonstrate a strategy for self-checking the answer. | ||
* Task analysis example: | * Task analysis example: | ||
Line 612: | Line 605: | ||
|- | |- | ||
− | | | + | | colspan=3 |'''Suggested Supports and Scaffolds:''' |
* Counters (chips) | * Counters (chips) | ||
* Picture and objects | * Picture and objects | ||
Line 621: | Line 614: | ||
* Graphic organizers (rows and columns) | * Graphic organizers (rows and columns) | ||
− | |||
|} | |} | ||
{|border=1 | {|border=1 | ||
− | | | + | | colspan=3 |'''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. |
|- | |- | ||
− | | | + | | colspan=2 |'''Strand:''' Patterns, Relationships and Functions |
| style="background-color:#fabf8f;"|'''Family: '''Problem Solving and Using Variables | | style="background-color:#fabf8f;"|'''Family: '''Problem Solving and Using Variables | ||
|- | |- | ||
− | | | + | | colspan=3 |'''Progress Indicator:'' '''M.PRF.1d''' '''Using symbolic equations to summarize how the quantity of something changes '' |
|- | |- | ||
− | | | + | ||'''Essential Understandings''' |
− | | | + | ||'''Concrete Understandings:''' |
* Use objects to solve one-step addition and subtraction equations with whole numbers. | * Use objects to solve one-step addition and subtraction equations with whole numbers. | ||
− | | | + | ||'''Representation:''' |
* Match a representation of an equation with a variable to a real-world problem. | * Match a representation of an equation with a variable to a real-world problem. | ||
* Set up an equation in which both sides are equal (adding or subtracting the same number/value from both sides of the equation). | * Set up an equation in which both sides are equal (adding or subtracting the same number/value from both sides of the equation). | ||
Line 656: | Line 648: | ||
|- | |- | ||
− | | | + | | colspan=3 |'''Suggested Instructional Strategies:''' |
* Explicitly teach strategies for determining the operation required to solve a single step real-world problem. | * Explicitly teach strategies for determining the operation required to solve a single step real-world problem. | ||
* Task analysis | * Task analysis | ||
Line 668: | Line 660: | ||
|- | |- | ||
− | | | + | | colspan=3 |'''Suggested Supports and Scaffolds:''' |
* Pictures and manipulatives | * Pictures and manipulatives | ||
* Template for solving an equation | * Template for solving an equation | ||
Line 674: | Line 666: | ||
* Calculator | * Calculator | ||
− | |||
|} | |} | ||
{|border=1 | {|border=1 | ||
− | | | + | | colspan=3 |'''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. |
|- | |- | ||
− | | | + | | colspan=2 |'''Strand: '''Patterns, Relationships and Functions |
| style="background-color:#e36c0a;"|'''Family: '''Proportional Relationships and Graphing''' ''' | | style="background-color:#e36c0a;"|'''Family: '''Proportional Relationships and Graphing''' ''' | ||
|- | |- | ||
− | | | + | | colspan=3 |'''Progress Indicator:'' '''M.PRF.1c''' '''Comparing two rates and evaluating them for a given situation (e.g., best value) '' |
|- | |- | ||
− | | | + | ||'''Essential Understandings''' |
− | | | + | ||'''Concrete Understandings:''' |
* Match/identify a simple ratio (1:X) as the relationship between two quantities. | * Match/identify a simple ratio (1:X) as the relationship between two quantities. | ||
* Given a situation use objects or a calculator to set up a ratio. | * Given a situation use objects or a calculator to set up a ratio. | ||
− | | | + | ||'''Representation:''' |
* Recognize the meaning of the placement of numbers in a ratio for a given situation. | * Recognize the meaning of the placement of numbers in a ratio for a given situation. | ||
* Show a ratio in three ways: number to number (1 to 2) expressed as a fraction (1/2) or using a colon 1:2. | * Show a ratio in three ways: number to number (1 to 2) expressed as a fraction (1/2) or using a colon 1:2. | ||
Line 711: | Line 702: | ||
|- | |- | ||
− | | | + | | colspan=3 |'''Suggested Instructional Strategies:''' |
* Multiple Exemplar Training:* | * Multiple Exemplar Training:* | ||
** Example for equal sets: "This is a proportional relationship. This is a proportional relationship. This is a proportional relationship. This is not a proportional relationship. Show me a proportional relationship." | ** Example for equal sets: "This is a proportional relationship. This is a proportional relationship. This is a proportional relationship. This is not a proportional relationship. Show me a proportional relationship." | ||
Line 723: | Line 714: | ||
** 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]] |
Line 735: | Line 726: | ||
* 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|3 to 1 ratio]] | |
* This does not show the ratio. | * This does not show the ratio. | ||
− | [[Image: | + | [[Image:4to1Ratio.PNG|125px| 4 to 1 ratio]] |
+ | |||
* Show me a picture that shows the ratio 3:1. | * Show me a picture that shows the ratio 3:1. | ||
Line 751: | Line 746: | ||
|- | |- | ||
− | | | + | | colspan=3 |'''Suggested Supports and Scaffolds:''' |
* Unit blocks of ones | * Unit blocks of ones | ||
* Colored tiles | * Colored tiles | ||
Line 759: | Line 754: | ||
* Interactive whiteboard or other technology to manipulate representations of ratios | * Interactive whiteboard or other technology to manipulate representations of ratios | ||
− | |||
|} | |} | ||
Line 766: | Line 760: | ||
{|border=1 | {|border=1 | ||
− | | | + | | colspan=3 |'''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. |
# Solve word problems leading to equations of the form ''px ''+ ''q ''= ''r ''and ''p''(''x ''+ ''q'') = ''r'', where ''p'', ''q'', and ''r ''are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. ''For example, the perimeter of a rectangle is'' ''54 cm. Its length is 6 cm. What is its width?'' | # Solve word problems leading to equations of the form ''px ''+ ''q ''= ''r ''and ''p''(''x ''+ ''q'') = ''r'', where ''p'', ''q'', and ''r ''are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. ''For example, the perimeter of a rectangle is'' ''54 cm. Its length is 6 cm. What is its width?'' | ||
# Solve word problems leading to inequalities of the form ''px ''+ ''q ''> ''r ''or ''px ''+ ''q ''< ''r'', where ''p'', ''q'', and ''r ''are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. ''For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.'' | # Solve word problems leading to inequalities of the form ''px ''+ ''q ''> ''r ''or ''px ''+ ''q ''< ''r'', where ''p'', ''q'', and ''r ''are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. ''For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.'' | ||
|- | |- | ||
− | | | + | ||'''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 |
|- | |- | ||
− | | | + | | colspan=2 |'''Strand:''' Patterns, Relationships and Functions |
| style="background-color:#fabf8f;"|'''Family: '''Problem Solving and Using Variables | | style="background-color:#fabf8f;"|'''Family: '''Problem Solving and Using Variables | ||
|- | |- | ||
− | | | + | | colspan=3 |'''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:''' |
* Identify situation in which quantities are equal or unequal. | * Identify situation in which quantities are equal or unequal. | ||
* Record/replace a variable in an equation with a fact from a story on a graphic organizer. | * Record/replace a variable in an equation with a fact from a story on a graphic organizer. | ||
− | | | + | ||'''Representation:''' |
* Create a pictorial array of a simple equation to translate wording. | * Create a pictorial array of a simple equation to translate wording. | ||
* Understand the following concepts, vocabulary, and symbols: +, -, X, ÷, =, ≠, <, >, equation, equal, inequality | * Understand the following concepts, vocabulary, and symbols: +, -, X, ÷, =, ≠, <, >, equation, equal, inequality | ||
|- | |- | ||
− | | | + | | colspan=3 |'''Suggested Instructional Strategies:''' |
* Explicitly teach equality vs. inequality. | * Explicitly teach equality vs. inequality. | ||
* Explicitly teach strategies for determining the operation required to solve a single step real-world problem. | * Explicitly teach strategies for determining the operation required to solve a single step real-world problem. | ||
Line 816: | Line 810: | ||
|- | |- | ||
− | | | + | | colspan=3 |'''Suggested Supports and Scaffolds:''' |
* Counters | * Counters | ||
* Number lines | * Number lines | ||
Line 823: | Line 817: | ||
* Interactive whiteboard | * Interactive whiteboard | ||
− | |||
|} | |} | ||
{|border=1 | {|border=1 | ||
− | | | + | | colspan=3 |'''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. |
|- | |- | ||
− | | | + | | colspan=2 |'''Strand: '''Patterns, Relationships and Functions |
| style="background-color:#e36c0a;"|'''Family: '''Proportional Relationships and Graphing''' ''' | | style="background-color:#e36c0a;"|'''Family: '''Proportional Relationships and Graphing''' ''' | ||
|- | |- | ||
− | | | + | | colspan=3 |'''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:''' |
* Identify how one variable changes in relation to another variable in a directly proportional relationship. | * Identify how one variable changes in relation to another variable in a directly proportional relationship. | ||
** ''a/b'' = ''c/d'' If ''a'' increases, what will happen to ''c''? | ** ''a/b'' = ''c/d'' If ''a'' increases, what will happen to ''c''? | ||
* Apply understanding to convert percents to decimals. | * Apply understanding to convert percents to decimals. | ||
− | | | + | ||'''Representation:''' |
* Use a proportion method to solve (part/whole = number/100). | * Use a proportion method to solve (part/whole = number/100). | ||
* Set up a proportion to solve for an unknown value. | * Set up a proportion to solve for an unknown value. | ||
Line 860: | Line 853: | ||
|- | |- | ||
− | | | + | | colspan=3 |'''Suggested Instructional Strategies:''' |
* Task Analysis example: Read the story problem/situation: ''If 3 out of 5 animals are dogs, what percent of the animals is made up of dogs?'' | * Task Analysis example: Read the story problem/situation: ''If 3 out of 5 animals are dogs, what percent of the animals is made up of dogs?'' | ||
## Fill in the proportion using the provided information in the story problem to record what is known and what is unknown/represented by "x" (what to solve for). | ## Fill in the proportion using the provided information in the story problem to record what is known and what is unknown/represented by "x" (what to solve for). | ||
Line 868: | Line 861: | ||
## 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. | ||
Line 882: | Line 875: | ||
|- | |- | ||
− | | | + | | colspan=3 |'''Suggested Supports and Scaffolds:''' |
* Highlight text that provides important information/vocabulary | * Highlight text that provides important information/vocabulary | ||
* Counters | * Counters | ||
Line 891: | Line 884: | ||
* Interactive whiteboard or other technology to manipulate representations | * Interactive whiteboard or other technology to manipulate representations | ||
− | |||
|} | |} | ||
{|border=1 | {|border=1 | ||
− | | | + | | colspan=3 |'''CCSS:''' 8.EE.7''' '''Solve linear equations in one variable. |
# Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form ''x ''= ''a'', ''a ''= ''a'', or ''a ''= ''b ''results (where ''a ''and ''b ''are different b). Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. | # Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form ''x ''= ''a'', ''a ''= ''a'', or ''a ''= ''b ''results (where ''a ''and ''b ''are different b). Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. | ||
|- | |- | ||
− | | | + | ||'''CCC:''' |
− | | | + | ||8.PRF.1g3 |
− | | | + | ||Solve linear equations with 1 variable. |
|- | |- | ||
− | | | + | | colspan=2 |'''Strand:''' Patterns, Relationships and Functions |
| style="background-color:#fabf8f;"|'''Family: '''Problem Solving and Using Variables | | style="background-color:#fabf8f;"|'''Family: '''Problem Solving and Using Variables | ||
|- | |- | ||
− | | | + | | colspan=3 |'''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:''' |
* Use manipulatives or graphic organizer to solve a problem. | * Use manipulatives or graphic organizer to solve a problem. | ||
* Identify the reciprocal operation in order to solve one step equations. | * Identify the reciprocal operation in order to solve one step equations. | ||
− | | | + | ||'''Representation:''' |
* Create a pictorial array of a simple equation to translate wording to solve for x or y. | * Create a pictorial array of a simple equation to translate wording to solve for x or y. | ||
* Understand the following concepts, vocabulary, and symbols: +, -, X, ÷, =, variable, equation. | * Understand the following concepts, vocabulary, and symbols: +, -, X, ÷, =, variable, equation. | ||
|- | |- | ||
− | | | + | | colspan=3 |'''Suggested Instructional Strategies:''' |
* Explicit strategy: Solve an equation by dividing both sides of the equation by the value in front of the variable and then simplify. | * Explicit strategy: Solve an equation by dividing both sides of the equation by the value in front of the variable and then simplify. | ||
* Use trial and error to determine the value of x or y. (Is the product too low, too high?) | * Use trial and error to determine the value of x or y. (Is the product too low, too high?) | ||
Line 938: | Line 930: | ||
|- | |- | ||
− | | | + | | colspan=3 |'''Suggested Supports and Scaffolds:''' |
* Counters | * Counters | ||
* Grids or graphic organizers to create arrays | * Grids or graphic organizers to create arrays | ||
Line 945: | Line 937: | ||
* Interactive whiteboard | * Interactive whiteboard | ||
− | |||
|} | |} | ||
{|border=1 | {|border=1 | ||
− | | | + | | colspan=3 |'''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.'' | ''of two moving objects has greater speed.'' | ||
|- | |- | ||
− | | | + | ||'''CCC:''' |
− | | | + | ||8.PRF.1e2 |
− | | | + | ||Represent proportional relationships on a line graph. |
|- | |- | ||
− | | | + | | colspan=2 |'''Strand:''' Patterns, Relationships and Functions |
| style="background-color:#e36c0a;"|'''Family: '''Proportional Relationships and Graphing''' ''' | | style="background-color:#e36c0a;"|'''Family: '''Proportional Relationships and Graphing''' ''' | ||
|- | |- | ||
− | | | + | | colspan=3 |'''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:''' |
* Identify parts of a line graph. | * Identify parts of a line graph. | ||
* Identify the 2 coordinates of a point on a line graph. | * Identify the 2 coordinates of a point on a line graph. | ||
Line 977: | Line 968: | ||
* Recognize a positive relationship between two variables. | * Recognize a positive relationship between two variables. | ||
− | | | + | ||'''Representation:''' |
* Graph a series of coordinates on a graph. | * Graph a series of coordinates on a graph. | ||
* Identify given coordinates (x,y) as a point on a graph. | * Identify given coordinates (x,y) as a point on a graph. | ||
Line 984: | Line 975: | ||
|- | |- | ||
− | | | + | | colspan=3 |'''Suggested Instructional Strategies:''' |
* Teach explicitly that a coordinate grid has two perpendicular lines, or axes, labeled like number lines. | * Teach explicitly that a coordinate grid has two perpendicular lines, or axes, labeled like number lines. | ||
* Teach explicitly how to recognize the relationship between y and x using the coordinates of several points (e.g., '''y''' increases as '''x '''increases; the ratio is the same for all values if they are directly proportional). | * Teach explicitly how to recognize the relationship between y and x using the coordinates of several points (e.g., '''y''' increases as '''x '''increases; the ratio is the same for all values if they are directly proportional). | ||
Line 999: | Line 990: | ||
|- | |- | ||
− | | | + | | colspan=3 |'''Suggested Supports and Scaffolds:''' |
* Grid paper with raised perpendicular lines (horizontal and vertical lines) and points | * Grid paper with raised perpendicular lines (horizontal and vertical lines) and points | ||
* Models | * Models | ||
Line 1,007: | Line 998: | ||
|- | |- | ||
− | | | + | | colspan=3 |'''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. |
|- | |- | ||
− | | | + | | colspan=2 |'''Strand:''' Patterns, Relationships and Functions |
| style="background-color:#e36c0a;"|'''Family: '''Proportional Relationships and Graphing''' ''' | | style="background-color:#e36c0a;"|'''Family: '''Proportional Relationships and Graphing''' ''' | ||
|- | |- | ||
− | | | + | | colspan=3 |'''Progress Indicator:''''' M.PRF.2e Using functions to describe quantitative relationships '' |
|- | |- | ||
− | | | + | ||'''Essential Understandings''' |
− | | | + | ||'''Concrete Understandings:''' |
* Indicate the point on a line that crosses the y-axis. | * Indicate the point on a line that crosses the y-axis. | ||
* Describe the rate of change qualitatively (e.g., steep = rapid change). | * Describe the rate of change qualitatively (e.g., steep = rapid change). | ||
− | | | + | ||'''Representation:''' |
* Interpret/define a line graph with coordinates for multiple points. | * Interpret/define a line graph with coordinates for multiple points. | ||
* Identify coordinates (points) on a graph. | * Identify coordinates (points) on a graph. | ||
Line 1,037: | Line 1,028: | ||
|- | |- | ||
− | | | + | | colspan=3 |'''Suggested Instructional Strategies:''' |
* Explicitly teach axes (x-axis is the horizontal axis and the y-axis is the vertical axis) and coordinates for points. | * Explicitly teach axes (x-axis is the horizontal axis and the y-axis is the vertical axis) and coordinates for points. | ||
* Explicitly teach identifying x,y coordinates for points on a graph. | * Explicitly teach identifying x,y coordinates for points on a graph. | ||
Line 1,062: | Line 1,053: | ||
|- | |- | ||
− | | | + | | colspan=3 |'''Suggested Supports and Scaffolds:''' |
* Grid paper with raised perpendicular lines (horizontal and vertical lines) and points | * Grid paper with raised perpendicular lines (horizontal and vertical lines) and points | ||
* Models | * Models | ||
Line 1,070: | Line 1,061: | ||
* Interactive white board | * Interactive white board | ||
− | |||
|} | |} | ||
{|border=1 | {|border=1 | ||
− | | | + | | colspan=3 |'''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. |
|- | |- | ||
− | | | + | | colspan=2 |'''Strand:''' Patterns, Relationships and Functions |
| style="background-color:#fabf8f;"|'''Family: '''Problem Solving and Using Variables | | style="background-color:#fabf8f;"|'''Family: '''Problem Solving and Using Variables | ||
|- | |- | ||
− | | | + | | colspan=3 |'''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:''' |
* Match an equation with one variable to a real-world context. | * Match an equation with one variable to a real-world context. | ||
− | | | + | ||'''Representation:''' |
* Create a pictorial array of a simple equation to translate wording. | * Create a pictorial array of a simple equation to translate wording. | ||
* Know the following vocabulary and symbols: +, -, X, ÷, =, linear, variable. | * Know the following vocabulary and symbols: +, -, X, ÷, =, linear, variable. | ||
|- | |- | ||
− | | | + | | colspan=3 |'''Suggested Instructional Strategies:''' |
* Task analysis | * Task analysis | ||
** Present the story problem based on a real-world, relevant context and provide a template for recording facts/operation to solve the real-world problem. | ** Present the story problem based on a real-world, relevant context and provide a template for recording facts/operation to solve the real-world problem. | ||
Line 1,118: | Line 1,108: | ||
|- | |- | ||
− | | | + | | colspan=3 |'''Suggested Supports and Scaffolds:''' |
* Counters | * Counters | ||
* Multiplication chart | * Multiplication chart | ||
* Calculator | * Calculator | ||
− | |||
|} | |} | ||
{|border=1 | {|border=1 | ||
− | | | + | | colspan=3 |'''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. |
|- | |- | ||
− | | | + | | colspan=2 |'''Strand: '''Patterns, Relationships and Functions |
| style="background-color:#e36c0a;"|'''Family: '''Proportional Relationships and Graphing''' ''' | | style="background-color:#e36c0a;"|'''Family: '''Proportional Relationships and Graphing''' ''' | ||
|- | |- | ||
− | | | + | | colspan=3 |'''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:''' |
* Match a point on a line as being part of a data set for a given line. | * Match a point on a line as being part of a data set for a given line. | ||
* Determine if a point is or is not on a line. | * Determine if a point is or is not on a line. | ||
− | | | + | ||'''Representation:''' |
* Identify coordinates (points) on a graph''' '''and in a data table. | * Identify coordinates (points) on a graph''' '''and in a data table. | ||
* Select a graph that represents a simple linear equation. | * Select a graph that represents a simple linear equation. | ||
Line 1,160: | Line 1,149: | ||
|- | |- | ||
− | | | + | | colspan=3 |'''Suggested Instructional Strategies:''' |
* Model lines, graphs, and coordinates of varying slopes; match coordinates to graphs. | * Model lines, graphs, and coordinates of varying slopes; match coordinates to graphs. | ||
* Explicitly teach the relationship between positive slope and a line that slopes up left to right and negative slope and a line that goes down left to right. | * Explicitly teach the relationship between positive slope and a line that slopes up left to right and negative slope and a line that goes down left to right. | ||
Line 1,172: | Line 1,161: | ||
|- | |- | ||
− | | | + | | colspan=3 |'''Suggested Supports and Scaffolds:''' |
* Grid paper with raised perpendicular lines (horizontal and vertical lines) and points | * Grid paper with raised perpendicular lines (horizontal and vertical lines) and points | ||
* Models | * Models | ||
Line 1,180: | Line 1,169: | ||
* Interactive white board | * Interactive white board | ||
− | |||
|} | |} | ||
+ | |||
+ | |||
+ | |||
+ | |||
+ | [[Category: Math]] | ||
+ | [[Category: Element Cards]] |
Latest revision as of 10:33, 16 September 2014
BACK TO Element Cards
Contents |
[edit] 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: 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
[edit] Websites
http://www.mathplayground.com/
[edit] 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/
[edit] 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:
| ||
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:
| ||
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:
| ||
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:
| ||
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:
| ||
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:
| ||
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:
| ||
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:
| ||
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.
| ||
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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