Element Cards Mathematics Patterns, Relations, and Functions
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|style="background-color:#FFFFFF;" 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. | |style="background-color:#FFFFFF;" 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. | ||
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− | | | + | |style="background-color:#FFFFFF;"|'''CCC:''' |
− | | | + | |style="background-color:#FFFFFF;"|K.PRF.1c1 |
− | | | + | |style="background-color:#FFFFFF;"|Solve one step addition and subtraction word problems, and add and subtract within 10 using objects, drawings, pictures. |
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− | | | + | |style="background-color:#FFFFFF;"|'''Essential Understandings''' |
− | | | + | |style="background-color:#FFFFFF;"|'''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. | ||
− | | | + | |style="background-color:#FFFFFF;"|'''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 style="background-color:#FFFFFF;"|'''Suggested Instructional Strategies:''' | + | |colspan=3 style="background-color:#FFFFFF;"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. | ||
** Rearrange the objects and ask the student how many object there are (the student understands cardinality of numbers if s/he states the same number without recounting the objects). | ** Rearrange the objects and ask the student how many object there are (the student understands cardinality of numbers if s/he states the same number without recounting the objects). | ||
* Teach explicitly how to create a group/row/set of objects for a given number or for a number provided in a simple word problem. | * Teach explicitly how to create a group/row/set of objects for a given number or for a number provided in a simple word problem. | ||
− | * Multiple Exemplar Training | + | * Multiple Exemplar Training* |
** An array/row: "This is a group/row of three apples. This is another group/row of three apples. This is another group/row of three apples. This is one apple. Show me a group/row of three apples." | ** An array/row: "This is a group/row of three apples. This is another group/row of three apples. This is another group/row of three apples. This is one apple. Show me a group/row of three apples." | ||
− | * Example / Nonexample | + | * Example / Nonexample* |
** Present a row of objects (≤ 10). Present a second row of objects that has a different number of objects. Ask the student to select the row with a specified number of objects. | ** Present a row of objects (≤ 10). Present a second row of objects that has a different number of objects. Ask the student to select the row with a specified number of objects. | ||
** Present three rows of objects (≤ 10), two that are equal and one that is not equal. As the student to match the two rows that both include the same number of specified objects (e.g., a row of three hats, a row of three hats, a row of 5 shoes). | ** Present three rows of objects (≤ 10), two that are equal and one that is not equal. As the student to match the two rows that both include the same number of specified objects (e.g., a row of three hats, a row of three hats, a row of 5 shoes). | ||
− | * Use System of Least Prompts to form an array (group/row) given a number: | + | * Use System of Least Prompts to form an array (group/row) given a number:* |
* "Make a row/group of three pencils." The student responds correctly. "Good work. You made a row/group of three pencils." OR The student doesn't respond. Wait 3-5 seconds and provide a gesture prompt by pointing to the pencils, OR The student doesn't respond. Wait 3 -5 seconds and provide a verbal prompt. "Pick up three pencils. Make a group of three pencils." OR The student makes an error; provide a physical prompt. Take the student's hand and give him or her three pencils and help them make a row of pencils. | * "Make a row/group of three pencils." The student responds correctly. "Good work. You made a row/group of three pencils." OR The student doesn't respond. Wait 3-5 seconds and provide a gesture prompt by pointing to the pencils, OR The student doesn't respond. Wait 3 -5 seconds and provide a verbal prompt. "Pick up three pencils. Make a group of three pencils." OR The student makes an error; provide a physical prompt. Take the student's hand and give him or her three pencils and help them make a row of pencils. | ||
− | * Model-Lead-Test ("Watch me make a row of four books. Let's make a row of four books. Now you try to make a row of four books.") | + | * Model-Lead-Test ("Watch me make a row of four books. Let's make a row of four books. Now you try to make a row of four books.")* |
− | * Model-Lead-Test ("Here is a story problem. It says there are seven dogs. Watch me make a set of seven dogs to match the story problem. Let's make a set of seven dogs together. Now you try to make a set of seven dogs."); repeat with the other number of object in the story problem. | + | * Model-Lead-Test ("Here is a story problem. It says there are seven dogs. Watch me make a set of seven dogs to match the story problem. Let's make a set of seven dogs together. Now you try to make a set of seven dogs."); repeat with the other number of object in the story problem.* |
* Task Analysis: Use two rows of pictures or objects to model a one step addition and subtraction problems. | * Task Analysis: Use two rows of pictures or objects to model a one step addition and subtraction problems. | ||
** Present a simple one step addition problem (e.g., The boys have four backpacks. The girls have two backpacks. How many backpacks to the boys and girls have?) | ** Present a simple one step addition problem (e.g., The boys have four backpacks. The girls have two backpacks. How many backpacks to the boys and girls have?) | ||
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− | |colspan=3 style="background-color:#FFFFFF;"|'''Suggested Supports and Scaffolds:''' | + | |colspan=3 style="background-color:#FFFFFF;"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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|colspan=2 style="background-color:#FFFFFF;"|'''Strand: '''Patterns, Relations and Functions | |colspan=2 style="background-color:#FFFFFF;"|'''Strand: '''Patterns, Relations and Functions | ||
− | |style="background-color:# | + | |style="background-color:#fbd4b4;"|'''Family: '''Describing and Extending Patterns |
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− | |colspan=3 style="background-color:#FFFFFF;"|'''Suggested Instructional Strategies:''' | + | |colspan=3 style="background-color:#FFFFFF;"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]]). 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). | ||
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− | |colspan=3 style="background-color:#FFFFFF;"|'''Suggested Supports and Scaffolds:''' | + | |colspan=3 style="background-color:#FFFFFF;"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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− | |colspan=3 style="background-color:#FFFFFF;"|'''Suggested Instructional Strategies:''' | + | |colspan=3 style="background-color:#FFFFFF;"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 style="background-color:#FFFFFF;"|'''Suggested Supports and Scaffolds:''' | + | |colspan=3 style="background-color:#FFFFFF;"colspan=3 |'''Suggested Supports and Scaffolds:''' |
* Counters (chips) | * Counters (chips) | ||
* Picture and objects | * Picture and objects | ||
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| style="background-color:#FFFFFF;"|'''Strand: '''Patterns, Relations and Functions | | style="background-color:#FFFFFF;"|'''Strand: '''Patterns, Relations and Functions | ||
− | | style="background-color:# | + | | style="background-color:#fbd4b4;"|'''Family: '''Describing and Extending Patterns |
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− | |colspan=3 style="background-color:#FFFFFF;"|'''Suggested Instructional Strategies:''' | + | |colspan=3 style="background-color:#FFFFFF;"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. | ||
* Teach explicitly how a growing pattern increases/changes by the same number (+1 or +2) pattern using colors, shapes, or objects | * Teach explicitly how a growing pattern increases/changes by the same number (+1 or +2) pattern using colors, shapes, or objects | ||
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− | |colspan=3 style="background-color:#FFFFFF;"|'''Suggested Supports and Scaffolds:''' | + | |colspan=3 style="background-color:#FFFFFF;"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| | + | :[[Image:Squarestack.JPG|98px]] |
* Interactive whiteboard or other technology to model growing patterns | * Interactive whiteboard or other technology to model growing patterns | ||
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− | |colspan=3 style="background-color:#FFFFFF;"|'''Suggested Instructional Strategies:''' | + | |colspan=3 style="background-color:#FFFFFF;"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:Tchartoranges.JPG| | + | ::[[Image:Tchartoranges.JPG|258px]] |
* 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 style="background-color:#FFFFFF;"|'''Suggested Supports and Scaffolds:''' | + | |colspan=3 style="background-color:#FFFFFF;"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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| style="background-color:#FFFFFF;"|'''Strand:''' Patterns, Relations and Functions | | style="background-color:#FFFFFF;"|'''Strand:''' Patterns, Relations and Functions | ||
− | | style="background-color:# | + | | style="background-color:#fabf8f;"|'''Family: '''Problem Solving and Using Variables |
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− | |colspan=3 style="background-color:#FFFFFF;"|'''Suggested Instructional Strategies:''' | + | |colspan=3 style="background-color:#FFFFFF;"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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− | | style="background-color:#FFFFFF;"|'''Suggested Supports and Scaffolds:''' | + | | style="background-color:#FFFFFF;"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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− | |colspan=3 style="background-color:#FFFFFF;"|'''Suggested Instructional Strategies:''' | + | |colspan=3 style="background-color:#FFFFFF;"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 style="background-color:#FFFFFF;"|'''Suggested Supports and Scaffolds:''' | + | |colspan=3 style="background-color:#FFFFFF;"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., X3 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 or multiplication (e.g., X3 growing pattern) | ||
− | :[[Image: | + | :[[Image:Squarestack2.JPG|221px]] |
* Counters | * Counters | ||
* 2D and 3D shapes, objects, or pictures | * 2D and 3D shapes, objects, or pictures | ||
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|colspan=2 style="background-color:#FFFFFF;"|'''Strand: '''Patterns, Relations and Functions | |colspan=2 style="background-color:#FFFFFF;"|'''Strand: '''Patterns, Relations and Functions | ||
− | | style="background-color:# | + | | style="background-color:#fbd4b4;"|'''Family: '''Representing and Modeling Problems |
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− | |colspan=3 style="background-color:#FFFFFF;"|'''Suggested Instructional Strategies:''' | + | |colspan=3 style="background-color:#FFFFFF;"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." | ||
* Teach multiple ways of describing multiplication (e.g., 2 x 2 = 4; 2 times 2 = 4; a 2 by 2 array is 4). | * Teach multiple ways of describing multiplication (e.g., 2 x 2 = 4; 2 times 2 = 4; a 2 by 2 array is 4). | ||
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* Use arrays to model multiplication and division problems. | * Use arrays to model multiplication and division problems. | ||
** Show (2 X 3): two (number of groups/rows) times three (counters in each group); using a rectangle, the height is the number of rows and the base is the number of units in each row: | ** Show (2 X 3): two (number of groups/rows) times three (counters in each group); using a rectangle, the height is the number of rows and the base is the number of units in each row: | ||
− | ::[[Image:3x2circles.JPG| | + | ::[[Image:3x2circles.JPG|69px]] |
** e.g., Show 6 ÷ 2: | ** e.g., Show 6 ÷ 2: | ||
− | ::[[Image:Circlesinovals.JPG| | + | ::[[Image:Circlesinovals.JPG|272px]] |
* 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 style="background-color:#FFFFFF;"|'''Suggested Supports and Scaffolds:''' | + | |colspan=3 style="background-color:#FFFFFF;"colspan=3 |'''Suggested Supports and Scaffolds:''' |
* Counters | * Counters | ||
* Number lines | * Number lines | ||
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− | |colspan=3 style="background-color:#FFFFFF;"|'''Suggested Instructional Strategies:''' | + | |colspan=3 style="background-color:#FFFFFF;"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: | ||
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− | |colspan=3 style="background-color:#FFFFFF;"|'''Suggested Supports and Scaffolds:''' | + | |colspan=3 style="background-color:#FFFFFF;"colspan=3 |'''Suggested Supports and Scaffolds:''' |
* Counters (chips) | * Counters (chips) | ||
* Picture and objects | * Picture and objects | ||
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− | | | + | |style="background-color:#FFFFFF;"|'''Strand:''' Patterns, Relationships and Functions |
− | | style="background-color:#fabf8f;"|'''Family: '''Problem Solving and Using Variables | + | |colspan=2 style="background-color:#fabf8f;"|'''Family: '''Problem Solving and Using Variables |
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− | |colspan=3 style="background-color:#FFFFFF;"|'''Suggested Instructional Strategies:''' | + | |colspan=3 style="background-color:#FFFFFF;"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 | ||
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− | |colspan=3 style="background-color:#FFFFFF;"|'''Suggested Supports and Scaffolds:''' | + | |colspan=3 style="background-color:#FFFFFF;"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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− | | | + | |style="background-color:#FFFFFF;"|'''Strand: '''Patterns, Relationships and Functions |
− | | style="background-color:#e36c0a;"|'''Family: '''Proportional Relationships and Graphing''' ''' | + | |colspan=2 style="background-color:#e36c0a;"|'''Family: '''Proportional Relationships and Graphing''' ''' |
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− | | colspan=2 style="background-color:#FFFFFF;"|'''Suggested Instructional Strategies:''' | + | | colspan=2 style="background-color:#FFFFFF;"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." | ||
** Example for representing ratios: There are three chairs for one/each table. The ratio is''' 3 to 1'''. The ratio is '''3:1'''. The ratio is '''3/1.''' The ratio is not '''1 to 3.''' Show me the ratio for three chairs for one table. | ** Example for representing ratios: There are three chairs for one/each table. The ratio is''' 3 to 1'''. The ratio is '''3:1'''. The ratio is '''3/1.''' The ratio is not '''1 to 3.''' Show me the ratio for three chairs for one table. | ||
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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]] | |
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+ | :* Here is a way to show the ratio / compare the two numbers: (___: ___) | ||
+ | :* Put the numbers of days here. Put the number of books here. | ||
− | + | :* You showed the ratio of days to books. Show/tell me the ratio. | |
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* Teach what" twice as many" (2 times the original) or "three times as many" (3 times the original) means. | * Teach what" twice as many" (2 times the original) or "three times as many" (3 times the original) means. | ||
* Multiple Exemplar Training example:\* | * Multiple Exemplar Training example:\* | ||
* 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]] | ||
− | + | * This picture shows the ratio.[[Image:4squareratio.JPG|100px]] | |
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− | * This picture shows the ratio. | + | |
* This does not show the ratio. | * This does not show the ratio. | ||
− | + | [[Image:4squareratio.JPG|100px]] | |
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* Show me a picture that shows the ratio 3:1. | * Show me a picture that shows the ratio 3:1. | ||
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− | | style="background-color:#FFFFFF;"|'''Suggested Supports and Scaffolds:''' | + | | style="background-color:#FFFFFF;"colspan=3 |'''Suggested Supports and Scaffolds:''' |
* Unit blocks of ones | * Unit blocks of ones | ||
* Colored tiles | * Colored tiles | ||
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|} | |} | ||
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+ | * Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies | ||
+ | |||
+ | |||
{|border=1 | {|border=1 | ||
− | | | + | |colspan=3style="background-color:#FFFFFF;"|'''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.'' | ||
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| style="background-color:#FFFFFF;"|'''Strand:''' Patterns, Relationships and Functions | | style="background-color:#FFFFFF;"|'''Strand:''' Patterns, Relationships and Functions | ||
− | | style="background-color:# | + | | style="background-color:#fabf8f;"|'''Family: '''Problem Solving and Using Variables |
|- | |- | ||
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|- | |- | ||
− | | style="background-color:#FFFFFF;"|'''Suggested Instructional Strategies:''' | + | | style="background-color:#FFFFFF;"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. | ||
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|- | |- | ||
− | | style="background-color:#FFFFFF;"|'''Suggested Supports and Scaffolds:''' | + | | style="background-color:#FFFFFF;"colspan=3 |'''Suggested Supports and Scaffolds:''' |
* Counters | * Counters | ||
* Number lines | * Number lines | ||
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{|border=1 | {|border=1 | ||
− | | | + | |colspan=3 style="background-color:#FFFFFF;"|'''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'' |
|- | |- | ||
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| style="background-color:#FFFFFF;"|'''Strand: '''Patterns, Relationships and Functions | | style="background-color:#FFFFFF;"|'''Strand: '''Patterns, Relationships and Functions | ||
− | | style="background-color:# | + | | style="background-color:#e36c0a;"|'''Family: '''Proportional Relationships and Graphing''' ''' |
|- | |- | ||
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|- | |- | ||
− | | style="background-color:#FFFFFF;"|'''Suggested Instructional Strategies:''' | + | | style="background-color:#FFFFFF;"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). | ||
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## The '''5''' is the whole. Write '''5''' in the proportion. | ## The '''5''' is the whole. Write '''5''' in the proportion. | ||
## 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]] | ||
+ | |||
# Fill in the numbers on each side. | # Fill in the numbers on each side. | ||
− | + | ||
− | + | :[[Image:Partpercentage2.JPG|383px]] | |
− | + | ||
− | + | # Use the calculator to multiply the numbers on each side of the equation. | |
+ | # Use the calculator to divide each side of the equation by 5. | ||
+ | # What percent is '''X'''? Write that number (3 is ___% of 5). | ||
* Explicit instruction on using ratio tables to find a percent of a quantity | * Explicit instruction on using ratio tables to find a percent of a quantity | ||
* Explicit instruction on cross multiplying | * Explicit instruction on cross multiplying | ||
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{|border=1 | {|border=1 | ||
− | | | + | |style="background-color:#FFFFFF;"colspan=3 |'''Suggested Supports and Scaffolds:''' |
* Highlight text that provides important information/vocabulary | * Highlight text that provides important information/vocabulary | ||
* Counters | * Counters | ||
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{|border=1 | {|border=1 | ||
− | | | + | |colspan=3 style="background-color:#FFFFFF;"|'''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. | ||
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| style="background-color:#FFFFFF;"|'''Strand:''' Patterns, Relationships and Functions | | style="background-color:#FFFFFF;"|'''Strand:''' Patterns, Relationships and Functions | ||
− | | style="background-color:# | + | | style="background-color:#fabf8f;"|'''Family: '''Problem Solving and Using Variables |
|- | |- | ||
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|- | |- | ||
− | | style="background-color:#FFFFFF;"|'''Suggested Instructional Strategies:''' | + | | style="background-color:#FFFFFF;"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?) | ||
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|- | |- | ||
− | | style="background-color:#FFFFFF;"|'''Suggested Supports and Scaffolds:''' | + | | style="background-color:#FFFFFF;"colspan=3 |'''Suggested Supports and Scaffolds:''' |
* Counters | * Counters | ||
* Grids or graphic organizers to create arrays | * Grids or graphic organizers to create arrays | ||
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{|border=1 | {|border=1 | ||
− | | | + | |colspan=3 style="background-color:#FFFFFF;"|'''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.'' | ||
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| style="background-color:#FFFFFF;"|'''Strand:''' Patterns, Relationships and Functions | | style="background-color:#FFFFFF;"|'''Strand:''' Patterns, Relationships and Functions | ||
− | | style="background-color:# | + | |colspan=2 style="background-color:#e36c0a;"|'''Family: '''Proportional Relationships and Graphing''' ''' |
|- | |- | ||
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|- | |- | ||
− | | style="background-color:#FFFFFF;"|'''Suggested Instructional Strategies:''' | + | | style="background-color:#FFFFFF;"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). | ||
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|- | |- | ||
− | | style="background-color:#FFFFFF;"|'''Suggested Supports and Scaffolds:''' | + | | style="background-color:#FFFFFF;"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 1,025: | Line 1,008: | ||
|- | |- | ||
− | | style="background-color:#FFFFFF;"|'''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. | + | |colspan=3 style="background-color:#FFFFFF;"|'''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. |
|- | |- | ||
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| style="background-color:#FFFFFF;"|'''Strand:''' Patterns, Relationships and Functions | | style="background-color:#FFFFFF;"|'''Strand:''' Patterns, Relationships and Functions | ||
− | | style="background-color:# | + | |colspan=2 style="background-color:#e36c0a;"|'''Family: '''Proportional Relationships and Graphing''' ''' |
|- | |- | ||
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|- | |- | ||
− | | style="background-color:#FFFFFF;"|'''Suggested Instructional Strategies:''' | + | | style="background-color:#FFFFFF;"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. | ||
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|- | |- | ||
− | | style="background-color:#FFFFFF;"|'''Suggested Supports and Scaffolds:''' | + | | style="background-color:#FFFFFF;"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 | ||
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{|border=1 | {|border=1 | ||
− | | | + | |colspan=3 style="background-color:#FFFFFF;"|'''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.'' |
|- | |- | ||
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| style="background-color:#FFFFFF;"|'''Strand:''' Patterns, Relationships and Functions | | style="background-color:#FFFFFF;"|'''Strand:''' Patterns, Relationships and Functions | ||
− | | style="background-color:# | + | |colspan=2 style="background-color:#fabf8f;"|'''Family: '''Problem Solving and Using Variables |
|- | |- | ||
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|- | |- | ||
− | | style="background-color:#FFFFFF;"|'''Suggested Instructional Strategies:''' | + | | style="background-color:#FFFFFF;"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. | ||
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|- | |- | ||
− | | style="background-color:#FFFFFF;"|'''Suggested Supports and Scaffolds:''' | + | | style="background-color:#FFFFFF;"colspan=3 |'''Suggested Supports and Scaffolds:''' |
* Counters | * Counters | ||
* Multiplication chart | * Multiplication chart | ||
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{|border=1 | {|border=1 | ||
− | | | + | |colspan=3 style="background-color:#FFFFFF;"|'''CCSS:''' F.LE.1 Distinguish between situations that can be modeled with linear functions and with exponential functions. |
|- | |- | ||
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| style="background-color:#FFFFFF;"|'''Strand: '''Patterns, Relationships and Functions | | style="background-color:#FFFFFF;"|'''Strand: '''Patterns, Relationships and Functions | ||
− | | style="background-color:# | + | |colspan=2 style="background-color:#e36c0a;"|'''Family: '''Proportional Relationships and Graphing''' ''' |
|- | |- | ||
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|- | |- | ||
− | | style="background-color:#FFFFFF;"|'''Suggested Instructional Strategies:''' | + | | style="background-color:#FFFFFF;"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. | ||
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|- | |- | ||
− | | style="background-color:#FFFFFF;"| | + | |colspan=3 style="background-color:#FFFFFF;"|'''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 |
Revision as of 16:27, 18 November 2013
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: Ratio and Proportions
NCSC Content Module: Linear Equations
NCSC Content Module: Expressions
NCSC Content Module: Functions
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:
|
Representation:
|
Suggested Instructional Strategies:
| ||
Suggested Supports and Scaffolds:
|
- 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:
|
Representation:
|
Suggested Instructional Strategies:
| ||
Suggested Supports and Scaffolds:
|
- 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:
|
Representation:
|
Suggested Instructional Strategies:
| ||
Suggested Supports and Scaffolds:
|
- 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:
|
Representation:
|
Suggested Instructional Strategies:
| ||
Suggested Supports and Scaffolds:
|
- 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:
|
Representation:
|
Suggested Instructional Strategies:
| ||
Suggested Supports and Scaffolds:
|
- 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:
|
Representation:
|
Suggested Instructional Strategies:
| ||
Suggested Supports and Scaffolds:
|
- 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:
|
Representation:
|
Suggested Instructional Strategies:
| ||
Suggested Supports and Scaffolds:
|
- 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:
|
Representation:
|
Suggested Instructional Strategies:
| ||
Suggested Supports and Scaffolds:
|
- 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:
|
Representation:
|
Suggested Instructional Strategies:
| ||
Suggested Supports and Scaffolds:
|
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:
|
Representation:
|
Suggested Instructional Strategies:
| ||
Suggested Supports and Scaffolds:
|
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:
|
Representation:
|
Suggested Instructional Strategies:
| ||
Suggested Supports and Scaffolds:
|
- 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:
|
Representation:
|
Suggested Instructional Strategies:
| ||
Suggested Supports and Scaffolds:
|
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:
|
Representation:
|
Suggested Instructional Strategies:
|
Suggested Supports and Scaffolds:
|
CCSS: 8.EE.7 Solve linear equations in one variable.
| ||
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:
|
Representation:
|
Suggested Instructional Strategies:
| ||
Suggested Supports and Scaffolds:
|
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:
|
Representation:
|
Suggested Instructional Strategies:
| ||
Suggested Supports and Scaffolds:
| ||
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:
|
Representation:
|
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 | ||
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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 '' | ||
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