Element Cards Mathematics Patterns, Relations, and Functions
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− | | style="background-color:#FFFFFF;"|'''Suggested Instructional Strategies:''' | + | |colspan=3 style="background-color:#FFFFFF;"|'''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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− | | style="background-color:#FFFFFF;"|'''Suggested Supports and Scaffolds:''' | + | |colspan=3 style="background-color:#FFFFFF;"|'''Suggested Supports and Scaffolds:''' |
* Unit blocks of ones | * Unit blocks of ones | ||
* Colored tiles | * Colored tiles | ||
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|colspan=3 style="background-color:#FFFFFF;"|'''Suggested Instructional Strategies:''' | |colspan=3 style="background-color:#FFFFFF;"|'''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." | ||
* 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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| style="background-color:#FFFFFF;"|'''Strand:''' Patterns, Relations and Functions | | style="background-color:#FFFFFF;"|'''Strand:''' Patterns, Relations and Functions | ||
− | | style="background-color:# | + | | style="background-color:#fde9d9;"|'''Family: '''Problem Solving and Using Variables |
|- | |- | ||
− | | style="background-color:#FFFFFF;" | + | |colspan=3 style="background-color:#FFFFFF;"|'''Progress Indicator:'' '''E.PRF.1c''' '''Modeling problem solving situations that involve addition and subtraction of whole numbers using objects, diagrams, and symbols'' |
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− | | style="background-color:#FFFFFF;"|'''Suggested Instructional Strategies:''' | + | |colspan=3 style="background-color:#FFFFFF;"|'''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. | ||
* Compare two sets of unequal number of objects and ask the student which set has been added to (larger set) OR which set has objects taken away (smaller set). | * Compare two sets of unequal number of objects and ask the student which set has been added to (larger set) OR which set has objects taken away (smaller set). | ||
− | * Model-Lead-Test: | + | * Model-Lead-Test:* |
** Model "adding to" and "taking away" using objects (e.g., "Watch me add to this group of objects…Let's add to this group of objects together…You try adding to this group of objects.). | ** Model "adding to" and "taking away" using objects (e.g., "Watch me add to this group of objects…Let's add to this group of objects together…You try adding to this group of objects.). | ||
** Indicate that the new group of objects is larger if adding to and smaller if taking away. | ** Indicate that the new group of objects is larger if adding to and smaller if taking away. | ||
* Teach explicitly how to create a group/row/set/array 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/array of objects for a given number or for a number provided in a simple word problem. | ||
− | * 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. Ask 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. Ask 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). | ||
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|} | |} | ||
− | + | ||
+ | * Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies | ||
+ | |||
{|border=1 | {|border=1 | ||
− | | | + | |colspan=3 style="background-color:#FFFFFF;"|'''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.'' |
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− | | 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:#fde9d9;"|'''Family: '''Describing and Extending Patterns |
|- | |- | ||
− | | style="background-color:#FFFFFF;" | + | |colspan=3 style="background-color:#FFFFFF;"|'''Progress Indicator:''''' E.PRF.2d Representing and analyzing patterns and rules (e.g. doubling, adding 3) using words, tables, graphs, and models '' |
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− | | style="background-color:#FFFFFF;"|'''Suggested Instructional Strategies:''' | + | |colspan=3 style="background-color:#FFFFFF;"|'''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." | ||
* Ask students to determine if a rule exists for a provided pattern. (A pattern follows a predictable sequence OR There is no predictable sequence in this example, i.e., no rule can be stated.) | * Ask students to determine if a rule exists for a provided pattern. (A pattern follows a predictable sequence OR There is no predictable sequence in this example, i.e., no rule can be stated.) | ||
− | * Model-Lead-Test | + | * Model-Lead-Test* |
** Teach/model 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 +2 would have 1 in the first row, 3 in the second row, 5 in the third row, and 7 in the fourth row). | ** Teach/model 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 +2 would have 1 in the first row, 3 in the second row, 5 in the third row, and 7 in the fourth row). | ||
** Teach/model a growing multiplication problem using pictures (1 flower, 2 bees; 2 flowers, 4 bees; 3 flowers, 6 bees). | ** Teach/model a growing multiplication problem using pictures (1 flower, 2 bees; 2 flowers, 4 bees; 3 flowers, 6 bees). | ||
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− | | style="background-color:#FFFFFF;"|'''Suggested Supports and Scaffolds:''' | + | |colspan=3 style="background-color:#FFFFFF;"|'''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:Squarestack.JPG|98.5px]] | |
− | + | ||
− | + | ||
* Counters | * Counters | ||
* 2D and 3D shapes, objects, or pictures | * 2D and 3D shapes, objects, or pictures | ||
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|} | |} | ||
− | + | ||
+ | * Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies | ||
+ | |||
{|border=1 | {|border=1 | ||
− | | | + | |colspan=3 style="background-color:#FFFFFF;"|'''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.'' |
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− | | 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:#fde9d9;"|'''Family: '''Representing and Modeling Problems |
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− | | style="background-color:#FFFFFF;"|'''Suggested Instructional Strategies:''' | + | |colspan=3 style="background-color:#FFFFFF;"|'''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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* 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|68.5px]] | |
** e.g., Show 6 ÷ 2: | ** e.g., Show 6 ÷ 2: | ||
+ | ::[[Image:Circlesinovals.JPG|271.5px]] | ||
* 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 | ||
− | * Multiple exemplars for equal and not equal | + | * Multiple exemplars for equal and not equal* |
− | * Model-Lead-Test | + | * Model-Lead-Test* |
|- | |- | ||
− | | style="background-color:#FFFFFF;"|'''Suggested Supports and Scaffolds:''' | + | |colspan=3 style="background-color:#FFFFFF;"|'''Suggested Supports and Scaffolds:''' |
* Counters | * Counters | ||
* Number lines | * Number lines | ||
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|} | |} | ||
− | + | ||
+ | * Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies | ||
+ | |||
{|border=1 | {|border=1 | ||
− | | | + | |colspan=3 style="background-color:#FFFFFF;"|'''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. | |
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. | ||
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− | | 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:#e36c0a;"|'''Family: '''Proportional Relationships and Graphing''' ''' |
|- | |- | ||
− | | style="background-color:#FFFFFF;" | + | |colspan=3 style="background-color:#FFFFFF;"|'''Progress Indicator:'' '''M.PRF.1a''' '''Describing how multiplication or division changes a quantity, including with fractions or decimals '' |
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− | | style="background-color:#FFFFFF;"|'''Suggested Instructional Strategies:''' | + | |colspan=3 style="background-color:#FFFFFF;"|'''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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− | | style="background-color:#FFFFFF;"|'''Suggested Supports and Scaffolds:''' | + | |colspan=3 style="background-color:#FFFFFF;"|'''Suggested Supports and Scaffolds:''' |
* Counters (chips) | * Counters (chips) | ||
* Picture and objects | * Picture and objects | ||
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{|border=1 | {|border=1 | ||
− | | | + | |colspan=3 style="background-color:#FFFFFF;"|'''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. |
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− | | style="background-color:#FFFFFF;"|'''Strand:''' Patterns, Relationships and Functions | + | |colspan=2 style="background-color:#FFFFFF;"|'''Strand:''' Patterns, Relationships and Functions |
− | | style="background-color:# | + | | style="background-color:#fabf8f;"|'''Family: '''Problem Solving and Using Variables |
|- | |- | ||
− | | style="background-color:#FFFFFF;" | + | |colspan=3 style="background-color:#FFFFFF;"|'''Progress Indicator:'' '''M.PRF.1d''' '''Using symbolic equations to summarize how the quantity of something changes '' |
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− | | style="background-color:#FFFFFF;"|'''Suggested Instructional Strategies:''' | + | |colspan=3 style="background-color:#FFFFFF;"|'''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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− | | style="background-color:#FFFFFF;"|'''Suggested Supports and Scaffolds:''' | + | |colspan=3 style="background-color:#FFFFFF;"|'''Suggested Supports and Scaffolds:''' |
* Pictures and manipulatives | * Pictures and manipulatives | ||
* Template for solving an equation | * Template for solving an equation | ||
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{|border=1 | {|border=1 | ||
− | | | + | |colspan=3 style="background-color:#FFFFFF;"|'''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."'' |
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− | | style="background-color:#FFFFFF;"|'''Strand: '''Patterns, Relationships and Functions | + | | colspan=2 style="background-color:#FFFFFF;"|'''Strand: '''Patterns, Relationships and Functions |
− | | style="background-color:# | + | | style="background-color:#e36c0a;"|'''Family: '''Proportional Relationships and Graphing''' ''' |
|- | |- | ||
− | | style="background-color:#FFFFFF;" | + | | colspan=3 style="background-color:#FFFFFF;"|'''Progress Indicator:'' '''M.PRF.1c''' '''Comparing two rates and evaluating them for a given situation (e.g., best value) '' |
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− | | style="background-color:#FFFFFF;"|'''Suggested Instructional Strategies:''' | + | | colspan=2 style="background-color:#FFFFFF;"|'''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." |
Revision as of 16:57, 15 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:
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Representation:
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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:
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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:
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Representation:
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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:
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Representation:
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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:
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Representation:
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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:
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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:
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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:
Day 1 2 3 4 Total Books Read 2
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Suggested Supports and Scaffolds:
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\* Refer to Instructional Resource Guide for full descriptions and examples of systematic instructional strategies
CCSS: 7.EE.4 Use variables to represent quantities in a real‐world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
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CCC: | 7.PRF.1g2 | Use variables to represent quantities in a real‐world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities |
Strand: Patterns, Relationships and Functions | Family: Problem Solving and Using Variables | |
Progress Indicator: M.PRF.1g Modeling, solving, and explaining contextualized problems using various representations such as graphs, tables, functions, and equations | ||
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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 | ||
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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 | ||
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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 | ||
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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 | ||
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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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