Conjecturing About Functions
Common Core State Standards
Math 
Math 
8 
8th Grade 
F 
Functions: 
B 
Use functions to model relationships between quantities. 
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. 
Download Common Core State Standards (PDF 1.2 MB) 
Common Core State Standards
Math 
Math 
Practice 
Mathematical Practice Standards 
MP2 
Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualizeto abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. 
Download Common Core State Standards (PDF 1.2 MB) 
Common Core State Standards
Math 
Math 
Practice 
Mathematical Practice Standards 
MP3 
Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, andif there is a flaw in an argumentexplain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. 
Download Common Core State Standards (PDF 1.2 MB) 

Lesson Idea (Common Core)Leprechaun Traps: Addition Within 100Grades K2 / Math / ReasoningMath.1.NBT.C.4 / Math.Practice.MP2 / Math.Practice.MP3
 529
 61

Lesson Idea (Common Core)12 O'Quad High: Trigonometry in FlightGrades 912 / Math / ReasoningMath.F.TF.5 / Math.Practice.MP2 / Math.Practice.MP3
 171
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Lesson Idea (Common Core)Beyond Fingers: Place Value & the Numbers 1119Grades K2 / Math / ReasoningMath.K.NBT.A.1 / Math.Practice.MP2 / Math.Practice.MP3
 638
 94

Lesson Idea (Common Core)Multiplying Whole Numbers & FractionsGrades 35 / Math / ReasoningMath.4.NF.B.4b / Math.Practice.MP2 / Math.Practice.MP3
 225
 35

Lesson Idea (Common Core)A Passion for FractionsGrades 35 / Math / ReasoningMath.5.NF.B.4b / Math.Practice.MP2 / Math.Practice.MP3
 517
 59
 Lesson Objective
 Analyze patterns and represent functions
 Length
 9 min
 Questions to Consider
 How do students represent functions in multiple ways?
 How does noticing structure prepare students for making conjectures?
 What can you learn from Ms. McPhillips about using the Common Core with students?
 Common Core Standards
 Math.8.F.B.4, Math.Practice.MP2, Math.Practice.MP3
Teacher & School Info

Audra McPhillips
 School Details
 John F. Deering Middle School West Warwick, RI
 Population
 1,011 students
 District Spending
 $13,164
Supporting Materials

Conjecturing About Functions Transcript

Lesson Plan: Conjecturing About Functions.PDF

Lesson Plan: Growing Dots Days One and Two.PDF

Lesson Plan: Growing Dots Days Three and Four.PDF

Lesson Plan: Growing Dots Exit Slip.PDF

Common Core State Standards Math Practice Charts
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Lesson Idea (Common Core) Conjecturing About Functions
Grades 68 / Math / Reasoning