1. Welcome 7th grade educators
Help yourself to breakfast.
Please have a seat in a desk with materials.
Write your name on the front and back of the name tent.

2. Unpacking the standards
7th Grade
Unpacking the standards
iZone Retreat
University of Memphis
Thursday, June 18, 2015
Presented by:
Angela Brumfield
(901)

3. Introductions
Please tell us your name and school. Tell us one thing you’re most excited about and most concerned about.

4. TN ACADEMIC STANDARDS

5. Domains by Grade Bands K 1 2 3 4 5 6 7 8 Geometry Measurement & Data
Statistics & Probability
No. and Operations Base 10
The Number System
Operations and Algebraic
Thinking
Operations and Algebraic Thinking
Expressions and Equations
Counting
Cardinality
Number and Operations
Fractions
Ratios and
Proportions
Relationships
Functions

6. Ratios and Proportional Relationships 7.RP
Analyze proportional relationships and use them to solve real-world and mathematical problems.
The Number System NS
Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
Expressions and Equations EE
Use properties of operations to generate equivalent expressions.
Solve real-life and mathematical problems using numerical and algebraic expressions and equations and analyze quantitative relationships between dependent and independent variables.
Geometry G
Draw, construct and describe geometrical figures and describe the relationships between them.
Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
Statistics and Probability SP
Use random sampling to draw inferences about a population.
Draw informal comparative inferences about two populations.
Investigate chance processes and develop, use, and evaluate probability models.

7. Critical areas
Developing understanding of and applying proportional relationships
Developing understanding of operations with rational numbers and working with expressions and linear equations
3. Solving problems involving scale drawings and informal geometric constructions, and working with two- and three-dimensional shapes to solve problems involving area, surface area, and volume
4. Drawing inferences about populations based on samples

8. FLUENCY
“Computational fluency refers to having efficient and accurate methods for computing. Students exhibit computational fluency when they demonstrate flexibility in the computational methods they choose, understand and can explain these methods, and produce accurate answers efficiently.
7.NS.A.1,2 - Fluency with rational number arithmetic
7.EE.B.3 - Solve multistep problems with positive and negative rational numbers in any form
7.EE.B.4 - Solve one‐variable equations of the form px + q = r and p(x + q) = r fluently

9. MATHEMATICAL PRACTICES
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.

10. mp 1 Make sense of problems and persevere in solving them
In grade 7, students solve problems involving ratios and rates and discuss how they solved the problems. Students solve real world problems through the application of algebraic and geometric concepts. Students seek the meaning of a problem and look for efficient ways to represent and solve it. They may check their thinking by asking themselves, “What is the most efficient way to solve the problem?”, “Does this make sense?”, and “Can I solve the problem in a different way?”.

11. Mp 2 Reason abstractly and quantitatively
In grade 7, students represent a wide variety of real world contexts through the use of real numbers and variables in mathematical expressions, equations, and inequalities. Students contextualize to understand the meaning of the number or variable as related to the problem and decontextualize to manipulate symbolic representations by applying properties of operations.

12. Mp 3 Construct viable arguments and critique the reasoning of others
In grade 7, students construct arguments using verbal or written explanations accompanied by expressions, equations, inequalities, models, and graphs, tables, and other data displays (i.e. box plots, dot plots, histograms, etc.). The students further refine their mathematical communication skills through mathematical discussions in which they critically evaluate their own thinking and the thinking of other students. They pose questions like “How did you get that?”, “Why is that true?”, “Does that always work?”. They explain their thinking to others and respond to others’ thinking.

13. Mp 4 Model with mathematics
In grade 7, students model problem situations symbolically, graphically, tabularly, and contextually. Students form expressions, equations, or inequalities from real world contexts and connect symbolic and graphical representations. Students explore covariance and represent two quantities simultaneously. They use measures of center and variability and data displays (i.e. box plots and histograms) to draw inferences, make comparisons and formulate predictions. Students use experiments or simulations to generate data sets and create probability models. Students need many opportunities to connect and explain the connections between the different representations. They should be able to use all of these representations as appropriate to any problem’s context.

14. Mp 5 Use appropriate tools strategically
Students consider available tools (including estimation and technology) when solving a mathematical problem and decide when certain tools might be helpful. For instance, students in grade 7 may decide to represent similar data sets using dot plots with the same scale to visually compare the center and variability of the data. Students might use physical objects or applets to generate probability data and use graphing calculators or spreadsheets to manage and represent data in different forms.

15. Mp 6 Attend to precision
In grade 7, students continue to refine their mathematical communication skills by using clear and precise language in their discussions with others and in their own reasoning. Students define variables, specify units of measure, and label axes accurately. Students use appropriate terminology when referring to rates, ratios, probability models, geometric figures, data displays, and components of expressions, equations or inequalities.

16. Mp 7 Look for and make use of structure
Students routinely seek patterns or structures to model and solve problems. For instance, students recognize patterns that exist in ratio tables making connections between the constant of proportionality in a table with the slope of a graph. Students apply properties to generate equivalent expressions (i.e x = 3 (2 + x) by distributive property) and solve equations (i.e. 2c + 3 = 15, 2c = 12 by subtraction property of equality), c = 6 by division property of equality). Students compose and decompose two- and three-dimensional figures to solve real world problems involving scale drawings, surface area, and volume. Students examine tree diagrams or systematic lists to determine the sample space for compound events and verify that they have listed all possibilities.

17. Mp 8 Look for and express regularity in repeated reasoning
In grade 7, students use repeated reasoning to understand algorithms and make generalizations about patterns. During multiple opportunities to solve and model problems, they may notice that a/b ÷ c/d = ad/bc and construct other examples and models that confirm their generalization. They extend their thinking to include complex fractions and rational numbers. Students formally begin to make connections between covariance, rates, and representations showing the relationships between quantities. They create, explain, evaluate, and modify probability models to describe simple and compound events.

18. Small group discussion
What are some ways that we, as teachers, can ensure that our students are given the opportunity to utilize the mathematical practices?

19. 8 mathematics teaching practices
Establish mathematics goals to focus learning.
Effective teaching of mathematics establishes clear goals for the mathematics that students are learning, situates goals within learning progressions, and uses the goals to guide instructional decisions.
Implement tasks that promote reasoning and problem solving.
Effective teaching of mathematics engages students in solving and discussing tasks that promote mathematical reasoning and problem solving and allow multiple entry points and varied solution strategies.
Use and connect mathematical representations.
Effective teaching of mathematics engages students in making connections among mathematical representations to deepen understanding of mathematics concepts and procedures and as tools for problem solving.
Facilitate meaningful mathematical discourse.
Effective teaching of mathematics facilitates discourse among students to build shared understanding of mathematical ideas by analyzing and comparing student approaches and arguments.

20. 5. Pose purposeful questions.
Effective teaching of mathematics uses purposeful questions to assess and advance students’ reasoning and sense making about important mathematical ideas and relationships.
Build procedural fluency from conceptual understanding.
Effective teaching of mathematics builds fluency with procedures on a foundation of conceptual understanding so that students, over time, become skillful in using procedures flexibly as they solve contextual and mathematical problems.
Support productive struggle in learning mathematics.
Effective teaching of mathematics consistently provides students, individually and collectively, with opportunities and supports to engage in productive struggle as they grapple with mathematical ideas and relationships.
Elicit and use evidence of student thinking.
Effective teaching of mathematics uses evidence of student thinking to assess progress toward mathematical understanding and to adjust instruction continually in ways that support and extend learning.

21. Think, write, pair, share
Think about the teaching mathematics practices. Which one(s) do you currently use in your classroom?
Write how this practice is used in your classroom.
Pair up with a shoulder partner and discuss the teaching mathematic(s) practice that you wrote about.
Share with the group.

22. 7.NS.A.1a
7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
a. Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.

23. 7.NS.A.1a example
Which of the following describe a situation where the combination results in zero? There may be more than one correct answer. A. The Saints gained 8 yards on a first down, and lost 6 yards on the second down. B. Hole #5 on Celebration Station’s Miniature Golf Course is a par 4. You took 4 putts to get the golf ball in the hole. C. Jeremiah’s family budgets $ for back to school clothing and supplies for Jeremiah and his sister. After 3 days of shopping, Jeremiah’s family spent $ on clothes and $ on supplies. D. Alison ran 4.5 miles and burned 575 calories. When she finished she ate a hamburger that was 500 calories. .

24. 7.NS.A.1a
Students can describe situations in which opposite quantities combine to make 0 and understand when quantities are additive inverses. Students will be able to apply this understanding of real-world contexts. .

25. 7.NS.A.1B
7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
b. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

26. 7.NS.A.1B example .

27. 7.NS.A.1B
Students should represent and explain how a number and its opposite have a sum of 0 and are additive inverses
Students should understand what happens when rational numbers are combined. Adding or subtracting a rational number can be represented by moving left (in the negative direction) or right (in the positive direction) on a horizontal number line.
Students can explain and justify why the sum of p + q is located a distance of lql in the positive or negative direction from p on a number line.

28. 7.NS.A.1c
7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
c. Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

29. 7.NS.A.1c example

30. 7.NS.A.1c example
6900−(−8100) =
=15000 feet

31. 7.NS.A.1c
Students should identify subtraction of rational numbers as adding the additive inverse property to subtract rational numbers. They should represent addition and subtraction problems of rational numbers with a horizontal or vertical number line. They should also apply properties of operations as strategies to add and subtract rational numbers

32. 7.NS.A.1d
7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
d. Apply properties of operations as strategies to add and subtract rational numbers.

33. 7.NS.A.1d example
Homework Task

34. 7.NS.A.1d
Students should be able to add and subtract rational numbers and understand how the properties of operations apply. Fractional rational numbers and whole numbers should be used in computations and explorations.

35. 7.NS.A.2a
2. Apply and extend previous understandings of multiplication and division of fractions to multiply and divide rational numbers.
a. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1)=1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.

36. 4 5 7.NS.A.2a example Carla Ramone
Carla and Ramone are playing the integer game.
The person with the highest score wins!
The score is tied 14-14, and the players are
down to two cards. They must now multiply
the value of each card pair to get the final score.
Carla thinks she has the better hand since her
cards have positive values. Ramone disagrees.
Who has the better hand? How do you know? 5 -4 -5
Carla
Ramone

37. 7.NS.A.2a example

38. 7.NS.A.2a examples
Create a real-life example that can be modeled by the expression −𝟐×𝟒, and then state the product.
2. Two integers are multiplied and their product is a positive number. What
must be true about the two integers?

39. 7.NS.A.2a
Students should recognize that there are similarities and differences between multiplying rational numbers and multiplying fractions and decimals . They should understand how to multiply signed numbers. They should also apply the properties of operations to multiply rational numbers and interpret the products of rational numbers by describing real-world contexts.
What is the math that students have to know and be able to do to proficiently master this standard?
Add to chart, if needed.
Ensure participants are filling in their look-for sheets.
I can recognize that the process for multiplying fractions can be used to multiply rational numbers including integers
 ?I can recognize and describe the rules when multiplying signed numbers
 ?I can apply the properties of operations, particularly distributive property, to multiply rational numbers
 ?I can interpret the products of rational numbers by describing real-world contexts

40. 7.NS.A.2b
Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing real world contexts.
Have whole group discussion. What do the students have to do and be able to understand?
Chart participants responses.

41. 7.NS.A.2b example
2:5
7:2 is the ratio of the total number of loaves of bread to the number of loaves of rye bread.

42. 7.NS.A.2b examples
Is the quotient of two integers always an integer? Use the work space below to create quotients of integers. Answer the question and use examples or a counterexample to support your claim.
What must be true of two integers if their quotient is an integer?
Are the answers to the three quotients below the same or different Why or why not?
−𝟏𝟏𝟏 ÷𝟕𝟕
𝟏𝟏𝟏 ÷(−𝟕𝟕)
c. −(𝟏𝟏𝟏 ÷𝟕𝟕)
2:5
7:2 is the ratio of the total number of loaves of bread to the number of loaves of rye bread.

43. 7.NS.A.2b
Students recognize that division is the reverse process of multiplication, and that integers can be divided provided the divisor is not zero. Students can comprehend the rules for dividing signed numbers and interpret the quotient of rational numbers by describing real-world contexts. The awareness of rational and irrational numbers can be observed by changing fractions to decimals.
What is the math that students have to know and be able to do to proficiently master this standard?
Add to chart, if needed.
Ensure participants are filling in their look-for sheets.

44. 7.NS.A.2c
2. Apply and extend previous understandings of multiplication and division of fractions to multiply and divide rational numbers. c. Apply properties of operations as strategies to multiply and divide rational numbers.
Have whole group discussion. What do the students have to do and be able to understand?
Chart participants responses.

45. 7.NS.A.2c example
A recipe calls for 2 ¾ cups of whole wheat flour. If Ms. Ambrose wanted to triple the recipe, how many cups of flour would she need?
Mr. Mischel wants to divide 3 ½ containers of fertilizer equally amongst 8 flower beds. How many containers will he need each day if he plans on filling 2 flower beds per day?
2:5
7:2 is the ratio of the total number of loaves of bread to the number of loaves of rye bread.

46. 7.NS.A.2c
Students should identify how properties of operations can be used to multiply and divide rational numbers. They should be able to apply properties of operations as strategies to multiply and divide rational numbers
What is the math that students have to know and be able to do to proficiently master this standard?
Add to chart, if needed.
Ensure participants are filling in their look-for sheets.

47. 7.NS.A.2D
7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
d. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.
Have whole group discussion. What do the students have to do and be able to understand?
Chart participants responses.

48. 7.NS.A.2d example
2:5
7:2 is the ratio of the total number of loaves of bread to the number of loaves of rye bread.

49. 7.NS.A.2d
Students will learn to make conjectures about which fractions have terminating decimal expansions using the long division algorithm.
What is the math that students have to know and be able to do to proficiently master this standard?
Add to chart, if needed.
Ensure participants are filling in their look-for sheets.

50. 7.NS.A.3
Solve real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.)
Have whole group discussion. What do the students have to do and be able to understand?
Chart participants responses.

51. 7.NS.A.3 example
requires students to be able to reason abstractly about fraction multiplication
Practice 5 Use appropriate tools strategically
Which class should get the most prize money? Should Mr. Aceves' class get more or less than half of the money? Mr. Aceves' class collected about twice as many box tops as Mr. Canyon's class - does that mean that Mr. Aceves' class will get about twice as much prize money as Mr. Canyon's class?”

52. 7.NS.A.3 example
requires students to be able to reason abstractly about fraction multiplication
Practice 5 Use appropriate tools strategically
Which class should get the most prize money? Should Mr. Aceves' class get more or less than half of the money? Mr. Aceves' class collected about twice as many box tops as Mr. Canyon's class - does that mean that Mr. Aceves' class will get about twice as much prize money as Mr. Canyon's class?”

53. 7.NS.A.3
Students will write and solve problems (real world included) using the four operations and rational numbers.
What is the math that students have to know and be able to do to proficiently master this standard?
Add to chart, if needed.
Ensure participants are filling in their look-for sheets.

54. 7.EE.A.1
Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
Have whole group discussion. What do the students have to do and be able to understand?
Chart participants responses.

55. 7.EE.A.1 example
2:5
7:2 is the ratio of the total number of loaves of bread to the number of loaves of rye bread.

56. 7.EE.A.1
This is a continuation of work from 6th grade using properties of operations and combining like terms. Students apply properties of operations and work with rational numbers (integers and positive / negative fractions and decimals) to write equivalent expressions.
What is the math that students have to know and be able to do to proficiently master this standard?
Add to chart, if needed.
Ensure participants are filling in their look-for sheets.

57. 7.EE.A.2
Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a a = 1.05a means that “increase” by 5% is the same as” multiply by 1.05”.
Have whole group discussion. What do the students have to do and be able to understand?
Chart participants responses.

58. 7.EE.A.2 example
Given a square pool as shown, write four different expressions to find the total number of tiles in the border. Explain how each of the expressions relates to the diagram and demonstrate that the expressions are equivalent. Which expression is most useful? Explain.
2:5
7:2 is the ratio of the total number of loaves of bread to the number of loaves of rye bread.

59. 7.EE.A.2
Students understand the reason for rewriting an expression in terms of a contextual situation. For example, students understand that a 20% discount is the same as finding 80% of the cost, c (0.80c). Students build on their understanding of order of operations and use the properties of operations to rewrite equivalent numerical expressions.
What is the math that students have to know and be able to do to proficiently master this standard?
Add to chart, if needed.
Ensure participants are filling in their look-for sheets.
One method that students can use to become convinced that expressions are equivalent is by substituting a numerical value for the variable and evaluating the expression.
Another method students can use to become convinced that expressions are equivalent is to justify each step of simplification of an expression with an operation property.
As students begin to build and work with expressions containing more than two operations, students tend to set aside the order of operations. For example having a student simplify an expression like 8 + 4(2x - 5) + 3x can bring to light several misconceptions. Do the students immediately add the 8 and 4 before distributing the 4? Do they only multiply the 4 and the 2x and not distribute the 4 to both terms in the parenthesis? Do they collect all like terms
8 + 4 – 5, and 2x + 3x? Each of these show gaps in students’ understanding of how to simplify numerical expressions with multiple operations.

60. blueprint

61. TNReady Math Blueprints (7th Grade)
overview, Part I – calc, Part II – noncalc,
Calculator Policy
FOR GRADES 3-8
Materials: Two different colored highlighters
Participant Manual: Math Blueprints
The goal of this graphic is to help accompany the information found on the Math Blueprints page in module 4. This provides some background context on how to read the blueprint.
Explain that this is the first page of the blueprint and that there is a similar summary table for every mathematics blueprint. The specific standards that will be assessed on Part I and Part II are listed in the other pages of the blueprint.
Explain that the far left-hand column lists the standard clusters. Click.
There are two parts to the math assessment. Tell participants to draw a vertical line between Part I and Part II on the blueprint for their specific grade level (located in appendix H) Click.
Draw a vertical line between Part II and Total # of items. Click.
Use a different colored highlighter to highlight the line that reads “ Major Work of the Grade.” Click.
Highlight the line that reads “Additional and Supporting.” Click. These are the two major categories of standards that can be drawn from for Part I and II.
Direct participants’ attention to Part I of the blueprint.
Explain that in Part I 100% of the standards assessed come from the major work of the grade category. In Part I calculators are allowed. Click
Direct participants’ attention to Part II of the blueprint.
Explain that 60-65% of Part II is from the major works of the grade and 35-40% are from additional and supporting. (*Explain that percentages will change based on which grade level blueprint you are looking at).
Direct participants’ to the final rows which have the total percent of items, score points and percent of the test. For the 3rd grade assessment 75-80% of the assessment is from the major work of the grade and 20-25% is from additional and supporting. Then at the bottom you have the total number of items for the whole assessment, the total number of score points and then the total of 100%. Notice that the total number of score points does not match the total number of items. This is because some items may be worth more than one point.

62. Scavenger Hunt – Grade 7
Which cluster(s) have the highest number of items in Part I? What percentage of the assessment is the cluster: Solve problems using equations and expressions? Which cluster is the smallest percentage of the test? And what is the percent? Is it in Part I or Part II?
Analyze proportional relationships
11-13%
Geometrical Figures. 4-6%
Part II
FOR GRADES 3-5*
Supplemental follow up activity: In order to go even deeper into understanding and internalizing the blueprint, direct participants to 3rd grade blueprint (p104). Do a quick scavenger hunt with the questions above.
Give participants 2 minutes to find the answers to the questions above. Then as a group have participants share out the answers to the questions, and click to show the answer to each question to check participants answers.
Then direct participants to the Blueprint Activity.
When conducting the whole group discussion suggest participants reference both the small group activity and the scavenger hunt while answering the question: “How will this inform or modify instruction for the school year?”
*If there are different clusters or points you would like to highlight from the blueprint please feel free to sub out a question or add to the list.

63. resources
Illustrative math
Eureka math
Tncore
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