6th GradeCore Connections 1Chapter 8

Lesson / MS-CCRS Taught / Focus for Lesson / MS-CCRS Specific Problem(s) / Optional Supplements and Adjustments / Pre-requisite standards and skills
8.1.1 / 6.SP.A.2
Understand that a set of data collected to answer a statistical question has a distribution, which can be described by its center, spread, and overall shape.
6.SP.A.3
Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.
6.SP.B.5c
Summarize numerical data sets in relation to their context, such as by:
c)Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. / The focus of this lesson is for students to gain an understanding of vocabulary of central tendencies.
(8-4 and 8-5) / 8-7 (6.SP.5c)
8-8 (6.G.3)
8-9 (6.EE.3)
8-11 (6.EE.2b) / The pre-skills for this chapter can be used as a pre-teach to calculating mean, median, and range to ensure students have some background knowledge.
Problem 8-2 may be needed to allow practice of what to do when there are two numbers in the middle when determining the median. / 5.MD.B.2
Use a line plots to display data in fractions of a unit.
Lesson / MS-CCRS Taught / Focus for Lesson / MS-CCRS Specific Problem(s) / Optional Supplements and Adjustments / Pre-requisite standards and skills
8.1.2 / 6.SP.A.2
Understand that a set of data collected to answer a statistical question has a distribution, which can be described by its center, spread, and overall shape.
6.SP.A.3
Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.
6.SP.B.5cd
Summarize numerical data sets in relation to their context, such as by:
c)Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.
d)Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. / Day 1: The focus of the lesson is to create and interpret graphs of data, paying attention to measures of center, spread, and shape of a graph.
(8-12, 8-13, and 8-14) / 8-24 (6.RP.1) / Day 1: CCSS emphasizes terms such as center and variability – CPM emphasizes terms of mean and range. Teachers should connect the two and use both types to ensure student understanding.
Problem 8-15 should be included on this day. / 5.MD.B.2
Use a line plots to display data in fractions of a unit.
Day 2: See notes. / 8-25 (6.SP.5d)
8-26
(6.SP.3; 5d)
8-28 (6.EE.3)
8-29 (6.EE.2b) / Day 2: After completing 8-15 in day 1, teachers should use day 2 as a repetitive practice lesson. The supplement should include items similar to PARCC and questioning in problem 8-17 about reading context from data given in dot plots and histograms.
Lesson / MS-CCRS Taught / Focus for Lesson / MS-CCRS Specific Problem(s) / Optional Supplements and Adjustments / Pre-requisite standards and skills
8.1.3 / 6.SP.A.2
Understand that a set of data collected to answer a statistical question has a distribution, which can be described by its center, spread, and overall shape.
6.SP.A.3
Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.
6.SP.B.5cd
Summarize numerical data sets in relation to their context, such as by:
c)Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.
d)Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. / The focus of this lesson is for students to understand mean absolute deviation and how to describe the shape of a graph of data.
(8-35 and 8-37) / 8-40 (6.SP.2)
8-41 (6.EE.7)
8-43
(6.EE.5; 8) / Problem 8-32 is a needed question to teach what mean absolute deviation is and how to find it. / 5.MD.B.2
Use a line plots to display data in fractions of a unit.
Lesson / MS-CCRS Taught / Focus for Lesson / MS-CCRS Specific Problem(s) / Optional Supplements and Adjustments / Pre-requisite standards and skills
8.1.4 / 6.SP.A.3
Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.
6.SP.B.4
Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
6.SP.B.5abcd
Summarize numerical data sets in relation to their context, such as by:
a)Reporting the number of observations.
b)Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.
c)Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.
d)Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. / Day 1: The focus is to introduce box and whisker plots. Attention should be given to interquartile range.
(8-50) / 8-51 (6.SP.2)
8-55
(6.EE.2c, 3) / Day 1: The lesson questions have large amounts of data. An adjusted lesson is provided to use instead. Problem 8-50 should be completed after the adjusted lesson. / 5.MD.B.2
Use a line plots to display data in fractions of a unit.
Day 2: See note. / 8-56 (6.SP.5b)
8-57 (6.NS.1)
8-59 (6.NS.4)
8-60
(6.EE.2c; 3) / Day 2: If the adjusted lesson is used, we will not need a day 2.
8.1.5 / 6.SP.B.4
Display numerical data in plots on a number line, including dot plots, histograms, and box plots. / The focus of the lesson is to have students create graphs and answer questions from them.
(8-61 and 8-62) / 8-66
(6.SP.2, 4, 5a)
8-67 (6.SP.4)
8-68 (6.SP.4) / Do not have students’ complete stem and leaf plots – these are not required by our standards. / None
Lesson / MS-CCRS Taught / Focus for Lesson / MS-CCRS Specific Problem(s) / Optional Supplements and Adjustments / Pre-requisite standards and skills
8.2.1 / 6.SP.A.1
Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, "How old am I?" is not a statistical question, but "How old are the students in my school?" is a statistical question because one anticipates variability in students' ages.
6.SP.B.5b
Summarize numerical data sets in relation to their context, such as by:
b)Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. / Day 1: The focus of the lesson is for students to identify statistical questions.
(8-71) / 8-74 (6.SP.1)
8-75 (6.SP.5c)
8-76 (6.NS.2, 3)
8-77 (6.NS.4)
8-78 (6.EE.5, 8) / 5.MD.B.2
Use a line plots to display data in fractions of a unit.
Day 2: See note. / 8-80 (6.EE.8) / The lesson should only take one day.
8.3.1 / 6.EE.B.7
Solve real-world and mathematical problems by writing and solving equations of the form x + p = q andpx = q for cases in which p, q and x are all nonnegative rational numbers.
6.EE.C.9
Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. / The focus of the lesson is for students to understand how to write an equation given a table or a graph.
(8-84, 8-86, and 8-87) / 8-90 (6.EE.5)
8-91
(6.SP.2, 4, 5a-d)
8-93 (6.NS.1, 3)
8-94 (6.RP.1) / 5.OA.B.3
Generate numerical patterns and graph ordered pairs.
Lesson / MS-CCRS Taught / Focus for Lesson / MS-CCRS Specific Problem(s) / Optional Supplements and Adjustments / Pre-requisite standards and skills
8.3.2 / 6.RP.A.3b
Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
b)Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?
6.EE.C.9
Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. / The focus for the lesson is to provide additional practice of solving ratio and rate problems. It also incorporates using a tape diagram as the standard suggests.
(8-96 and 8-97) / 8-101
(6.RP.3b,
6.EE.7, 9)
8-102
(6.RP.2, 6.EE.9)
8-103
(6.EE.2c, 3) / 5.OA.B.3
Generate numerical patterns and graph ordered pairs.
Lesson / MS-CCRS Taught / Focus for Lesson / MS-CCRS Specific Problem(s) / Optional Supplements and Adjustments / Pre-requisite standards and skills
8.3.3 / 6.RP.A.3b, d
Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
b)Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?
d)Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. / The focus of the lesson is to further practice with unit rate and also to have students work problems that encompass unit conversions.
(8-107 and 8-113) / 8-116
(6.RP.2, 6.EE.9)
8-117 (6.RP.3d)
8-119 (6.EE.2c)
8-120 (6.NS.1)
Closure
8-123 (6.EE.9)
8-125 (6.SP.3)
8-126
(6.SP.2,3,4,5a-d)
8-127 (6.NS.7c)
8-128 (6.SP.1) / None

Assessment Understanding According to PARCC (Section Quiz and Chapter Assessment)

MS-CCRS / EOY or PBA / Math Practice / Clarifications / Calculator or No Calculator / Chapter Mastery
6.RP.A.3b
Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? / EOY and PBA / 2, 5,
and 8 /
  • Expectations for unit rates in this grade are limited to non-complex fractions. The initial numerator and denominator should be whole numbers.
PBA ONLY
6.C.8.1 – Present solutions to multi-step problems in the form of valid chains of reasoning, using symbols such as equals signs appropriately (for example, rubrics award less than full credit for the presence of nonsense statements such as 1+4=5+7=12, evens if the final answer is correct), or identify or describe errors in solutions to multi-step problems and present corrected solutions.
  • MP: 2, 3, and 6
  • Calculator allowed
/ Calculator / Now
Full mastery can be expected.
Future
No further lessons in the text.
MS-CCRS / EOY or PBA / Math Practice / Clarifications / Calculator or No Calculator / Chapter Mastery
6.RP.A.3d
Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
d)Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. / EOY and PBA / 2, 5, 6,
7, and 8 /
  • Tasks may or may not have context.
  • Tasks require students to multiply and/or divide dimensioned quantities.
  • Half of the tasks require students to correctly express the units of the result.
  • Expectations for ratios in this grade are limited to ratios of non-complex fractions. (See footnote, CCSS p.42) The initial numerator and denominator should be whole numbers.
PBA ONLY
6.C.8.1 – Present solutions to multi-step problems in the form of valid chains of reasoning, using symbols such as equals signs appropriately (for example, rubrics award less than full credit for the presence of nonsense statements such as 1+4=5+7=12, evens if the final answer is correct), or identify or describe errors in solutions to multi-step problems and present corrected solutions.
  • MP: 2, 3, and 6
/ Calculator / Now
Full mastery can be expected.
Future
No further lessons in the text.
MS-CCRS / EOY or PBA / Math Practice / Clarifications / Calculator or No Calculator / Chapter Mastery
6.EE.B.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. / EOY and PBA / 1, 2, 6, and 7 /
  • Tasks are algebraic, not arithmetic. See Progression for Expressions and Equations, pp. 3,4.
  • Half of the tasks involve whole-number values of p, q, and/or x; half of the tasks involve fraction or decimal values of p, q, and/or x.
  • Fractions and decimals should not appear together in the same problem.
  • These tasks only involve equations with addition and multiplication.
  • A valid equation and the correct answer are both required for full credit.
PBA ONLY
6.C.6 – Given an equation, present the solution steps as a logical argument that concludes with a solution.
  • Tasks do not require students to write an equation or inequality.
  • MP: 3 and 6
/ Calculator / Now
Full mastery can be expected.
Future
No further lessons in the text.
MS-CCRS / EOY or PBA / Math Practice / Clarifications / Calculator or No Calculator / Chapter Mastery
6.EE.C.9
Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. / EOY and PBA / 2, 4,
6, and 8 /
  • Tasks that involve writing an equation should not go beyond the equation types described in 6.EE.7 (and where and are all nonnegative rational numbers).
PBA ONLY
6.C.8.2 – Present solutions to multi-step problems in the form of valid chains of reasoning, using symbols such as equals signs appropriately (for example, rubrics award less than full credit for the presence of nonsense statements such as 1+4=5+7=12, even if the final answer is correct), or identify or describe errors in solutions to multi-step problems and present corrected solutions.
  • MP: 2, 3, and 6
  • Calculator allowed
/ Calculator / Now
Full mastery can be expected.
Future
No further lessons in the text.
6.SP.A.1
Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, "How old am I?" is not a statistical question, but "How old are the students in my school?" is a statistical question because one anticipates variability in students' ages. / EOY / NA /
  • Tasks do not assess mode and range.
/ No Calculator / Now
Full mastery can be expected.
Future
No further lessons in the text.
6.SP.A.2
Understand that a set of data collected to answer a statistical question has a distribution, which can be described by its center, spread, and overall shape. / EOY / 4 /
  • Tasks might present several distributions graphically and ask which two have nearly the same center, nearly the same spread, or nearly the same overall shape.
  • Tasks do not assess mode and range.
/ No Calculator / Now
Full mastery can be expected.
Future
No further lessons in the text.
MS-CCRS / EOY or PBA / Math Practice / Clarifications / Calculator or No Calculator / Chapter Mastery
6.SP.A.3
Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. / EOY / 4 /
  • Tasks might ask students to rate statements True/False/Not Enough Information, such as, “The average height of trees in Watson Park is 65 feet. Are there any trees in Watson Park taller than 65 feet?”
  • Tasks do not assess mode and range.
/ No Calculator / Now
Full mastery can be expected.
Future
No further lessons in the text.
6.SP.B.4
Display numerical data in plots on a number line, including dot plots, histograms, and box plots. / EOY / 2 and 5 /
  • Tasks ask students to identify which display corresponds to a given set of data.
  • Tasks do not assess mode and range.
/ No Calculator / Now
Full mastery can be expected.
Future
No further lessons in the text.
6.SP.B.5a
Summarize numerical data sets in relation to their context, such as by:
a)Reporting the number of observations / EOY / 4 /
  • Tasks have a text-based and a graphics-based overview of a numerical data set.
  • Tasks require students to identify/select from unambiguously true or false statements such as, “About half of the data set, the median would not change”, etc.
  • Tasks do not assess mode and range.
/ Calculator / Now
Full mastery can be expected.
Future
No further lessons in the text.
6.SP.B.5b
Summarize numerical data sets in relation to their context, such as by:
b)Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. / EOY / 4 /
  • Tasks have a text-based and a graphics-based overview of a numerical data set.
  • Tasks require students to identify/select from unambiguously true or false statements such as, “About half of the data set, the median would not change”, etc.
  • Tasks do not assess mode and range.
/ Calculator / Now
Full mastery can be expected.
Future
No further lessons in the text.
MS-CCRS / EOY or PBA / Math Practice / Clarifications / Calculator or No Calculator / Chapter Mastery
6.SP.B.5c
Summarize numerical data sets in relation to their context, such as by:
c)Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. / EOY / 4 /
  • Tasks have a text-based and a graphics-based overview of a numerical data set.
  • Tasks require students to identify/select from unambiguously true or false statements such as, “About half of the data set, the median would not change”, etc.
  • Tasks do not assess mode and range.
/ Calculator / Now
Full mastery can be expected.
Future
No further lessons in the text.
6.SP.B.5d
Summarize numerical data sets in relation to their context, such as by:
d)Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. / EOY / 4 /
  • Tasks have a text-based and a graphics-based overview of a numerical data set.
  • Tasks require students to identify/select from unambiguously true or false statements such as, “About half of the data set, the median would not change”, etc.
  • Tasks do not assess mode and range.
/ Calculator / Now
Full mastery can be expected.
Future
No further lessons in the text.

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