6TH GRADE PACING GUIDE

MATH INNOVATIONS UNIT 5: AT THIS RATE

March-May

Standards:

6.SP.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.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.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.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

6.SP.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.

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 one beak.” “For every vote candidate A received, candidate C received nearly three votes.”

6.RP.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b≠0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is ¾ cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”

6.RP.3abcd 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. A) Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. 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? C) Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. D) Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

Standard/Target / Section/Lesson / # Days / Formative Assessment
Section 1: Using Proportional Reasoning / ACT:
1.1: Comparing without Computing / 3
Geometry/Algebra Quiz
6.RP.1 Knowledge Target: Write ratio notation--_:_, _to_, _/_. Knowledge Target: Recognize that ratios appear in a variety of different contexts; part-to-whole, part-to-part, and rates. Reasoning Target: Generalize that all ratios relate two quantities or measures within a given situation in a multiplicative relationship. Reasoning Target: Analyze your context to determine which kind of ratio is represented. / 1.2: Parts and Wholes / 3
6.RP.1 Knowledge Target: Know order matters when writing a ratio. Knowledge Target: Know ratios compare two quantities; the quantities do not have to be the same unit of measure.
6.RP.3abcd Reasoning Target: Apply ratio reasoning to convert measurement units in real-world and mathematical problems. Reasoning Target: Apply ratio reasoning to convert measurement units by multiplying or dividing in real-world or mathematical problems. / 1.3: Comparing and Computing / 1
6.RP.1 Knowledge Target: Know ratios can be simplified. / 1.4: Fair Shares / 1
Geometry/Algebra Quiz
6.RP.3abcd Knowledge Target: Know that a percent is a ratio of a number to 100. Reasoning Target: Solve real-world and mathematical problems involving ratio and rate, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. / 1.5: Comparing Using Diagrams
*Add: Know that a percent is a ratio of a number to 100. / 2
6.RP.2 Knowledge Target: Identify and calculate a unit rate. Knowledge Target: Use appropriate math terminology as related to rate. Reasoning Target: Analyze the relationship between a ratio a:b and a unit rate a/b where b≠0.
6.RP.3abcd Knowledge Target: Find a % of a number as a rate per 100. Reasoning Target: Apply the concept of unit rate to solve real-world problems involving unit pricing. Reasoning Target: Solve real-world problems involving finding the whole, given a part and a percent. / 1.6: Unit Price
*Add: Find a % of a number as a rate per 100.
*Add: Solve real-world problems involving finding the whole, given a part and a percent. / 2 / #5
Study Guide / 1
Percent Proficiency: / Quiz / 1
Section 2: Analyzing Change / ACT:
2.1: Growing, Growing / 1
6.RP.3abcd Knowledge Target: Make a table of equivalent ratios using whole numbers. Knowledge Target: Find the missing values in a table of equivalent ratios. Reasoning Target: Use tables to compare proportional quantities. / 2.2: Constant Change / 1 / #74
Geometry/Algebra Quiz
6.RP.3abcd Knowledge Target: Plot pairs of values that represent equivalent ratios on the coordinate plane. Reasoning Target: Apply the concept of unit rate to solve real-world problems involving constant speed. / 2.3: Graphing Change / 1
Study Guide / 1
Percent Proficiency: / Quiz / 1
*These targets are for every lesson in Section 3.
6.SP.5abcd Knowledge Target: Organize and display data in tables and graphs. Knowledge Target: Report the number of observations in a data set or display. Knowledge Target: Describe the data being collected, including how it was measured and its units of measurement. Knowledge Target: Calculate quantitative measures of center, e.g., mean, median, mode. Knowledge Target: Calculate quantitative measures of variance, e.g., range, interquartile range, mean absolute deviation. Knowledge Target: Identify outliers. Reasoning Target: Determine the effect of outliers on quantitative measures of a set of data, e.g., mean, median, mode, range, interquartile range, mean absolute deviation. Reasoning Target: Choose the appropriate measure of central tendency to represent the data. Reasoning Target: Analyze the shape of the data distribution and the context in which the data were gathered to choose the appropriate measures of central tendency and variability and justify why this measure is appropriate in terms of the context. / Section 3: Using Data to Make Comparisons / ACT:
6.SP.1 Knowledge Target: Recognize that data can have variability. Knowledge Target: Recognize a statistical question (examples versus non-examples).
6.SP.4 Knowledge Target: Identify the components of dot plots. Product Target: Create a dot plot to display a set of numerical data. / 3.1: Describing Data
*Add: Recognize a statistical question (examples versus non-examples). / 2 / #81, 111
6.SP.2 Knowledge Target: Know that a set of data has a distribution. Knowledge Target: Describe a set of data by its center, e.g., mean and median. Knowledge Target: Describe a set of data by its spread and overall shape, e.g. by identifying data clusters, peaks, gaps and symmetry.
6.SP.3 Knowledge Target: Recognize measures of central tendency for a data set summarizes the data with a single number. Knowledge Target: Recognize measures of variation for a data set describes how its values vary with a single number.
6.SP.4 Knowledge Target: Identify the components of box plots. Knowledge Target: Find the median, quartile, and interquartile range of a set of data. Product Target: Create a box plot to display a set of numerical data. / 3.2: Box-and-Whisker Plots / 1
Geometry/Algebra Quiz
6.SP.3 Knowledge Target: Recognize there are measures of central tendency for a data set, e.g., mean, median, mode. Knowledge Target: Recognize there are measures of variances for a data set, e.g., range, interquartile range, mean absolute deviation.
6.SP.4 Reasoning Target: Analyze a set of data to determine its variance. / 3.3: The Mean / 2 / #14, 56, 70, 77, 114, #13 Compass sample test questions, #1 set 5
6.SP.4 Knowledge Target: Identify the components of histograms. Product Target: Create a histogram to display a set of numerical data. / 3.4: Statistical Displays / 2
Study Guide / 1
Percent Proficiency: / Quiz / 1
Study Guide / 1
Percent Proficiency: / Unit Exam / 1
Lewis County Middle School