Semester Two

Semester 2

Ratios and Proportional Relationships 6.RP

Understand ratio concepts and use ratio reasoning to solve problems. 

• 1. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. 

  • I can understand ratios and the language used to describe two amounts. 

• 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. 

  • I can understand how to find a rate when give a specific ratio. 

• 3. 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, finding 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. 

  • C. Find a percent of a quantity as a rate per 100; 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. 

    • I can solve word problems related to ratios in order to find the rate. 

    • I can make tables of equivalent ratios, find missing values in the tables, plot those values on a coordinate plane, and use the tables to compare ratios. 

    • I can solve unit rate problems. 

    • I can find a percent of a quantity as a rate per 100. 

    • I can solve problems involving finding the whole if I am given a part and the percent. 

    • I can use what I know about ratios to convert units of measurement. 

Geometry 6.G 

Solve real-world and mathematical problems involving area, surface area, and volume.

• 1.  Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of real-world and mathematical problems. 

  • I can find the area of a rectangle using the standard algorithm.

  • I can find the area of shapes by composing or decomposing compound figures.

  • I can apply what I know about taking apart and putting together shapes to find the area in real-world situations. 

• 2.  Draw polygons in the coordinate plane given coordinates for vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. 

  • I can draw polygons in the coordinate plane when I am given the coordinates for the vertices. 

  • I can use the coordinates of the vertices of a polygon on the coordinate plane to find the length of a side, joining points with the same first coordinate or the same second coordinate. 

  • I can apply what I have learned about polygons on coordinate planes to real-world and mathematical situations.

  • I can understand the distance between two numbers (positive or negative) on a number line. 

• 3.  Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formula V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. 

  • I can use unit cubes to find the volume of a right rectangular prism and I understand that the mathematical formula ( V = l w h or V = b h) will give me the same result. 

  • I can use the mathematical formulas V = l w h or V = b h to determine the volume of real world objects.

• 4. Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. 

  • I can show how three-dimensional figures can be made using dimensional nets. 

  • I can figure out the surface area of a three-dimensional shape by using a net. 

Statistics and Probability 6.SP

Develop understanding of statistical variability.

• 1. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. 

  • I understand that the data in questions involving statistics is varied as it relates to the question and answers. 

Summarize and describe distributions.

• 1. Display numerical data in plots on a number line, including dot plots, histograms, and box plots. 

  • I can show numerical data on a number line. 

  • I can show numerical data on a dot plot. 

  • I can show numerical data on a histogram. 

  • I can show numerical data on a box plot. 

• 2. 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 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. 

    • I can summarize sets of numerical data that are different. 

    • I can summarize data by stating the number of observations. 

    • I can summarize data by describing the characteristics of what is being investigated, including how it was measured. 

    • I can summarize data by giving numerical measures of center and variability. 

    • I can summarize data by describing the overall pattern of the data and noticing unusual deviations from the overall pattern. 

    • I can summarize data by explaining how the distribution of the data on a graph determines its measure of center (median and/or mean). 

Develop understanding of statistical variability.

• 1. 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. 

  • I understand that a set of data collected to answer a statistical question has an overall shape, including a center and spread, when plotted on a graph. 

• 2. Recognize that a measure of center for a numerical data set summarizes of its values with a single number, while a measure of variation describes how its values vary with a single number. 

  • I understand that a set of numerical data has measure of center that summarizes all of its values with a single number. 

  • I understand that in a set of numerical data, the measure of variation describes how its values vary with a single number.