Unit 6

Problem Solving with Length, Money, and Data

Math

Unit Length and Description:

4 weeks

Unit 6 provides another opportunity for students to practice their algorithms and problem-solving skills with perhaps the most well-known, interesting units of all: dollars, dimes, and pennies. Measuring and estimating length is revisited in this module in the context of units from both the customary system (e.g., inches and feet) and the metric system (e.g., centimeters and meters). As they study money and length, students represent data given by measurement and money data using picture graphs, bar graphs, and line plots.

Standards:

 Major Cluster: MD – Measurement and Data Measure and estimate lengths in standard units. 2.MD.1 Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. 2.MD.2 Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. 2.MD.3 Estimate lengths using inches, feet, centimeters, and meters. 2.MD.4 Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. Relate addition and subtraction to length. 2.MD.5 Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. 2.MD.6 Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, …, and represent whole-number sums and differences within 100 on a number line diagram. Supporting Clusters: MD – Measurement and Data Work with money. 2.MD.8 Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using \$ and ˘ symbols appropriately.  Example:  If you have 2 dimes and 3 pennies, how many cents do you have? Represent and interpret data 2.MD.9 Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object.  Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. 2.MD.10 Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories.  Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. Standards for Mathematical Practice: Should be evident in every lesson. MP.1   Make sense of problems and persevere in solving them.  MP.2   Reason abstractly and quantitatively.  MP 4. Model with mathematics. MP.5   Use appropriate tools strategically. MP.6   Attend to precision Instructional Outcomes   2.MD.1: Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. ·        I can identify tools that can be used to measure length. ·        I can identify the unit of length for the tool used to the nearest whole unit (inches, centimeters, feet, meters). (e.g. rulers, yardsticks, measuring tapes, meter sticks) ·        I can determine which tool to use to measure the length of an object. (inches, centimeters, feet, meters) ·        I can measure the length of objects by using appropriate tools to the nearest whole unit. (e.g. rulers, yardstick, meter stick, measuring tape)   2.MD.2: Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. ·        I can recognize what units of measurement are comparable. (e.g. inch/cm, m/yard) ·        I can measure the length of an object using different lengths for the two measurements to the nearest whole unit. ·        I can choose the appropriate tools to measure an object. (e.g. in/cm) ·        I can explain how the two measurements relate to the size of the unit chosen.   2.MD.3: Estimate lengths using units of inches, feet, centimeters, and meters. ·        I can name strategies for estimating length (e.g. a meter is about the length from floor to above a door knob). ·        I can recognize the size of inches, feet, centimeters, and meters. ·        I can estimate lengths in units of inches, feet, centimeters and meters. ·        I can determine if an estimate is reasonable.   2.MD.4: Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. ·        I can determine how much longer one object is than another in standard length units.   2.MD.5: Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. ·        I can add and subtract lengths within 100. ·        (e.g. 45 cm – 24 cm = 21 cm or bar model) ·        I can solve addition and subtraction word problems involving lengths that are given in the same units within 100. ·        I can solve addition and subtraction word problems involving length that have equations within 100 with a symbol for the unknown number.   2.MD.6: Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, … , and represent whole-number sums and differences within 100 on a number line diagram. ·        I can describe the characteristics of a number line (e.g. points, equal spacing, consecutive numbers, line). ·        I can explain length as the distance between zero and another mark on the number line diagram within 100. ·        I can use a number line to represent the solution of whole number sums related to length within 100 (e.g. Jump forward). ·        I can represent whole numbers on a number line within 100 with equally spaced points.   2.MD.8: Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using \$ (dollars) and ˘ (cents) symbols appropriately. ·        I can identify and recognize the value of dollar bills, quarters, dimes, nickels and pennies. ·        I can identify the \$ and cent symbol. ·        I can recognize that the decimal sign I used to separate the whole from the part of the whole in money. ·        I can solve word problems involving coins using dollar and cent symbols appropriately (e.g. Quarters, dimes, nickels, and pennies). ·        I can solve word problems involving dollars using dollar and cent symbols appropriately. ·        I can count coin, dollar, and dollar coin combinations (e.g. Skip counting). ·        I can solve word problems involving dollars and coins using dollar symbols appropriately.   2.MD.9: Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. ·        I can read tools of measurement to the nearest unit (e.g. Thermometer, ruler, rain gauge, scale). ·        I can represent measurement data on a line plot. ·        I can measure lengths of several objects to the nearest whole unit. ·        I can measure lengths of objects by making repeated measurements of the same objects (e.g. Plant’s height, temperature, weight). ·        I can create a line plot with a horizontal scale marked in whole numbers using measurements.   2.MD.10: Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. ·        I can solve problems relating to data in graphs by using addition and subtraction. ·        I can make comparisons between categories in the graph using more than, less than, etc. with up to four sets of data. ·        I can draw a picture graph to represent a given set of data with up to four categories. ·        I can draw a bar graph to represent a given set of data with up to four categories.

Enduring Understandings:

·        Measurement is a way to describe and compare objects or ideas. A specific process is used to measure attributes.

·        Standard measurement allows us to communicate with others to describe the physical world.

·        Measurement is a consistent duration and distance.

·        The length of objects can be measured using customary units or Metric units.

·        A reasonable estimate is one that is close to the actual measurement.

·        Line plots are useful tools for collecting data because they show the number of things along a numeric scale.

·        We collect and use data to help us answer questions and make decisions.

Essential Questions:

·        What properties can be measured (length, height, volume, width, area, weight, time, money and temperature)?

·        How do we measure (unit, tool, and process)?

·        What standard units are necessary?

·        How do we use different types of measurements?

·        What are tools of measurement and how are they used?

·        When should you estimate? When do you need an exact answer? What makes a useful estimate?

·        What information can we gather from data, charts, and graphs?

·        How do we conduct a survey?

·        How can we gather and organize data?

·        How can represent the data we gather?