Topic+Fifteen

= Topic Fifteen: Solving Measurement Problems = Pacing (Duration of Unit):
 * ~ = Desired Results = ||
 * __Transfer:__

1. Makes sense of problems and persevere in solving them. 2. //__Reason abstractly and quantitatively.__// 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. __//Use appropriate tools strategically.//__ 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||
 * __Established Goals:__
 * 4.MD.2: Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.
 * 4.MD.3: Apply the area and perimeter formulas for rectangles in real-world and mathematical problems. //For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.//
 * 4.MD.4: Make a line plot to display a data set of measurements in fractions of a unit (** 1 ** / ** 2 **, ** 1 ** / ** 4 **, ** 1 ** / ** 8 **). Solve problems involving addition and subtraction of fractions by using information presented in line plots. //For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.//

__Prerequisite Skills:__ > b. A plane figure which can be covered without gaps or overlaps by //n// unit squares is said to have an area of //n// square units
 * 3.MD.2: Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters ( l ).[[file:///C:/Users/csantosuosso/Downloads/0311%20(16).doc#_ftn1|[1]]] Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.
 * 3.MD.5: Recognize area as an attribute of plane figures and understand concepts of area measurement.a. A square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area, and can be used to measure area.
 * 3.MD.8: Solve real-world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.

__"I Can" Statements:__
 * I can use the four operations (+, -, x, ) to solve word problems involving measurement; including simple fractions and decimals.
 * I can use what I know about area and perimeter to solve real world problems involving rectangles.
 * I can make a line plot to show measurements involving fractions.
 * I can solve problems involving addition and subtraction of fractions by using information presented in line plots. ||
 * __Big Ideas:__
 * __Measurement:__ Some attributes of objects are measurable and can be quantified using unit amounts.
 * __Data Collection and Representation:__ Some questions can be answered by collecting and analyzing data, and the question to be answered determines the data that needs to be collected and how best to collect it. Data can be represented visually using tables, charts, and graphs. They type of data determines the best choice of visual representation.
 * __Practices, Processes, and Proficiencies__: Mathematics content and practices can be applied to solve problems. || __Essential Questions:__


 * What do area and perimeter mean and how can each be found?
 * How can line plots and other tools help to solve measurement problems? ||
 * __Students will know...__
 * Some problems can be solved by applying the formula for the perimeter of a rectangle or the formula for the area of a rectangle.
 * Some measurement problems can be represented and solved using models.
 * Making change is often easiest by counting up from the smaller amount to the larger amount.
 * Some data can be represented using a line plot and the line plot can be used to answer certain questions about the data.
 * Some problems can be solved by breaking apart of changing the problem into simpler ones, solving simpler ones, and using these solutions to solve the original problem. Recording information in a table can help students understand and solve some problems.

__Vocabulary:__ perimeter, area, line plot || __Students will be skilled at...__


 * Using the formulas for the perimeter and area of rectangles to solve real-world problems.
 * Using diagrams to show data and analyze how the quantities are related to solve real-world measurement problems.
 * Solving real-world problems that involve money and giving change by counting.
 * Constructing line plots using given data and using the line plot to answer questions about the data set.
 * Breaking a problem into smaller, more manageable pieces and finding a pattern to fit. ||
 * ~ = Assessment Evidence = ||
 * __Performance Assessment:__

__[|4.MD.3-MARS Task-Fair Play]__ || __Other Evidence:__ ||
 * ~ = Learning Plan = ||
 * __Learning Activities:__

15-1:Some problems can be solved by applying the formula for the perimeter of a rectangle or the formula for the area of a rectangle. 15-2:Some measurement problems can be represented and solved using models. 15-3:Making change is often easiest by counting up from the smaller amount to the larger amount. 15-4:Some data can be represented using a line plot and the line plot can be used to answer certain questions about the data. 15-5:Some problems can be solved by breaking apart of changing the problem into simpler ones, solving simpler ones, and using these solutions to solve the original problem. Recording information in a table can help students understand and solve some problems. ||
 * __Resources:__

__Problem of the Month:__ __[|Surrounded and Covered]__

__Centers:__ __[|How Many Tables?]__ __[|Fencing a Garden]__ __[|Designing a Zoo Enclosure]__ __[|Length of Ants Line Plot]__ __[|Objects in My Desk Line Plot]__ ||