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4th Grade Measurement and Data Standards Solve problems involving measurement and conversion of measurements 4.MD.A.1: Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. Students need to understand equivalent conversions. For example 12 inches equals 1 foot, 16 ounces equals one pound, and 100 centimeters equals 1 meter. Students learn this process by creating conversion charts. http://www.math-salamanders.com/image-files/metric-to-standard-conversion-chartlength.gif Students will continue working with conversions in word problems. For example, Bobby made a paper airplane that flew 6 feet. How many inches did it fly? Students will begin solving word problems by using the conversion charts, however once they have developed a clear understanding of the relationship of equivalent fractions, they can begin using multiplication to find the conversion. 12 X 6 = 72. Solve problems involving measurement and conversion of measurement 4.MD.A.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. Solve problems involving measurement and conversion of measurements 4.MD.A.3: Apply the area and perimeter formulas for rectangles in real world and mathematical problems. Students will learn the area formula (Area=Length X Width) and the perimeter for rectangles. They should have already been introduced to variables and understand that they represent an unknown number. Misconceptions: Students may confuse area and perimeter. Students will start to learn area by counting the number of squares inside a given rectangle. They will then move to multiplying just the number that represents the length and width of the shape to find the area. After students understand how to find the area of a shape with all lengths given, they will find the area of a shape with a missing length. For example, the width of a rectangle is 80 ft, and the total area is 6,400 square feet. What is the length? A=L x W Perimeter: Students will understand that perimeter is the distance around the shape. To find the perimeter students must add all sides of the shape. Students will also need to understand that rectangles have opposite congruent sides, which is important for word problems where they are required to find the missing distance of one or two sides of the rectangle. 6,400 = L x 80 L= 80 Represent and interpret data 4.MD.B.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. Misconceptions: Students may skip numbers on the number line and use sloppy representations of data that will hinder their analysis of the information. For this problem ask studwhat the difference would be between the shortest and longest ribbons. Geometric measurement: understand concepts of angle and measure angles 4.MD.C.5 Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement 4.MD.C.5.A An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a "one-degree angle," and can be used to measure angles. Students will learn how two rays form the angles and how to connect them to real world situations. For example doing a 360 or 180 turn while skateboarding. With a 360 turn they see that they turned all the way around and landed facing the same way they started. When making a 180 turn that means they only made half of a 360 turn Another real world situation they can connect this to is using a clock. By looking at where the hands are on the clock and determining what kind of angle there is. For 360 they can see you need to make a full circle, 180 is half the circle, 90 is one quarter of the circle, and 270 is three-quarters of the circle. For example when the clock reads 3pm the angle measure would be 90 degrees because the hands have only made a one quarter turn. Geometric measurement: understand concepts of angle and measure angles 4.MD.C.6 Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. Students will learn that the tool used to measure angles is a protractor. They will be able to see that protractors measure the angle opening, which is what determines the angle measure. Students will learn how to read a protractor precisely by being able to see if the angle is obtuse (>90), acute (< 90), or right (= 90) and then determine if the smaller or larger numbers on the protractor Misconception: If the ray falls between two numbers the student could miscount the 1 degree marks between the two numbers. Geometric measurement: understand concepts of angle and measure angles. 4.MD.C.7 Recognize angle measure as additive. When an angle is decomposed into nonoverlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. The students will learn how to find unknown angles by using properties of the angles, operations, and creating equations to help solve for the missing angle measures. Recomposing angles means that given the measurement of one angle, you can combine two other given angles to obtain that first angle measure. Decomposing angles means to break them into smaller amounts. Example: 30 degree angle could be made up of a 10 degree angle plus a 20 degree angle put together.