Gary School Community Corporation Mathematics Department Unit Document. Unit Number: 3 Grade: 4


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1 Gary School Community Corporation Mathematics Department Unit Document Unit Number: 3 Grade: 4 Unit Name: Measurement with Angles and Rectangles Duration of Unit: 20 Days UNIT FOCUS In this unit, students explore measurement with mixed units for length, mass, and capacity. They learn relative sizes of measurement units and solidify their understanding of the relationship between metric units and the place value chart and explore multiple strategies for solving measurement problems involving unit conversion. With angle measure playing a key role in their work, students learn how to create and measure angles, as well as create and solve equations to find unknown angle measures. Students will develop the perimeter and area algorithms for rectangles and solve multistep measurement word problems involving complex figures. Standards for Mathematical Content 4.M.4: Apply the area and perimeter formulas for rectangles to solve realworld problems and other mathematical problems. Recognize area as additive and find the area of complex shapes composed of rectangles by decomposing them into nonoverlapping rectangles and adding the areas of the nonoverlapping parts; apply this technique to solve realworld problems and other mathematical problems. Standard Emphasis Critical Important Additional 4.C.1: Add and subtract multidigit whole numbers fluently using a standard algorithmic approach. 4.M.1: Measure length to the nearest quarterinch, eighthinch, and millimeter. 4.M.2: Know relative sizes of measurement units within one system of units, including km, m, cm; kg, g; lb, oz; l, ml; hr, min, sec. Express measurements in a larger unit in terms of a smaller unit within a single system of measurement. Record measurement equivalents in a twocolumn table. 4.M.3: Use the four operations (addition, subtraction, multiplication and division) to solve realworld problems involving distances, intervals of time, volumes, masses of objects, and money. Include addition and subtraction problems involving simple fractions and problems that require expressing measurements given in a larger unit in terms of a smaller unit. 4.M.6: Measure angles in wholenumber degrees using appropriate tools. Sketch angles of specified measure. Vertical Articulation documents for K 2, 3 5, and 6 8 can be found at: (scroll to bottom)
2 4.DA.1: Formulate questions that can be addressed with data. Use observations, surveys, and experiments to collect, represent, and interpret the data using tables (including frequency tables), line plots, and bar graphs. 4.DA.3: Interpret data displayed in a circle graph. Mathematical Process Standards: PS.1: Make sense of problems and persevere in solving them. PS.2: Reason abstractly and quantitatively PS.4: Model with mathematics PS.5: Use appropriate tools strategically Big Ideas/Goals Linear measures can be represented using inches, feet, yards or centimeters and meters. Unit conversions can be applied to solve and reason about word problems. Conversions between units can be recorded in a twocolumn table. Measures can be expressed as mixed numbers. Angle measures can be determined using a protractor or angle ruler. Angles of an estimated size can be sketched by comparison to benchmark angles. The area of a rectangle is the number of unit squares that cover the rectangle. The perimeter of a rectangle is the number of units represented by the distance around the rectangle. The area of a complex shape can be determined by adding the area of its nonoverlapping Essential Questions/ Learning Targets How can a ruler be used to accurately measure side length in both the English and Metric Systems? How does place value help to moving from larger to smaller units when measuring? How does a twocolumn table help organize data about measurement units? How can a measure of inches be represented as a fractional part of a foot or a yard? What is the method for measuring an angle in a figure? How can benchmark angles help to estimate an unknown angle? What is a realworld example where finding area of a rectangle would be necessary to solve the problem? If the length and width of a rectangle were known, how could I find its perimeter? If a complex figure is composed of nonoverlapping rectangles, how could I find its area? I Can Statements I can accurately find side lengths using both English and Metric measuring tools. I can explain relative sizes of measurement units between individual systems. I can solve problems using the four operations to find distance, size, time, volume, and area. I can express measurements given in a larger unit in terms of a smaller unit. I can measure angles in whole number degrees using appropriate tools. I can sketch angles of a specified measure. I can apply the area formula for rectangles to solve problems. I can find the perimeter of a rectangle by applying the formula for perimeter. I can find the area of complex shapes composed of nonoverlapping rectangles. 2
3 parts. A circle graph represents a complete set of data and its segments represent fractional parts of the data with specific attributes. The angle measure in a circle graph helps to determine the fractional part represented in a segment of the graph. If the answer to a data question is ¼, how do I represent that on a circle graph? If the angle of a segment in a circle graph is 90 degrees, what fractional part of the data is represented in that segment? I can interpret data displayed in a circle graph. I can formulate questions that can be addressed with data. UNIT ASSESSMENT TIME LINE Beginning of Unit PreAssessment Assessment Name: PreAssessment Assessment Type: Teacher Observation with Observation recording sheet Assessment Standards: 4.M.1, 4.M.2 Assessment Description: Groups of 3 or 4 students exploring with measuring tools either at their own pod or at stations. This assessment should help the teacher determine where intervention is needed regarding use of measuring devices before beginning the unit. Throughout the Unit Formative Assessment Assessment Name: Measuring classroom objects Assessment Type: Group performance task with recording sheets Assessing Standards: 4.M.1, 4.M.2 Assessment Description: Students should work in pairs or groups of 3 to move to different stations around the classroom in order to measure using various tools required for this unit, including rulers, measuring tapes, scales, and liquid volume measures. Assessment Name: Measurement Conversions Assessment Type: TBD Assessing Standards: 4.M.1, 4.M.2 Assessment Description: Students should be required to complete twocolumn charts for conversions such as inchesfeet, yardsinches, hoursminutes, etc. There should also be some problems that require the student to describe their strategy used for conversion of units to mixed numbers or smaller units and also for them to solve the problems. Assessment Name: Applying Perimeter and Area Formulas Assessment Type: Mixed open ended with word problems Assessing Standards: 4.M.3, 4.M.4 Assessment Description: These items should include both examples where students find the area and perimeter of given figures, then also problems where there is a missing side or where they need to sketch the rectangle based on a description in a word problem and develop their own strategy for finding the area and perimeter of a rectangle. There should also be a problem included that involves finding the area of a complex figure. 3
4 Assessment Name: Measuring Angles Assessment Type: Performance Task Assessing Standards: 4.M.6 Assessment Description: Students should be required to use a protractor or angle ruler to measure given angles. They should also refer to benchmark angles to sketch required angles. A standard clock could be used to not only measure angles formed by the hour and minute hands but it could also be used to make the connection with fractional parts and a circle graph. Assessment Name: Clock Fractions and Circle Graphs Assessment Type: Performance Task Assessing Standards: 4.M.3, 4.M.6, 4.DA.3 Assessment Description: Students will explore conversion of units from minutes to hours and also the fractional parts of a clock and how those fractional hour parts relate to whole number minute parts, similar to the twocolumn charts they developed earlier in the unit. They will also relate the clock fractions to a circle graph and how the fractional parts of the circle graph will help to interpret data presented. End of Unit Summative Assessments Assessment Name: Final Summative Assessment Assessment Type: TBD Assessing Standards: 4.M.1, 4.M.2, 4.M.3, 4.M.4, 4.M.5, 4.M.6, 4.DA.3 Assessment Description: This assessment should include various tasks for actual measurement of units, conversion tables (2column) for units in the same category, sketching and measuring angles, and interpretation of units on a clock or in a circle graph. PLAN FOR INSTRUCTION Unit Vocabulary Key terms are those that are newly introduced and explicitly taught with expectation of student mastery by end of unit. Prerequisite terms are those with which students have previous experience and are foundational terms to use for differentiation. Key Terms for Unit Prerequisite Math Terms 4
5 Measurement Gram Mass Weight liter Kilometer Conversion Benchmark angle Protractor Angle ruler Circle graph Data Clock fractions Interpret inch centimeter meter feet yard Unit Resources/Notes Include district and supplemental resources for use in weekly planning Rulersmetric and English Angle ruler or protractor Balance scale and appropriate weights Twocolumn charts for unit conversions Various classroom objects for measuring weight, distance, angles Measure tapes Meter sticks Targeted Process Standards for this Unit PS.1: Make sense of problems and persevere in solving them Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway, rather than simply jumping into a solution attempt. They consider analogous problems and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, Does this make sense? and "Is my answer reasonable?" They understand the approaches of others to solving complex problems and identify correspondences between different approaches. Mathematically proficient students understand how mathematical ideas interconnect and build on one another to produce a coherent whole. 5
6 PS.2: Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. PS.4: Model with mathematics Mathematically proficient students apply the mathematics they know to solve problems arising in everyday life, society, and the workplace using a variety of appropriate strategies. They create and use a variety of representations to solve problems and to organize and communicate mathematical ideas. Mathematically proficient students apply what they know and are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, twoway tables, graphs, flowcharts and formulas. They analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. PS.5: Use appropriate Tools Strategically Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts. 6
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