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Color Key for Maps Red = Prior learning from CCGPS Yellow = State changes/rewording Purple = Footnote from CCGPS Teaching guide Priority Standards Troup County School System CCGPS Math Curriculum Map Fourth Grade – Third Quarter Major Standard major emphasis in grade level Supporting Standard medium emphasis in grade level Additional Standard minor emphasis in grade level Click on the standard for example assessment questions! CCGPS Example/Vocabulary System Resources MCC4.MD.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. a. Understand the relationship between gallons, cups, quarts, and pints. b. Express larger units in terms of smaller units within the same measurement system. c. Record measurement equivalents in a two column table. MCC4.MD.1 Students may use a two-column chart to convert from larger to smaller units and record equivalent measurements. They make statements such as, if one foot is 12 inches, then 3 feet has to be 36 inches because there are 3 groups of 12. In third grade, students had to measure and estimate liquid volumes and masses of objects using grams, kilograms and liters. They had to add, subtract, multiply or divide to solve onestep word problems involving masses or volumes that are given in the same units. For example, Joey had 2 liters of coke and his friend gave him 4 more liters. How many liters does Joey have now? Third grade students did not have to convert. Example 2: Example1: MCC4.MD.1 The Hands On Standards lessons can also be used in whole group as introductory lessons. Whole Group Conversion Concentration Game Metric Relationships A Pound of What? pg 96 Capacity Line Up pg. 91 Too Heavy? Too light? pg. 86 Exploring An Ounce pg. 77 Setting Standard pg. 58 Worth the Weight pg. 63 More Punch Please (cups, pints, quarts, gallons) pg. 96 Metric Measurement Sheet Coach book sheet Measuring Mania pg. 17 Students do not need to compare customary with metric units. Troup County Schools 2014 4th Grade Math CCGPS Curriculum Map Third Quarter 1 Continued from page 1 Essential Questions: What is the relationship between kilometers, meters and centimeters? What is the relationship between kilograms and grams? What is the relationship between pounds and ounces? What is the relationship between liters and milliliters? Continued from page 1 Foundational understandings to help with measure concepts: Understand that larger units can be subdivided into equivalent units (partition) Understand that the same unit can be repeated to determine the measure Understand the relationship between the size of a unit and the number of units needed. Vocabulary km, m, cm, kg, g, L, mL, inch, foot, yard, mile, ounce, pound, cup, pint, quart, gallon, hour, minute, second What is the relationship between hours, minutes, and seconds? How do I convert from a larger measurement unit to a smaller one? What happens to a measurement when we change units? Continued from page 1 Differentiation Activities Writing to Win Capacity Creatures Differentiation for: Customary Units of Length Customary Units of Weight Customary Units of Liquid Volume Metric Units of Lengths Metric Units of Mass and Liquid Volume Units of Time Patterns in Measurement Units (conversion tables) Grocery Store Conversions Baking Time Water Balloon Fun pg. 105 Click here for other lessons and assessments How are fluid ounces, cups, pints, quarts, and gallons related? Troup County Schools 2014 4th Grade Math CCGPS Curriculum Map Third Quarter 2 CCGPS MCC4.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. In third grade, students had to solve one-step word problems that involved kilograms, grams, liters, and elapsed time. They did not have to convert within these word problems. Essential Questions: How do I use the four operations to solve word problems involving distance, time, volume, mass, and money? Example/Vocabulary System Resources MCC4.MD.2 MCC4.MD.2 This standard includes multi-step word problems related to expressing measurements from a larger unit in terms of a smaller unit (e.g., feet to inches, meters to centimeters, dollar to cents). Students should have ample opportunities to use number line diagrams to solve word problems. The Hands On Standards lessons can also be used in whole group as introductory lessons. Example: Charlie and 10 friends are planning a pizza party. They purchased 3 quarts of milk. If each glass holds 8 oz will everyone get at least one glass of milk? Possible Solution Charlie plus 10 friends = 11 total people 11 people x 8 ounces (glass of milk) = 88 total ounces 1 quart = 2 pints = 4 cups = 32 ounces Therefore 1 quart = 2 pints = 4 cups = 32 ounces 2 quarts = 4 pints = 8 cups = 64 ounces 3 quarts = 6 pints = 12 cups = 96 ounces Additional Examples: Division/fractions: Susan has 2 feet of ribbon. She wants to give her ribbon to her 3 best friends so each friend gets the same amount. How much ribbon will each friend get? Students may record their solutions using fractions or inches. (The answer would be 2/3 of a foot or 8 inches. Students are able to express the answer in inches because they understand that 1/3 of a foot is 4 inches and 2/3 of a foot is 2 groups of 1/3) Addition: Mason ran for an hour and 15 minutes on Monday, 25 minutes on Tuesday, and 40 minutes on Wednesday. What was the total number of minutes Mason ran? Troup County Schools 2014 4th Grade Math CCGPS Curriculum Map Third Quarter Whole Group Converting Word Problems Measurement Word Problems Elapsed Time Ruler 1 Elapsed Time Ruler 2 24 Hour Number Line Too Heavy? Too Light? Elapsed Time Word Problems Liquid Volume Word Problems Metric Mass Word Problems Water Balloon Fun Money Word Problems (scroll down) Differentiation Activities Differentiation for Elapsed Time Journal Prompt Shopping Sheet Weekly Allowance Sheet Wonka Quartet Sheet Differentiation for Measurement Problems Elapsed Time Anchor Chart Click here for other lessons and assessments 3 See page 3 Continued from page 3 Subtraction: A pound of apples costs $1.20. Rachel bought a pound and a half of apples. If she gave the clerk a $5.00 bill, how much change will she get back? See page 3 Multiplication: Mario and his 2 brothers are selling lemonade. Mario brought one and a half liters, Javier brought 2 liters, and Ernesto brought 450 milliliters. How many total milliliters of lemonade did the boys have? Situations should include those that require decomposing and composing units of measure. Number line diagrams that feature a measurement scale can represent measurement quantities. Examples include: ruler, diagram marking off distance along a road with cities at various points, a time table showing hours throughout the day, or a volume measure on the side of a container. Example: At 7:00 Candace wakes up to go to school. It takes her 8 minutes to shower, 9 minutes to get dressed and 17 minutes to each breakfast. How many minutes does she have until the bus comes at 8:00 AM? Use the number line to help solve problem. Vocabulary Liquid volume, elapsed time, money, mass, length, distance Troup County Schools 2014 4th Grade Math CCGPS Curriculum Map Third Quarter 4 CCGPS MCC4.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. In third grade, students had to find the area and perimeter of shapes. They had to also solve real world problems involving perimeters including finding the perimeter given the side lengths, find the unknown side, and create and recognize rectangles with the same perimeter and different areas or with the same area and different perimeters. Essential Questions: How do I find the area of a rectangle? Example/Vocabulary System Resources MCC4.MD.3 MCC4.MD.3 The Hands On Standards lessons can also be used in whole group as introductory lessons. Whole Group A Dinner Party Fencing Garden Design a Zoo Area and Perimeter Lesson (scroll down for blacklines) Karl’s Garden Task Drawing Area and Perimeter Area and Perimeter Word Probs More Area/Perimeter Probs Link to Different Types of Graph Paper Area and Perimeter Book Peri Story Chocolate Covered Candies pg. 28 Perimeter and Area LV pg. 37 Parking Lot pg. 43 While students are expected to use formulas to calculate area and perimeter of rectangles, they need to understand and be able to communicate their understanding of why the formulas work. The formula for area is l x w and the answer will always be in square units. The formula for perimeter can be: 2 l + 2 w or 2 (l + w) (the answer will always be in linear units). This standard calls for students to generalize their understanding of area and perimeter by connecting the concepts to mathematical formulas. These formulas should be developed through experience not just memorization. Example: Mr. Rutherford is covering the miniature golf course with an artificial grass. How many 1-foot squares of carpet will he need to cover the entire course? How can the formula for the area of plane figures be used to solve problems? How do I find perimeter of a rectangle? How can the formula for the perimeter of plane figures be used to solve problems? Vocabulary Area Perimeter Formula Rectangular Width Length Troup County Schools 2014 4th Grade Math CCGPS Curriculum Map Third Quarter Differentiation Activities Hands On Standards: Perimeter and Area (lesson 1) Short Small Group Idea Writing to Win Differentiation for Perimeter Differentiation for Area Differentiation for Area Combined Differentiation for Unknown Measure Differentiation for Prob Solv Area Indoor Playground pg. 50 Click here for other lessons and assessments 5 CCGPS MCC4.MD.4 Make a line plot to display a data set of measurements in fractions of a unit (1/2, ¼, 1/8). Solve problems involving addition and subtraction of fractions with common denominators 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. In third grade, students had to measure lengths on a ruler marked with halves and fourths of an inch. They then had to show the data on a line plot with the units marked off as whole numbers, halves, or quarters. Essential Questions: How do I make a line plot to display a data set? How can I use a line plot to solve problems involving addition and subtraction of fractions? Example/Vocabulary MCC4.MD.4 This standard provides a context for students to work with fractions by measuring objects to an eighth of an inch. Students are making a line plot of this data and then adding and subtracting fractions based on data in the line plot. Example: Students measured objects in their desk to the nearest ½, ¼, or 1/8 inch. They displayed their data collected on a line plot. How many objects measured ¼ inch? ½ inch? If you put all the objects together end to end what would be the total length of all the objects? System Resources MCC4.MD.4 Whole Group Ants on A Line Plot Objects in My Desk Line Plot Short Instructional Activity Measure Mania (practice measuring 1/2 , ¼, 1/8 of an inch) Creating Line Plots Gone Fishing How Tall Are We Differentiation Activities What’s The Story? Pg. 22 Differentiation for Line Plots Click here for other lessons and assessments A line plot shows the “shape” of the data and provides the foundation for future data concepts, such as mode and range. Vocabulary Data set Line plot Nearest ½, ¼, 1/8 inch Troup County Schools 2014 4th Grade Math CCGPS Curriculum Map Third Quarter 6 CCGPS MCC4.G.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures. Example/Vocabulary System Resources MCC4.G.1 MCC4.G.1 The Hands On Standards lessons can also be used in whole group as introductory lessons. Whole Group Geoboard Line Segments Angles on Geoboard Angle Barrier Game This standard asks students to draw two-dimensional geometric objects and to also identify them in twodimensional figures. Students do not easily identify lines and rays because they are so abstract. This is new learning. Essential Questions: How do I draw lines, line segments, rays, angles, perpendicular lines, parallel lines, and identify them in two-dimensional figures? What Makes A Shape pg. 12 Angle Shape Sort pg. 17 Be An Expert pg. 28 Is This A Right Angle pg. 24 Angle Sort Body Angles (good intro to angles) Hunt for Angles, Perpendicular and Parallel Lines Example: Draw two different types of quadrilaterals that have two pairs of parallel sides? Is it possible to have an acute right triangle? Justify your reasoning using pictures or words. Parallel, Perpendicular, Lines Games Packet Example: How many acute, obtuse, and right angles are in this shape? Troup County Schools 2014 4th Grade Math CCGPS Curriculum Map Third Quarter 7 See page 6 Continued from page 6 Example: Draw and list the properties of a parallelogram. Draw and list the properties of a rectangle. How are your drawings and lists alike or different? Parallel or Perpendicular Lines: Students should become familiar with the concept of parallel and perpendicular lines. Two lines are parallel if they never intersect and are always equidistant. Two lines are perpendicular if they intersect in right angles (90 degrees). Students may use transparencies with lines to arrange two lines in different ways to determine that the 2 lines might intersect in one point or many never intersect. Continued from page 6 Differentiation Activites Hands On Standards: Parallel and Perpendicular Lines (lesson1) Writing to Win Quick Tasks Differentiation for Lines, Rays, Angles Differentiation for Parallel and Perpendicular Lines Names of Polygons Chart Click here for other lessons and assessments Vocabulary Troup County Schools 2014 4th Grade Math CCGPS Curriculum Map Third Quarter 8 CCGPS MCC4.G.2 Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. In third grade, students had to understand that shapes in different categories (rhombuses, rectangles, and others) may share attributes (like having four sides), and that the shared attributes can define a larger category (like quadrilaterals). Students had to recognize rhombuses, rectangles, and squares as quadrilaterals, and draw examples of quadrilaterals that don’t belong in any of these subcategories. Essential Questions: How do I classify and identify twodimensional figures according to attributes of line relationships or angle size? What is a right triangle? Example/Vocabulary MCC4.G.2 Two dimensional figures may be classified using different characteristics such as, parallel or perpendicular lines or by angle measurement. Example: System Resources MCC4.G.2 The Hands On Standards lessons can also be used in whole group as introductory lessons. Whole Group Constructing Quadrilaterals Quadrilateral Criteria Right Triangles on Geoboard Quadrilateral Round Up (venn diagrams) pg. 49 Do you agree with the label on each of the circles in the Venn Diagram above? Describe why some shapes fall in the overlapping sections of the circles. Example: Draw and name a figure that has two parallel sides and exactly two right angles. Example: For each of the following, sketch an example if it is possible. If it is possible, say so, and explain why or show a counterexample. A parallelogram with exactly one right angle. An isosceles right triangle. A rectangle that is NOT a parallelogram Every square is a quadrilateral Every trapezoid is a parallelogram Example: Identify which of these shapes have perpendicular or parallel sides and justify your selection. Thoughts About Triangles pg. 34 My Many Triangles pg. 42 Properties of Triangles Marshmallow Angles Differentiation Activities Hands On Standards: Plane Shapes (lesson 2) Identify and Classify Triangles (lesson 3) Differentiation for Classifying Triangles Differentiation for Classifying Quadrilaterals Investigating Quads pg. 57 Quad Pieces Ring Labels (classifying) Mystery Rings (enrichment) Click here for other lessons and assessments Troup County Schools 2014 4th Grade Math CCGPS Curriculum Map Third Quarter 9 Continued from page 8 See page 8 See page 8 Angle Measurement: This expectation is closely connected to MD5, MD6, (this will come up later in the quarter). Students’ experiences with drawing and identifying right, acute, and obtuse angles support them in classifying two-dimensional figures based on specified angle measurements. They use the benchmark angles of 90°, 180°, and 360° to approximate the measurement of angles. Right triangles can be a category for classification. A right triangle has one right angle. There are different types of right triangles. An isosceles right triangle has two or more congruent sides and a scalene right triangle has no congruent sides. Vocabulary Right triangles Scalene triangles Isosceles triangle Equilateral Triangle Congruent Parallel Perpendicular Troup County Schools 2014 4th Grade Math CCGPS Curriculum Map Third Quarter 10 CCGPS Example/Vocabulary MCC4.G.3 Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. MCC4.G.3 Students need experiences with figures which are symmetrical and non-symmetrical. Figures include both regular and non-regular polygons. Folding cut-out figures will help students determine whether a figure has one of more lines of symmetry. This is new learning. This standard only includes line symmetry not rotational symmetry. Essential Questions: What is a line of symmetry? Example: For each figure, draw all of the lines of symmetry. What pattern do you notice? How many lines of symmetry do you think there would be for regular polygons with 9 and 11 sides? Sketch each figure and check your predictions. How can I draw a line of symmetry? Vocabulary Line symmetry Symmetric figures Fold System Resources MCC4.G.3 The Hands On Standards lessons can also be used in whole group as introductory lessons. Whole Group Super Hero Symmetry pg. 65 Line Symmetry pg. 70 Decoding ABC Symmetry Symmetry on Geoboards Symmetry in Shapes Symmetry in Regular Polygons Symmetry with Coin Designs Quilt Symmetry pg. 79 Decoding ABC Symmetry pg.84 Differentiation Activities Hands On Standards: Line Symmetry (lesson 4) Symmetrical Figures (lesson 5) Creating Lines of Symmetry Sheet Writing to Win Geometry Town pg. 89 Lines of Symmetry for Circles Lines of Symmetry for Triangles Lines of Symmetry for Quads Differentiation for Symmetry Differentiation for Drawing Lines of Symmetry Click here for other lessons and assessments Troup County Schools 2014 4th Grade Math CCGPS Curriculum Map Third Quarter 11 CCGPS MCC4.MD.5 Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: 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. b. An angle that turns through n onedegree angles is said to have an angle measure of n degrees. This is new learning. Essential Questions: How are a circle and an angle related? How can I explain the concept of angle measurement? Example/Vocabulary MCC4.MD.5 This standard brings up a connection between angles and circular measurement (360 degrees). The diagram below will help students understand that an angle measurement is not related to an area since the area between the 2 rays is different for both circles yet the angle measure is the same. System Resources MCC4.MD.5 The Hands On Standards lessons can also be used in whole group as introductory lessons. Whole Group Which Wedge is Right? Pg. 124 Angles In Your Name Angle Tangle pg. 132 Watch this video that explains the standard. Finding Angles in Pizza This standard calls for students to explore an angle as a series of “one-degree turns”. A water sprinkler rotates one-degree at each interval. If the sprinkler rotates a total of 100 degrees, how many one-degree turns has the sprinkler made? Watch this Youtube Video! (It will clear up all misunderstandings Differentiation Activities Hands On Standards: Understanding Angles (lesson 2) Differentiation for Beginning Angles in a Circle of MD.5, 6, 7) Differentiation for Degrees Vocabulary Angle, circle, rays, common endpoint, intersect, onedegree angle, degrees, angle measurement. Troup County Schools 2014 4th Grade Math CCGPS Curriculum Map Third Quarter Journal Prompt Click here for other lessons and assessments 12 CCGPS MCC4.MD.6 Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. This is new learning. Essential Questions: How do I measure an angle using a protractor? Example/Vocabulary MCC4.MD.6 Before students begin measuring angles with protractors, they need to have some experience with benchmark angles. They transfer their understanding that a 360° rotation about a point makes a complete circle to recognize and sketch angles that measure approximately 90° and 180°. They extend this understanding and recognize and sketch angles that measure approximately 45° and 30°. They use appropriate terminology (acute, right, and obtuse) to describe angles and rays (perpendicular). How do I sketch an angle? Students should be able to recognize benchmark angles: 90 degree angle= 1⁄4 of a circle 180 degree angle = 1⁄2 of a circle 270 degree angle = 3⁄4 of a circle 360 degrees = full circle A protractor is a tool marked off in intervals of 0 to 180 degrees and is used to measure the size of an angle. A Protractor has two scales, each of which starts at zero degrees. One scale is read clockwise and the other is read counterclockwise. When measuring, students see that hey can choose the scale that makes sense for the angle positioning. While students use the protractor to measure or draw angles, encourage them to use reasoning to decide if an angle measure makes sense. They use their knowledge of acute, obtuse, right, and straight angles to decide on the reasonableness of angles measures. Vocabulary Protractor, rays, perpendicular, degrees, measure, acute, right, straight, obtuse, angles, inner scale, outer scale Troup County Schools 2014 4th Grade Math CCGPS Curriculum Map Third Quarter System Resources MCC4.MD.5 The Hands On Standards lessons can also be used in whole group as introductory lessons. Whole Group Learn How to Use Protractor (super intro lesson) Angle Powerpoint Angles in Quadrilaterals Angles in Triangles Predicting & Measuring Angles Guess My Angle Game pg. 149 Measuring An Angle Build An Angle Ruler pg. 140 Sending the Right Signal Differentiation Activities Hands On Standards: Measure and Classify Angles (lesson 3) Differentiation for Measuring and Drawing Angles Angle Barrier Game Turn Turn Turn pg. 157 Writing to Win Click here for other lessons and assessments 13 CCGPS MCC4.MD.7 Recognize angle measure as additive. When an angle is decomposed into non-overlapping 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 or letter for the unknown angle measure. This is new learning. Essential Questions: How can angle measures be additive? How do I solve addition and subtraction problems to find unknown angle measurement? Example/Vocabulary MCC4.MD.7 This standard addresses the idea of decomposing (breaking apart) an angle into smaller parts. System Resources MCC4.MD.7 The Hands On Standards lessons can also be used in whole group as introductory lessons. Whole Group Unknown Angle Word Probs How Many Degrees Angles in a Right Triangle Example: A lawn water sprinkler rotates 65° and then pauses. It then rotates an additional 25°. What is the total degree of the water sprinkler rotation? To cover a full 360° how many times will the water sprinkler need to be moved? If the water sprinkler rotates a total of 25° then pauses, how many 25° degree cycles will it go through for the rotation to reach at least 90°? Small Tasks to do with this standard Example: If the two rays are perpendicular, what is the value of m? Water Sprinklers Example: Joey knows that when a clock’s hands are exactly on 12 and 1, the angle formed by the clock’s hands measures 30°. What is the measure of the angle formed when a clock’s hands are exactly on the 12 and the 4? The primary concept is solving problems with adjacent angles. Non-overlapping Unknown Diagram Decompose Additive MCC4.MD.7 Vocabulary Troup County Schools 2014 4th Grade Math CCGPS Curriculum Map Third Quarter Finding An Unknown Angle Task Angles in Shapes Summing It UP pg. 162 Differentiation Activities Hands On Standards: Tessellation Angles (lesson 4) Pattern Block Angles Differentiation for Joining and Separating Angles Differentiation for Prob Solving Click here for other lessons and assessments 14 CCGPS MCC4.MD.8 Recognize area as additive. Find areas of rectilinear figures by decomposing them into nonoverlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems. Example/Vocabulary MCC4.MD.8 This standard uses the word rectilinear. A rectilinear figure is a polygon that has all right angles. System Resources MCC4.MD.8 The Hands On Standards lessons can also be used in whole group as introductory lessons. Whole Group Find Area of Rectilinear Shapes Area of Rectilinear Shapes Area of Irregular Figures Design A Flower Bed Rectilinear Area Poster Square Count Shortcut Students in 3rd grade learned how to find the area of a rectangle using tiling, the formula, and the distributive property. Differentiation Activities Essential Questions: Differentiation for Area of Combining Rectangles How do I find the area of a rectilinear figure? Troup County Schools 2014 4th Grade Math CCGPS Curriculum Map Third Quarter 15 Example: A storage shed is pictured below. What is the total area? How could the figure be decomposed to help find the area? Example: Students can decompose a rectilinear figure into different rectangles. They find the area of the figure by adding the areas of each of the rectangles together. Vocabulary Area, additive, rectilinear, decompose, non-overlapping Troup County Schools 2014 4th Grade Math CCGPS Curriculum Map Third Quarter 16 Ongoing Standards for Mathematical Practice 1. Make sense of problems and persevere in solving them. Mathematically proficient students in grade 4 know that doing mathematics involves solving problems and discussing how they solved them. Students explain to themselves the meaning of a problem and look for ways to solve it. Fourth graders may use concrete objects or pictures to help them conceptualize and solve problems. They may check their thinking by asking themselves, “Does this make sense?” They listen to the strategies of others and will try different approaches. They often will use another method to check their answers. 2. Reason abstractly and quantitatively. Mathematically proficient fourth graders should recognize that a number represents a specific quantity. They connect the quantity to written symbols and create a logical representation of the problem at hand, considering both the appropriate units involved and the meaning of quantities. They extend this understanding from whole numbers to their work with fractions and decimals. Students write simple expressions, record calculations with numbers, and represent or round numbers using place value concepts. 3. Construct viable arguments and critique the reasoning of others. In fourth grade mathematically proficient students may construct arguments using concrete referents, such as objects, pictures, and drawings. They explain their thinking and make connections between models and equations. They refine their mathematical communication skills as they participate in mathematical discussions involving questions like “How did you get that?” and “Why is that true?” They explain their thinking to others and respond to others’ thinking. 4. Model with mathematics. 5. Use appropriate tools strategically. Mathematically proficient fourth grade students experiment with representing problem situations in multiple ways including numbers, words (mathematical language), drawing pictures, using objects, making a chart, list, or graph, creating equations, etc. Students need opportunities to connect the different representations and explain the connections. They should be able to use all of these representations as needed. Fourth graders should evaluate their results in the context of the situation and reflect on whether the results make sense. Mathematically proficient fourth graders consider the available tools (including estimation) when solving a mathematical problem and decide when certain tools might be helpful. For instance, they may use graph paper or a number line to represent and compare decimals and protractors to measure angles. They use other measurement tools to understand the relative size of units within a system and express measurements given in larger units in terms of smaller units. Troup County Schools 2014 4th Grade Math CCGPS Curriculum Map Third Quarter 17 Ongoing Standards for Mathematical Practice 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. As fourth graders develop their mathematical communication skills, they try to use clear and precise language in their discussions with others and in their own reasoning. They are careful about specifying units of measure and state the meaning of the symbols they choose. For instance, they use appropriate labels when creating a line plot. In fourth grade mathematically proficient students look closely to discover a pattern or structure. For instance, students use properties of operations to explain calculations (partial products model). They relate representations of counting problems such as tree diagrams and arrays to the multiplication principal of counting. They generate number or shape patterns that follow a given rule. Students in fourth grade should notice repetitive actions in computation to make generalizations Students use models to explain calculations and understand how algorithms work. They also use models to examine patterns and generate their own algorithms. For example, students use visual fraction models to write equivalent fractions. Troup County Schools 2014 4th Grade Math CCGPS Curriculum Map Third Quarter 18 Standard MCC4. G.1 and G.2 MD.5, 6, 7 MD.1 MD.4 Additional Resources for Professional Development Article – Naming Shapes Article – Teaching About Quadrilaterals Video – Great video on how to teach these standards (You tube so watch at home) Video – Another great video on how to teach MD.5 (You tube so watch at home) Video – Scroll down to Geometry Section and Click on Angles Article – Angles Again Article – Teaching Angles Video – Scroll down to Measurement Section and click on “Converting Units” Video – Line Plots Troup County Schools 2014 4th Grade Math CCGPS Curriculum Map Third Quarter 19