CCSS Mathematics Implementation Guide Grade 3 (Draft) First Nine Weeks

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1 0 03 First Nine Weeks Big Ideas We are able to use place value understanding to round whole numbers to the nearest 0 or 00. What are the steps in rounding whole numbers? When would rounding be useful?. Make sense of Do in order from the top down MA MA MA.3.3-.: Compare and analyze whole number quantities through 999,999 and represent in word form. 3.NBT. Use place value understanding to round whole numbers to the nearest 0 or 00. **Please Note: Since the geometry standards are so numerous (see fourth nine weeks), geometric vocabulary and MA MA3.3-. Classify triangles (scalene, isosceles, equilateral;,and their angles as right, acute, obtuse)ma circles (center, radius, circumference, diameter) should be incorporated in daily warm-ups, Odyssey lessons, mini-lessons, etc.. Model with 8 Envision Topic Lessons -, & 9 Envision Topic Lesson (rounding) Rounding with Mr. Nussbaum ( Rounding Games ( Virtual place value blocks ( g t_.html) Place value games ( imals.html) Rounding to nearest 0: Rounding BrainPop: rounding/preview.weml Comparing Numbers: ine=9 Odering Numbers: Look for and make July 3, 0

2 We are able to fluently add and subtract within,000. How can you add or subtract numbers up to,000? What is the relationship between addition and subtraction? We are able to interpret products of whole numbers What is multiplication? When do you use it? NBT. Fluently add and subtract within,000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. MA Find missing numbers in addition and subtraction. 3.OA. Interpret products of whole numbers, eg., interpret x as the total number of objects in groups of objects each. For example, describe the context in which a total number of objects can be expressed as x. See addendum 8 Envision Topic (Addition) Envision Topics 3 & (Subtraction) Modeling Addition with virtual place value blocks ( g_3 _t_.html?from=topic_t_.html) Modeling Subtraction with virtual place value blocks ( g_3 _t_.html?from=topic_t_.html) SuperTeacher on.html Envision Topics,, & 8 Visualize multiplication of two numbers with areas. (arrays) ( t_.html?from=topic_t_.html). Make sense of. Model with. Look for and make July 3, 0

3 When we divide, we break down larger numbers into smaller equal groups. What strategies would be used to divide? When would they be used? OA. Interpret a whole-number quotients of whole numbers, e.g., interpret /8 as the number of objects in each share when objects are partitioned equally into 8 shares, or as a number of shares when objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed /8. See addendum Envision Topics, 8, & 9 We are able to use multiplication and division to solve word problems using different strategies (arrays, equal groups, pictures, symbols). What strategies can be used to solve multiplication and division word problems? 3.OA.3 Use multiplication and division within 00 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. MA Multi-digit (Example: x ) Envision th grade book Topic Problem solving with all operations Make sense of. Model with. Look for and make July 3, 0

4 0 03 Second Nine Weeks Big Ideas We use rules of multiplication to make it easier to solve problems What are the properties of multiplication? When do we use them? 3.OA. Apply properties of operations as strategies to multiply and divide. Examples: If x= is known, then x= is also known. (Commutative Property of multiplication.) 3xx can be found by 3x=, then x=30, or by x=0, then 3x0=30. (Associative Property of multiplication.) Knowing that 8x=0 and 8x=, one can find 8x as 8x(+)=(8x)+(8x)=0+yy=. (Distributive Property of multiplication.) 8 Envision th grade book Topic When we know multiplication facts, it is easier to solve problems. How does knowing multiplication and division facts help us solve problems. 3.OA. Fluently multiply and divide within 00, using strategies such as the relationship between multiplication and division (e.g., knowing that 8x=0, one knows 0/=8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. 8 Division games to help build fluency with division facts ( n.html) Multiplication games to help build fluency/ understand the concept of multiplication facts ( modelsmultidigit.html) Flashcards: Make sense of. Model with. Look for and make July 3, 0

5 We can solve two-step word problems by creating a number sentence. How can you solve a two-step word problem? OA.8 Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Envision th grade book Topic lesson What strategies would you use to check if your answer makes sense? When we use number patterns, it is easier to learn multiplication and addition facts. What are number patterns? How can I use number patterns to learn how to add and multiply? We know that a fraction is part of a whole. How can I show one part of a whole? 3.OA.9 Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that times a number is always even, and explain why times a number can be decomposed into two equal addends. 3.NF. Understand a fraction /b as the quantity formed by part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size /b. See addendum 3 Create patterns using attribute blocks Create number patterns with We know that there are fractional parts between 0 and on the number line. How do you divide 0 to on a number line into equal parts? Explain your thinking. 3.NF.a Represent a fraction /b on a number line diagram by defining the interval from 0 to as the whole and partitioning it into b equal parts. Recognize that each part has size /b and that the endpoint of the part based at 0 locates the number /b on the number line.. Make sense of. Model with. Look for and make July 3, 0

6 We can divide a number line into equal fractional parts. How do you divide a number line into equal fractional parts starting at zero? NF.b Represent a fraction a/b on a number line diagram by marking off a lengths /b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line. Why is it important? We can show equivalent fractions using a variety of models. How do you use a model to show equivalent fractions? Which model will help you show your thinking? 3.NF.3a &b Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line and create a visual fraction model. See addendum MA Use the fewest possible number of coins when making change. 3 8 Fraction Frenzy: Visual Fractions: We use graphs to show information. When might I want to use a graph to show information? Which type of graph would I use? 3.MD.3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one-and two-step how many more and how many less problems using information presented in the scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent pets. Envision Topic 0 Lesson Create a Graph Make sense of. Model with. Look for and make July 3, 0

7 0 03 Third Nine Weeks Big Ideas We know rulers are tools used to measure length using whole numbers and fractions When would you use a ruler? MA MA MA MA MA Organize, interpret, analyze, and compare tables, bar graphs, picture graphs, and dot plots. MA3.3-. Find the range of a data set Envision Topic Ruler game How do you measure using a ruler? How can you show your data on a line plot 3.MD. Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units whole numbers, halves, or quarters We can tell time to the nearest minute. How can I use a picture or number line to show changes in time? 3.MD. Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. Envision Topic Stop the Clock How can what you know about fractions help you understand telling time?. Make sense of. Model with. Look for and make July 3, 0

8 We can classify shapes based on their number of sides. How are shapes classified? What are the different categories? 0 03 MA.3.3-., MA3.3-. Classify polygons (triangles, quadrilaterals, pentagons, hexagons, and octagons): Analyze the results of combining and subdividing these shapes. Transformations (Slides, flips, turns). MA MA3.3-. points, lines, line segments, rays, parallel, perpendicular, and intersecting. Envision Topic 0 3.G. Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.. Make sense of. Model with. Look for and make July 3, 0

9 We can classify shapes based on their number of sides. How are shapes classified? What are the different categories? 0 03 Fourth Nine Weeks MA.3.3-., MA3.3-. Classify polygons (triangles, quadrilaterals, pentagons, hexagons, and octagons): Analyze the results of combining and subdividing these shapes. Transformations (Slides, flips, turns). MA MA3.3-. points, lines, line segments, rays, parallel, perpendicular, and intersecting. Envision Topic 0 3.G. Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.. Make sense of. Model with. Look for and make July 3, 0

10 0 03 Big Ideas We can divide shapes into equal parts. How can I divide this shape into equal areas? 3.G. Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into parts with equal area, and describe the area of each part as ¼ of the area of the shape. Envision Topic How many ways can you show multiple parts of a shape? We know that sometimes rectangles with the same areas may have different perimeters. 3.MD.8 Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding the unknown side lengths, and exhibiting rectangles with the same perimeter and different areas or with the same area in different perimeters. Envision Topic Can you give an example of when a rectangle has the same area, but different perimeters?. Make sense of. Model with. Look for and make July 3, 0

11 We know the inside space of a plane figure is called the area. We measure area in square units MD. Measure areas by counting unit squares (square cm, square m, square in., square ft., and improvised units). See addendum Envision Topic What is area and when do we need to measure the area? Why do we measure area in square units? We use the area of a whole rectangle to find the area of the smaller parts inside of it. What strategies do you use to find the area of multiple rectangles? 3.MD.c Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a x b and a x c. Use area models to represent the distributive property in mathematical reasoning. See addendum We can separate an irregular figure into different rectangles to find the area. How do you find the area of an irregular shape? 3.MD.d Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems. See addendum Envision Topic Explain your thinking. MA MA3.3-. Unlikely and Likely and Probability. Make sense of. Model with. Look for and make July 3, 0

12 Can be embedded in 3.OA. : 0 03 Addendum Supporting standards that are NOT critical, but can be taught if time allows 3.OA. Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8x?=8, ={} / 3, x=? Can be embedded in 3.OA.: 3.OA.. Understand division as an unknown factor problem. For example, find 3/8 by finding the number that makes 3 when multiplied by 8. Can be embedded in 3.NF.: 3.NF.3d Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole number. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. Can be embedded in 3.NF.3a: 3.NF.3c. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3= 3/; recognize that / = ; locate / and at the same point of a number line diagram.. Make sense of. Model with. Look for and make July 3, 0

13 0 03 Can be embedded in 3.MD.: 3.MD.a. A square with side length unit, called a unit square, is said to have one square unit of area, and can be used to measure area. 3.MD.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. Can be embedded in 3.MD.c: 3.MD.a Find the area of the rectangle with whole number side lengths by tiling, and show that the area is the same as would be found by multiplying the side lengths. Can be embedded in 3.MD.d: 3.MD.b Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning. First 0 Days of Math: Other Useful Websites: Interactive Protractor (Lots of Fun): Make sense of. Model with. Look for and make July 3, 0