# 2012 gr3math ican

## Transcript

1 Elizabethtown Independent Schools Grade Third Math Standards and “I Can Statements” Priority Standard (M) – Multiple Unit Standard (P) – CC.3.OA.1 Interpret products of whole numbers, e.g., interpret 5 × 7 as the total - Standard number of objects in 5 g roups of 7 objects each. For example, describe a context in which a objects can be expressed as 5 × 7. total number of (P), (M)  I can multiply to find the product .  I can show products using equal groups, arrays, repeated addition , area models and ines . number l Standard - CC.3.OA.2 Interpret whole - number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned int o 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 as 56 ÷ 8. (M)  I can find the quotient of whole numbers using equal groups.  I can tell what the numbers in a division prob lem mean. I can explain what division means.   using equal sharing , arrays and number lines . I can show division Standard - CC.3.OA.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measu rement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. (P)  I can multiply to solve word problems by using drawings and equations with a symbol for the unknown number .  I can divide to solve w ord problems by using drawings and equations with a symbol for the unknown number .

2  I can decide when to multiply or divide to solve word problems. Standard CC.3.OA.4 Determine the unknown whole number in a multiplication or - three whole numbers. For example, determine the unknown division equation relating number that makes the equation true in each of the equations: 8 × ? = 48, 5 = __÷ 3, 6 × 6 = ?. I can find any  missing number in a multiplication problem. I can find any missing number in a divisi on problem.  - CC.3.OA.5 Apply properties of operations as strategies to multiply and divide. Standard Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 2 = 30, or by 5 × 2 = 10 then 3 × 10 = 30. 3 × 5 × 2 can be found by 3 × 5 = 15 then 15 × (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 ×2) = 40 + 16 = 56. (Distributive property.) (Students need not use formal ter ms for these properties.)  I can use the properties of multiplication and division to solve problems.  I can explain the commutative property of multiplication.  I can explain the associative property of multiplication.  I can explain the distributive pr operty of multiplication. - Standard Understand division as an unknown - factor problem. For example, CC.3.OA.6 divide 32 ÷ 8 by finding the number that makes 32 when multiplied by 8. (M)  I can identify the multiplication problem related to the division pro blem.  I can use multiplication to solve division problems. I can recognize and explain the relationship between multiplication and division.  Standard - CC.3.OA.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. (P), (M) By the end of Grade 3, know from memory all products of one - digit numbers.

3  I can memorize all products within 100.  s to solve a multiplication problem. I can use strategie  I can use strategies to solve a division problem. CC.3.OA.8 Standard - step word problems using the four operations. Represent - Solve two Assess the these problems using equations with a letter standing for the unknown quantity. reasonableness of answers using mental computation and estimation strategies including rounding. (This standard is limited to problems posed with whole numbers and having whole - he number answers; students should know how to perform operations in t conventional order when there are no parentheses to specify a particular order (Order of Operations).  I can solve problems using the order of operations .  I can identify different strategies for estimating.  I can construct an equation with a letter st anding for the unknown quantity.  I can solve two - step word problems using the four operations.  I can justify my answer using estimation strategies and mental computation. Standard CC.3.OA.9 Identify arithmetic patterns (including patterns in the addi tion table - or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends. (M)  I can identify patterns.  I can explain relationships between the numbers in a pattern. - CC.3.NBT.1 Use place value understanding to round whole numbers to the Standard nearest 10 or 100. (P), (M)  I can round a whole number to the nearest 10.  I can round a whole number to the neares t 100.

4 Standard - CC.3.NBT.2 Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. (A range of algorithms may be used.) (P), (M) I can identify strategies for adding within 1000.  I can identify strategies for subtracting within 1000.  I can fluently add within 1000.  I can fluently subtract within 1000.  Standard CC.3.NBT.3 Multiply one - digit whole numbers by multiples of 10 in t he range - - 10 90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. (A range of algorithms may be used.)  to multiply one - digit whole numbers by multiples of 10. I can use strategies Standard - CC.3.NF.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. (P)  I can define a unit fraction. I can recognize a unit fraction as part of a whole and a set  .  I can draw, identify and explain the parts of a written fraction.  I can compare fractions using equal to, less than, and greater than one. Standard CC.3.NF.2 Understand a fraction as a number on the number line; represent - fractions on a nu mber line diagram. a. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 l ocates the number 1/b on the number line. (Grade 3 expectations in this domain are limited to fractions with denominators 2,3,4,6, and 8.)  I can define the interval from 0 to 1 on a number line as the whole.

5  I can divide a whole on a number line into equa l parts.  I can recognize that the equal parts between 0 and 1 stand for a fraction.  I can represent each equal part on a number line with a fraction. Standard CC.3.NF.2b Represent a fraction a/b on a number line diagram by marking off a - rom 0. Recognize that the resulting interval has size a/b and that its endpoint lengths 1/b f locates the number a/b on the number line. I can define the interval from 0 to 1 on a number line as the whole.   I can divide a whole on a number line into equal parts. I can represent each equal part on a number line with a fraction.   I can explain that the endpoint of each equal part represents the total number of equal parts. | - - - | - - - | - - - | - - - | 0 1/4 2/4 3/4 4/4 - CC.3.NF.3 Explain equivalence of fractions in special cases, and compare Standard 3a Understand two fractions as equivalent fractions by reasoning about their size. 3b Recognize and (equal) if they are the same size, or the same point on a number line. ge nerate simple equivalent fractions (e.g., 1/2 = 2/4, 4/6 = 2/3), Explain why the fractions are equivalent, e.g., by using a visual fraction model.  I can describe equivalent fractions.  I can recognize simple equivalent fractions. I can compare fractions b y their size to determine equivalence.   I can use number lines and area models , etc. to explain why fractions are equivalent .

6 Standard - CC.3.NF.3a Understand two fractions as equivalent (equal) if they are the same ne. (Grade 3 expectations in this domain are limited size, or the same point on a number li to fractions with denominators 2, 3, 4, 6, and 8.) Recognize and generate simple equivalent fractions (e.g., 1/2 = 2/4, - CC.3.NF.3b Standard 4/6 = 2/3), Explain why the fractions y using a visual fraction model. are equivalent, e.g., b (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.) - CC.3.NF.3c Express whole numbers as fractions, and recognize fractions that Standard mples: Express 3 in the form 3 = 3/1; recognize that are equivalent to whole numbers. Exa 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.)  I can recognize whole numbers wri tten in fractional parts on a number line.  I can recognize the difference in a whole number and a fraction.  I can express whole numbers as fractions.  I can explain how a fraction is equivalent to a whole number. Standard CC.3.NF.3d Compare two fr actions 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. Record the results of comparisons with the symbols >, =, or <, and justify t he conclusions, e.g., by using a visual fraction model. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.)  I can explain what a numerator means.  I can explain what denominator means.  I can recognize whet her fractions refer to the same whole.  I can decide if comparison of fractions can be made (if they refer to the same whole).  I can explain why fractions are equivalent.  I can compare two fractions with the same numerator by reasoning about their size.

7  I can compare two fractions with the same denominator by reasoning about their size. I can record the results of comparisons using symbols >, =, or <.  CC.3.MD.1 Tell Standard - and write time to the nearest minute and measure time s. Solve word problems involving addition and subtraction of time intervals in minute intervals in minutes, e.g., by representing the problem on a number line diagram. (P) I can recognize minute marks on analog clock face and minute position on digital  clock face.  l and write time to the nearest minute. I can tel I can compare an analog clock face with a number line.  I can use a number line to add and subtract time.   I can solve word problems related to adding and subtracting minutes. Standard - CC.3.MD.2 Measure and est imate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). (Excludes compound units such as cm^3 and finding the geometric volume of a container.) Add, subtract, multiply, or divide - word problems involving masses or volumes that are given in the same to solve one step units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. (Excludes multiplicative comparison problems (problems involving notions of “times as much. ”)  I can estimate liquid volume using liters.  I can estimate mass using grams and kilograms. I can add, subtract, multiply and divide units of liters, grams, and kilograms.   I can use strategies to represent a word problem involving liquid volume or m ass.  I can solve one step word problems involving masses given in the same units.

8  I can solve one step word problems involving liquid volume given in the same units (eg. by using cups, pints, quarts, and gallons). I can measure liquid volumes using l iters.   I can measure mass of objects using grams (g), and kilograms (kg). CC.3.MD.3 Standard - Draw a scaled picture graph and a scaled bar graph to represent a - and two categories. Solve one step “how many more” and “how many data set with several - ” problems using information less presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets. (P), (M)  I can identify and explain the scale of a graph.  I can interpret a bar/picture graph to det ermine ‘how many more” and “how many less”.  I can analyze a graph with a scale greater than one. I can choose a proper scale for a bar graph or picture graph.   I can create a scaled picture graph to show data.  I can create a scaled bar graph to show data. Standard CC.3.MD.4 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 quarters. whole numbers, halves, or I can define horizontal axis.   I can identify each mark on the line plot as data or a number of objects.  I can determine appropriate unit of measurement.  I can determine appropriate scale for line plot.  I can measure and record lengths u sing rulers marked with halves and fourths of an inch.  I can create a line plot where the horizontal scale is marked off in appropriate units - whole numbers, halves, or quarters.

9 Standard - CC.3.MD.5 Geometric measurement: of plane figures and understand concepts of area Recognize area as an attribute 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. b. A plane figure which can be covered without gap s or overlaps by n unit squares is said -- (P) to have an area of n square units.  I can define “unit square”. I can define area.   I can find the area of a plane figure using unit squares. I can cover the area of a plane figure with unit squares without gaps or overlaps.  Standard - CC.3.MD.6 Geometric measurement: Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).  I can measure areas by counting unit squares.  I can use unit squares of cm, m, in, ft , and other sizes of unit squares to measure area. Standard - CC.3.MD.7a Geometric measurement: Relate area to the operations of Find the area of a rectangle with whole - multiplication and addition. number side lengths by tiling it, and show that the ar ea is the same as would be found by multiplying the side lengths.  I can find the area of a rectangle by tiling it in unit squares.  I can find the side lengths of a rectangle in units. I can compare the area found by tiling a rectangle to the area fo und by multiplying  the side lengths. Standard - CC.3.MD.7b 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. (M)

10  I can multiply side lengths to find areas of rectangles. I can solve real world problems using area.   I can use arrays to represent multiplication problems. CC.3.MD.7c Use tiling to show in a concrete c Standard - ase that the area of a rectangle - number side lengths a and (b + c) is the sum of a × b and a × c. Use area models with whole to represent the distributive property in mathematical reasoning. (M) I can use an array to multiply.  I can find the area of a r  ectangle by modeling the distributive property using multiplication and addition. I can use tiling to find the area of rectangles using the distributive property.  - Standard CC.3.MD.7d Recognize area as additive. Find areas of rectilinear figures by composing them into non de overlapping rectangles and adding the areas of the non - - overlapping parts, applying this technique to solve real world problems.  I can find areas of rectangles.  I can add area of rectangles.  I can recognize that areas of each rect angle in a rectilinear (straight line) figure can be added together to find the area of the figure. I can separate a polygon into rectangles to find the area of each rectangle to solve  real world problems.  - overlapping rectangles. I can separate polygons into non Standard - CC.3.MD.8 Geometric measurement: 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 t he same perimeter and different areas or with the same area and different perimeters. (P)  I can define a polygon. I can define perimeter.   I can find the perimeter when given the length of sides.

11  I can find the perimeter when there is an unknown sid e length.  I can create rectangles with the same perimeter and different areas.  I can create rectangles with the same area and different perimeters. CC.3.G.1 Understand that shapes in different categories (e.g., rhombuses, Standard - thers) may share attributes (e.g., having four sides), and that the shared rectangles, and o attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals do not belong to any of these subcategories. that - dimensional shapes based on their attributes.  I can identify and define two I can identify rhombuses, rectangles, and squares as quadrilaterals.   I can define attributes.  I can describe, analyze, and compar e properties of two - dimensional shapes.  I can compare and classify shapes by attributes, sides and angles.  I can group shapes with shared attributes. I can draw examples that are and are not quadrilaterals.  Standard - CC.3.G.2 Partition shapes into p arts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part is 1/4 of the area of the shape. (M)  I can divide shapes into equal parts .  I can describe the area of each part as a fractional part of the whole.  I can divide a shape into parts with equal areas and describe the area of each part as a unit fraction of the whole.