# OPERATIONS AND ALGEBRAIC THINKING NUMBER AND OPERATIONS IN BASE TEN NUMBER AND OPERATIONS: FRACTIONS

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1 OPERATIONS AND ALGEBRAIC THINKING REPRESENT AND SOLVE PROBLEMS INVOLVING MULTIPLICATION AND DIVISON UNDERSTAND PROPERTIES OF MULTIPLICATION AND THE RELATIONSHIP BETWEEN MULTIPLICATION AND DIVISION MULTIPLY AND DIVIDE WITHIN 100 SOLVE PROBLEMS INVOLVING THE FOUR OPERATIONS, AND IDENTIFY AND EXPLAIN PATTERNS IN ARITHMETIC NUMBER AND OPERATIONS IN BASE TEN USE PLACE VALUE UNDERSTANDING AND PROPERTIES OF OPERATIONS TO PERFORM MULTI-DIGIT ARITHMETIC NUMBER AND OPERATIONS: FRACTIONS DEVELOP UNDERSTANDING OF FRACTIONS AS NUMBERS MEASUREMENT AND DATA SOLVE PROBLEMS INVOLVING MEASUREMENT AND ESTIMATION OF INTERVALS OF TIME, LIQUID VOLUMES, AND MASSES OF OBJECTS REPRESENT AND INTERPRET DATA GEOMETRIC MEASUREMENT: UNDERSTAND CONCEPTS OF AREA AND RELATE AREA TO MULTIPLICATION AND ADDITION GEOMETRIC MEASUREMENT: RECOGNIZE PERIMETER AS AN ATTRIBUTE OF PLANE FIGURES AND DISTINGUISH BETWEEN LINEAR AND AREA MEASURES GEOMETRY REASON WITH SHAPES AND THEIR ATTRIBUTES USER LICENSE 430

2 OPERATIONS AND ALGEBRAIC THINKING REPRESENT AND SOLVE PROBLEMS INVOLVING MULTIPLICATION AND DIVISION 3.OA.A.1 Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 x 7. EQUAL GROUPS RELATE ADDITION AND MULTIPLICATION BUILDING ARRAYS ARRAY PICTURE CARDS OA.A.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 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 as IDENTIFY THE UNKNOWN OA.A.3 Use multiplication and division within 100 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. WORD PROBLEMS ARRAYS (SET 1) ARRAYS (SET 2) EQUAL GROUPS NUMBER OF EQUAL GROUPS SIZE OF EQUAL GROUPS EQUAL ROWS IN A MARCHING BAND SHARING MARBLES LITERATURE LINK TASK CARDS: ONE HUNDRED HUNGRY ANTS SIX DINNER SID AMANDA BEAN S AMAZING DREAM THE DOORBELL RANG OA.A.4 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 8 x? = 48, 5 =? 3, 6 x 6 =? MISSING NUMBERS: MULTIPLICATION MISSING NUMBERS: DIVISION

3 UNDERSTAND PROPERTIES OF MULTIPLICATION AND THE RELATIONSHIP BETWEEN MULTIPLICATION AND DIVISION 3.OA.B.5 Apply properties of operations as strategies to multiply and divide. Examples: if 6x4=24 is known then 4x6=24 is also known (Communicative properties of multiplication). 3x5x2 can be found by 3x5=15, then 15x2=30, or by 5x2=10, then 3x10=30 (Associative property of multiplication). Knowing that 8x5=40 and 8x2=16, one can find 8x7 as 8x (5+2) = (8x5) + (8x2) = 40+16=56 (Distributive property). TURN YOUR ARRAY DECOMPOSE A FACTOR (V.1) DECOMPOSE A FACTOR (V.2) LITERATURE LINK TASK CARD: EACH ORANGE HAD EIGHT SLICES OA.B.6 Understand division as an unknown-factor problem. For example, find 32 8 by finding the number that makes 32 when multiplied by 8. DIVISION AS AN UNKNOWN FACTOR INSTRUCTIONS (X1 & X2) (X5 & X10) (X3 & X6) (X4 & X8) (X7 & X9) MULTIPLY AND DIVIDE WITHIN OA.C.7 Fluently multiple and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8x5=40, one knowns 40 5=8) or properties of operations. By the end of Grade 3, know from memory all products of two 1-digit numbers. FILL THE GRID DOMINO MULTIPLICATION MULTIPLES: LOOK, SAY, COVER, WRITE, CHECK MULTIPLICATION BUMP (X2 X10) MULTIPLICATION FOUR IN A ROW INSTRUCTIONS (X1, 2, 5, 10) (X3, 4, 5, 6) (X6, 7, 8, 9) MULTIPLES GAMES (X2 X10) MULTIPLY IT! I HAVE WHO HAS? (X2 & X5) (X2 & X10) (X3 & X5) (X3 & X7) (X4 & X6)

4 (X4 & X10) (X6 & X8) (X7 & X9) SIX STICKS DIVISION RACE INSTRUCTIONS DIVISION RACE 1 (DIVISORS 2, 5, 10) DIVISION RACE 2 (DIVISORS 3, 4, 6) DIVISION RACE 3 (DIVISORS 7, 8, 9) DIVISION SQUARES INSTRUCTIONS DIVISION SQUARES (DIVISORS 2, 5, 10) DIVISION SQUARES (DIVISORS 3, 6, 9) DIVISION SQUARES (DIVISORS 4, 7, 8) DIVISION SPIN (DIVISORS 2 9) DIVISION BUMP (DIVISORS 2 10) SOLVE PROBLEMS INVOLVING THE FOUR OPERATIONS, AND IDENTIFY AND EXPLAIN PATTERNS IN ARITHMETIC 3.OA.D.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 estimate strategies including rounding. WORD PROBLEMS: TWO STEP (SET 1) WORD PROBLEMS: TWO STEP (SET 2) OA.D.9 Identify arithmetic patterns (including patterns in the addition 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. ROLL A RULE (V. 1) ROLL A RULE (V. 2) CREATE A NUMBER PATTERN (V. 1) CREATE A NUMBER PATTERN (V. 2) ODD AND EVEN SUMS ODD AND EVEN PRODUCTS PATTERNS IN THE ADDITION TABLE PATTERNS IN THE MULTIPLICATION TABLE DRAWING MULTIPLICATION PATTERNS

5 NUMBER AND OPERATIONS IN BASE TEN USE PLACE VALUE UNDERSTANDING AND PROPERTIES OF OPERATIONS TO PERFORM MULTI-DIGIT ARITHMETIC 3. NBT. A. 1 Use place value understanding to round whole numbers to the nearest 10 or 100. WHAT S THE NEAREST TEN? WHAT S THE NEAREST HUNDRED? ROUND TO THE NEAREST TEN ROUND TO THE NEAREST HUNDRED ESTIMATING SUMS (V.1) ESTIMATING SUMS (V.2) ESTIMATING DIFFERENCES (V.1) ESTIMATING DIFFERENCES (V.2) NBT. A. 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. CLOSE TO ZERO (3-DIGIT) ADD THE DIFFERENCE (v.1-2) DIGIT ADDITION SPLIT DIGIT SUBTRACTION SPLIT DOUBLING TO 1, WORD PROBLEMS: ADDITION & SUBTRACTION (within 1,000) LITERATURE LINK TASK CARD: 365 PENGUINS NBT. A. 3 Multiply one-digit whole numbers by multiples of 10 in the range (e.g., 9x80, 5x60) using strategies based on place value and properties of operations. MULTIPLES OF TEN MULTIPLY MULTIPLY ONE-DIGIT NUMBERS BY MULTIPLES OF TEN

6 NUMBER AND OPERATIONS: FRACTIONS DEVELOP UNDERSTANDING OF FRACTIONS AS NUMBERS 3.NF.A.1 Understand a fraction 1/b as a quantity formed by 1 part when a whole is portioned into b equal parts: understand a fraction a/b as the quantity formed by a parts of size 1/b. MAKING FRACTION STRIPS (V.1) MAKING FRACTION STRIPS (V.2) CUISENAIRE FRACTIONS MY FRACTION BAR RIDDLE FRACTION POSTERS NAME THE FRACTION REPRESENTING UNIT FRACTIONS MATCH THE LENGTH LITERATURE LINK TASK CARDS: GATOR PIE (V.1& 2) PICTURE PIE NF.A.2 Understand a fraction as a number on the number line; represent fractions on a number 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 portioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line. FRACTIONS ON A NUMBER LINE B. Represent a fraction a/b on a number line diagram by marking off a lengths 1/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. ROLL A FRACTION N.F.A.3 Explain equivalence of fractions in special cases and compare fractions by reasoning about their size. A. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. PIZZA FOR DINNER

7 B. Recognize and generate simple equivalent fractions (e.g., ½ = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, by using a visual method. EQUIVALENT FRACTIONS EXPLORATION (V. 1) EQUIVALENT FRACTIONS EXPLORATION (V. 2) BUILD EIGHT HEXAGONS EQUIVALENT FRACTIONS ON A GEOBOARD C. Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram. MAKE ONE WHOLE (V.1) MAKE ONE WHOLE (V.2) D. 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. Record the results of comparisons with the symbols >, =, or < and justify the conclusions, e.g., by using a visual fraction model. COMPARE FRACTIONS OF A WHOLE (V.1) COMPARE FRACTIONS OF A WHOLE (V.2) WHO ATE MORE?

8 MEASUREMENT AND DATA SOLVE PROBLEMS INVOLVING MEASUREMENT AND ESTIMATE OF INTERVALS OF TIME, LIQUID VOLUMES, AND MASSES OF OBJECTS 3.MD.A.1 Tell and write the 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. TIME MATCH (V. 3) TIME MATCH (V. 4) TIME BARRIER GAME (V. 3) TIME BUMP (NEAREST MINUTE) WORD PROBLEMS: TIME INTERVALS MD.A.2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. ESTIMATING WEIGHT WEIGH IT TWICE MARBLE GRAB MEASURE ONE LITER MORE OR LESS THAN A LITER? CAPACITY LINEUP WORD PROBLEMS: LIQUID VOLUME AND MASS REPRESENT AND INTERPRET DATA 3.MD.B.3 Draw a scaled picture graph and a scaled bar graph to represent a date set with several categories. Solve one and two-step how many more and how many less problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets. REPRESENT AND INTERPRET DATA GRAPHING M&M S GUMMY BEAR GRAPH PAPER BALL THROW JAKE S SURVEY

9 3.MD.B.4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show data by making a line plot, where the horizontal scale is marked off in appropriate units whole numbers, halves, or quarters. MEASURE TO THE NEAREST HALF-INCH MEASURE TO THE NEAREST QUARTER-INCH SQUID EYES! MEASURING STRIPS LINE PLOT MEASURING NAMES LINE PLOT (V. 1) MEASURING NAMES LINE PLOT (V. 2) LITERATURE LINK TASK CARDS: INCHWORM AND A HALF (V. 1& 2) JIM AND THE BEANSTALK GEOMETRIC MEASUREMENT: UNDERSTAND CONCEPTS OF AREA AND RELATE AREA TO MULTIPLICATION AND ADDITION 3.MD.C.5 Recognize area as an attribute of plane figures and understand concepts of area measurement. A A square with side length 1 unit, called a unit square, has one square unit of area, and can be used to measure area. SQUARE UNITS SQUARE METERS 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. FIND THE AREA AREA ON THE GEOBOARD MD.C.6 Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units.) COVER YOUR NOTEBOOK MEASURING OBJECTS IN SQUARE CENTIMETERS RECTANGLES WITH COLOR TILES AREA COMPARE GRID PAPER ANIMALS

10 3.MD.C.7 Relate area to the operations of multiplication and addition. A Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths. FIND THE AREA OF A RECTANGLE COMPLETE THE RECTANGLE (V.2) 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. WORD PROBLEMS: AREA 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. BUILD RECTANGLES OF TWO COLORS JACK S RECTANGLES 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. THREE RECTANGLES FIND AREAS OF RECTILINEAR FIGURES (V.1) FIND AREAS OF RECTILINEAR FIGURES (V.2) DESIGN A FLOWER BED GEOMETRIC MEASUREMENT: RECOGNIZE PERIMETER AS AN ATTRIBUTE OF PLANE FIGURES AND DISTINGUISH BETWEEN LINEAR AND AREA MEASURES 3.MD.D.8 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 the same perimeter and different areas or with the same area and different perimeters. SQUARES ON A GEOBOARD PERIMETER ON THE GEOBOARD MEASURING PERIMETER PERIMETER WITH COLOR TILES THE PERIMETER STAYS THE SAME THE AREA STAYS THE SAME RECTANGULAR ROBOT DESIGN A RABBIT ENCLOSURE WORD PROBLEMS: PERIMETER

11 GEOMETRY REASON WITH SHAPES AND THEIR ATTRIBUTES 3.G.A.1 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. GEOBOARD SQUARES COMPARING QUADRILATERALS SHAPE MATCH CLASSIFY SHAPES USING A VENN DIAGRAM QUADRILATERAL RIDDLE G.A.2 Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For examples, partition a shape into 4 parts with equal area, and describe the area of each part as ¼ of the area of the shape. PARTITION SHAPES PARTITION A SQUARE (V.1) PARTITION A SQUARE (V.2) PARTITION A SQUARE (V.3)

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