EOG REVIEW UNIT 3rd Grade Common Core State Standards

Day 1 3.OA.1-2 1. Interpret products of whole numbers, e.g., interpret 5 × 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 × 7. 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 56 ÷ 8. 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.1 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 × ? = 48, 5 = _ ÷ 3, 6 × 6 = ?

Ten Minute Math Jason earns $8 each week for walking the neighbor's dog in the afternoons. After 6 weeks how much as Jason earned? Write the equation and find the answer.

Working with Array Cards Activity 1 Working with Array Cards Materials: copy of array picture cards Write a multiplication word problem to go with the first array card. Write the number sentence or expression that matches your problem. Write a division word problem to go with the first array card. Repeat the process using the second array card. Are the two array cards similar? Explain.

Activity 2 What’s in the Bag? I have 24 objects in my bag. They are arranged into equal groups. How could they be arranged? What multiplication expression would you use to describe the quantity in my bag?   Tanya says, “Twenty-four is four groups of 6” and draws this:  Martin says, “Twenty-four is eight groups of 3” and draws this:   What multiplication expression would Tanya write to describe the quantity in the bag? Divide your paper into 4 sections and draw an array to represent what could be in each bag. Make sure you write a multiplication expression to describe the quantity in each bag.

Activity 2 18 Objects 15 Objects 32 Objects 48 Objects

Day 2 3.OA.1-4 1. Interpret products of whole numbers, e.g., interpret 5 × 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 × 7. 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 56 ÷ 8. 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.1 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 × ? = 48, 5 = _ ÷ 3, 6 × 6 = ?

Ten Minute Math Gifts from Grandma Juanita spent $9 on each of her 6 grandchildren at the fair. How much money did she spend? Nita bought some games for her grandchildren for $8 each. If she spent a total of $48, how many games did Nita buy? Helen spend an equal amount of money on each of her 7 grandchildren at the fair. If she spent a total of $42, how much did each grandchild get?

Multiplication and Division Story Cards Activity 1 Multiplication and Division Story Cards   Fold your sheet of paper in half, “hamburger style.” On the left side of the paper, cut three flaps. On the right side of the paper, draw things that come in groups. Materials:   One sheet of 8 ½ X 11 paper or cardstock for each student Crayons or colored pencils (markers are not recommended) Scissors Rulers

Activity 2 ___ X 2 = __1 3 7 56 9 6 ___ 0 2 ___ 4 Make it True Puzzle 1 ___ X 2 = __1 3 7 56 9 6 ___ 0 2 ___ 4

Activity 2 Make it True Puzzle 2 __ ÷ 9 = 5 3 32 ___ 6 2 8 ____

Day 3 3.OA.5-6 5. Apply properties of operations as strategies to multiply and divide.2Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (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.) 6. Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.

Ten Minute Math Mr. Little asked the class to explain why the product of 4 X 3 X 5 is the same as the product of 4 X 5 X 3. Use models, pictures or words to explain why this is true.

The Distributive Property Activity 1 The Distributive Property

Activity 2 Upside Down Arrays Materials- Array Card Sets Place the array cards upside down. One student picks up an array card and covers one of the dimensions. For example, if a you pick up an 8 x 5 array card and covers the 8, you would say to your partner, “40 ÷8 = ___” Your partner would then solve using a related multiplication fact. Your partner should complete the table as he/she solves. For example, “I know 8 x 5 = 40, so the missing dimension is 5.” Players continue taking turns until all spaces are filled.

Multiplication unknown Activity 2 Upside Down Arrays Array Total Side Showing Division Sentence Multiplication unknown Missing Number 40 8 40 ÷ 8 = ? 8 x ? = 40 5

Day 4 3.OA.7 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. By the end of Grade 3, know from memory all products of two one-digit numbers.

Ten Minute Math 1. Which multiplication fact can you use to solve 5 = 20 ÷ ____ Explain how you know. 2. Jenna has 48 pictures to use in her photo album. The album has 8 pages in it and she wants to put the same number of pictures on each page. Write two multiplication facts Jenna can use to find how many pictures to put on each page

Counting Around the Class Activity 1 Counting Around the Class

Activity 2 Coloring Arrays Roll 4 dice. Multiply 2 of the numbers together. Color in the array on the board.

Day 5 3.OA.8-9 Solve problems involving the four operations, and identify and explain patterns in arithmetic. 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.3 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.

Ten Minute Math 1. Masha had 120 stamps. First she gave her sister half of the stamps and then she used three to mail letters. How many stamps does Masha have left? 2. Mrs. Giesler’s third grade class wants to go on a field trip to the science museum. The cost of the trip is $245. The class can earn money by running the school store for 6 weeks. The students can earn $15 each week if they run the store. How much more money does the third grade class still need to earn to pay for their trip? Write an equation to represent this situation.

Activity 1 Table Patterns Color all the multiples of the number nine. What do you notice about the digits in the multiples of 9? 2. Color all the square numbers. Do you notice any patterns in the numbers on either side of the products of the square numbers? × 1 2 3 4 5 6 7 8 9 10 12 14 16 18 20 15 21 24 27 30 28 32 36 40 25 35 45 50 42 48 54 60 49 56 63 70 64 72 80 81 90 100 Group students and challenge them to find all the patterns they notice in the multiplication and addition tables from the resource packet

Day 6 3.NBT1-3 1. Use place value understanding to round whole numbers to the nearest 10 or 100. 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. 3. Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations.

Explain how you know using models, pictures or words. Ten Minute Math Look at the number 273 Between which two tens does it fall? Between which two hundreds does it fall? Explain how you know using models, pictures or words.

Challenge: Write 3 original rounding problems to be shared. Activity 1 When rounding to the nearest ten: a. What is the smallest whole number that will round to 50? b. What is the largest whole number that will round to 50? c. How many different whole numbers will round to 50?   When rounding to the nearest hundred: a. What is the smallest whole number that will round to 500? b. What is the largest whole number that will round to 500? c. How many different whole numbers will round to 500? Challenge: Write 3 original rounding problems to be shared. http://www.illustrativemathematics.org/illustrations/745

Day 7 3.G.1 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.

Ten Minute Math Chose two quadrilaterals from the following: rhombus, parallelogram, rectangle, square, and trapezoid Draw each quadrilateral Explain how the two quadrilaterals are alike and how they are different Repeat with another pair of quadrilaterals

Quadrilateral Riddles and Fun Activity 1 Quadrilateral Riddles and Fun WORD BANK Equal sides angles vertices square rectangle rhombus quadrilateral trapezoid Directions: 1. Make two different quadrilaterals on their geoboard. Have them record the quadrilaterals on their geopaper. 2. Use the vocabulary we just reviewed to explain how the shapes are alike and how they are different.    3. When finished share with a partner or small group and then add to their similarities and differences any new ideas they learned from their group. Discuss words used from Word Bank   1. Write 4 clues to describe the quadrilateral they created. Use the word bank to help write your clues.    2. When finished, find a partner that is finished and play “Quadrilateral Riddle” by reading your clues to your partner and the partner guesses which polygon they created. Continue to play by finding additional partners when you finish.

Quadrilateral Riddles and Fun Activity 2 Quadrilateral Riddles and Fun WORD BANK Equal sides angles vertices square rectangle rhombus quadrilateral trapezoid Directions: 1. Write 4 clues to describe the quadrilateral they created. Use the word bank to help write your clues.    2. When finished, find a partner that is finished and play “Quadrilateral Riddle” by reading your clues to your partner and the partner guesses which polygon they created. Continue to play by finding additional partners when you finish.   1. Write 4 clues to describe the quadrilateral they created. Use the word bank to help write your clues.    2. When finished, find a partner that is finished and play “Quadrilateral Riddle” by reading your clues to your partner and the partner guesses which polygon they created. Continue to play by finding additional partners when you finish.

Day 8 3.G.2 2. 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 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.

Ten Minute Math Are the following circles partitioned in half? Explain how you know.

Partitioning Shapes into Half Activity 1 Partitioning Shapes into Half Look at the three figures to the right and explain how you know they are partitioned into half.

Partitioning Shapes into Half Activity 1 Partitioning Shapes into Half Look at the three circle to the right and explain how you know they are partitioned into half.

Day 9 3.NF.1-2 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. 2. Understand a fraction as a number on the number line; represent fractions on a number line diagram. 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 locates the number 1/b on the number line. 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.

Ten Minute Math Redraw and color in ¼ of each shape above. How could you convince someone that each piece is ¼ of the whole even though the shapes are divided differently?

Activity 1 Equal Sharing   Three students want to share 7 candy bars so that each child gets the same amount. How much candy bar can each child get? Label your answer and show each child’s share.

Activity 1 Equal Sharing   1. Four boys want to share 22 cookies so that each boy gets the same amount of cookies. How much cookie should each boy receive? 2. Jeremy has 21 cheese sticks. He is going to share them equally with five other friends. How much cheese stick will Jeremy and his five friends receive? 3. Six girls want to share 14 cupcakes equally. How many cupcake would each girl get? 4. Four children want to share 10 chocolate bars so that everyone gets the same amount. How much chocolate bar can each child have?

Day 10 3.NF.2 2. Understand a fraction as a number on the number line; represent fractions on a number line diagram. 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 locates the number 1/b on the number line. 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.

Ten Minute Math 0 5/3 Where is the number 1 located on the number line above? Explain how you know.

Fractions on the Number Line Activity 1 Fractions on the Number Line 1/4 Where should you to place the fraction 2/3?

Fractions on the Number Line Activity 1 Fractions on the Number Line 1 Where should you to place the fraction 7/4 ?

Fractions on the Number Line Activity 1 Fractions on the Number Line Which fraction is greater 5/8 or 3/4

Day 11 3.NF.3 3. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. Recognize and generate 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. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram. 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.

Ten Minute Math Which is close to 1 on the number line, 4/5 or 5/4? Explain your reasoning.

Activity 1 Is This Duck “One-Half Red?” Refer to student handout

Is This Duck “One-Half Red?” Activity 1 Is This Duck “One-Half Red?” 1.You will use pattern blocks to build this duck on Triangle Grid Paper. 2. After building the duck, remove each pattern block one at a time and color the shape the same color as the pattern block. Continue until each pattern block is removed and the area of the each pattern block is colored.   3. Label each pattern block shape using unit fractions.

Day 12 3.NF.3 3. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. Recognize and generate 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. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram. 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.

Ten Minute Math Who correctly compares the numbers 2/3 and 2/5? Ben said that 2/3 is greater than 2/5. Lee said that 2/3 is equal to 2/5. Mia said that 2/3 is less than 2/5. Compare 2/3 and 2/5 using pictures and symbols.

Fractional Parts of Rectangles Activity 1 Fractional Parts of Rectangles Part 1 Working with a partner, use square tiles to build a rectangle that is ½ red. If working with a partner, each person should build the same model. Each student(s) should label the rectangle as ½ red. Record the solution on one-inch grid paper by coloring squares to match the rectangle. Using fraction notation, label the fractional parts of your rectangle. Find ways to prove that your rectangle is exactly one-half red.   Part 2 Working with a partner, each student will build a rectangle with a different area that is ½ red. Show your solution on one-inch grid paper by coloring squares to match your rectangle. Find ways to prove your new rectangle is also ½ red Show each solution on one-inch grid paper by coloring squares to match your rectangles. Questions to Pose:   Before: • What strategies might you use to determine one half? During: • How did you decide the number of tiles needed to build a different rectangle that is ½ red? • How many solutions strategies might you find for building rectangles that are ½ red? • Explain how the numbers in the fractions relate to the different tiles you used to create your rectangles. After: • Explain how Activity#1 is different from Activity #2. • How did you decide how many tiles you need to build the rectangle in Activity #2? • What strategies did you use to find solutions? • Why is Activity #2 more difficult? • Did anyone find more than one or two solutions for Activity #2?

Fractional Parts of Rectangles Activity 2 Fractional Parts of Rectangles Part 1 Use square tiles to build a rectangle that is 1/2 red, 1/4 yellow, and 1/4 green. Show your solution on one-inch grid paper by coloring squares to match your rectangle. Using fraction notation, label the fractional parts of your rectangle. Prove your new rectangle is 1/2 red, 1/4 yellow, and 1/4 green.   Part 2 Find at least one other rectangle with a different area that is 1/2 red, 1/4 yellow, and 1/4 green. Questions to Pose:   Before: • What strategies might you use to determine one half? During: • How did you decide the number of tiles needed to build a different rectangle that is ½ red? • How many solutions strategies might you find for building rectangles that are ½ red? • Explain how the numbers in the fractions relate to the different tiles you used to create your rectangles. After: • Explain how Activity#1 is different from Activity #2. • How did you decide how many tiles you need to build the rectangle in Activity #2? • What strategies did you use to find solutions? • Why is Activity #2 more difficult? • Did anyone find more than one or two solutions for Activity #2?

Day 13 3.MD.3-4 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 scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets. 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— whole numbers, halves, or quarters.

Ten Minute Math James measured eight Lego blocks that were in his desk to the nearest quarter inch. He came up with the following measurements: 1 inch, 1 ½ inches, 1 ¼ inches, 1 inch, 1 ¾ inches, 1 ½ inches. Display this data on a line plot. How many blocks measured 1 ½ inches? 1 inch? Write an original question using the information in the line plot.

Activity 1 Making a Picture Graph Questions to Pose:   (Beginning) What relationships did you find among the pattern blocks? How might you find the value of the duck if a hexagon is equal to 1? (Middle) What equivalences were you able to find? (Ending) Explain your solution strategy to another group.

Day 14 (Mrs. Smith to complete in Review Rotation) 3.MD.5-7 5. Recognize area as an attribute of plane figures and understand concepts of area measurement. 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. 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. 6. Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). 7. Relate area to the operations of multiplication and addition. 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. 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. 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 × b and a × c. Use area models to represent the distributive property in mathematical reasoning. 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.

Ten Minute Math Tammy’s bedroom is 9 feet long and 8 feet wide. Kathy’s bedroom is 10 feet long and 8 feet wide. Who has the bedroom with the greatest area? Who has the bedroom with the greatest perimeter? Explain how you know.

Day 15 (Mrs. Smith to complete in Review Rotation) 3.MD.8 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.

(Refer to print out of shapes glued in Math Journal) Ten Minute Math The Square Counting Shortcut: Imagine that each square in the picture measured one centimeter on each side. What is the area of each letter? Try to work it out without counting each square individually. (Refer to print out of shapes glued in Math Journal)