# Place Value Chart. Number Sense 345,562 > 342,500 24,545 < 38, ,312=212,312

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1 INDIANA ACADEMIC STANDARDS Number Sense 4.NS.1 Read and write whole numbers up to 1,000,000. Use words, models, standard form, and expanded form to represent and show equivalent forms of whole numbers up to 1,000,000. Place Value Chart Standard Form: 1,672 Expanded Form: 1, Word Form: one thousand six hundred seventy two Model: 4.NS.2 Compare two whole numbers up to 1,000,000 using >, <, and = symbols. 345,562 > 342,500 24,545 < 38, ,312=212,312 4.NS.8 Find all factor pairs for a whole number in the range Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range is a multiple of a given one-digit number. List all the factor pairs of 72. 1x72, 2x36, 3x24, 4x18, 6x12, 8x9 Is 42 a multiple of 3? Explain your thinking. List the multiples of 3 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42 Forty-two is a multiple of 3 because when I created a list of multiples for the number three, I was able to prove it was a multiple by counting by threes. 1

2 Number Sense 4.NS.9 Use place value understanding to round multi-digit whole numbers to any given place value. Ask yourself...is it closer to 0 or 10, 0 or 100, 0 or 1,000 Round 425,738 to the nearest: Hundred Thousand 400,000 Ten Thousand 430,000 Thousand 426,000 Hundred 425,700 Ten 425,740 2

3 Fractions 4.NS.5 Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark, such as 0, 1/2, and 1). Recognize comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions (e.g., by using a visual fraction model). Use <, =, > to compare each pair of fractions. Explain your thinking. Use cross multiplication to determine which fraction is greater NS.6 Write tenths and hundredths in decimal and fraction notations. Use words, models, standard form and expanded form to represent decimal numbers to hundredths. Know the fraction and decimal equivalents for halves and fourths (e.g., 1/2=0.5=0.50, 7/4=1 3/4=1.75). Six tenths Number Fraction Decimal Five hundredths Thirty-two thousandths NS.7 Compare two decimals to hundredths by reasoning about their size based on the same whole. Record the results of comparisons with the symbols >. =, <, and justify the conclusions (e.g., using a visual model). Use <, =, or > to compare each pair of decimals < < = > < < > <

4 Geometry 4.G.1 Identify, describe, and draw parallelograms, rhombuses, and trapezoids using appropriate tools (ruler, technology) 4.G.2 Recognize and draw lines of symmetry in twodimensional figures. Identify figures that have lines of symmetry 4.G.3 Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint. 4.G.4 Classify triangles and quadrilaterals based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles (right, acute, obtuse) 4.G.5 Identify, describe, and draw rays, angles and perpendicular lines using appropriate tools. Identify these in 2-dimensional figures. 4

5 Measurement 4.M.1 Measure length to the nearest quarter-inch, eighthinch and millimeter. Use a ruler to measure the line segment to the nearest quarter inch, eighth-inch, and millimeter. 4.M.2 Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz; l, ml; hr, min, sec. Express measurements in a larger unit in terms of a smaller unit within a single system of measurement. 5

6 Measurement 4.M.3 Use the four operations to solve real-world problems involving distances, intervals of time, volumes, masses of objects, and money. Complete the tables to show the relationship between the units. Hours Minutes Meters Centimeters Ted played outside for 3 1/2 hours. Sue played outside for 1 1/2 hours. How many hours did they play outside altogether? How many more minutes did Ted play outside than Sue? = n n = 120 minutes or 2 hours Hours Minutes Ted 3 1/2 (3 x 60) + 30 = = 210 Sue 1 1/2 (1 x 60) + 30 = = 90 6

7 Measurement 4.M.4 Apply the area and perimeter formulas for rectangles to solve real-world problems. Recognize area as additive and find the area of complex shapes composed of rectangles by decomposing them into non-overlapping rectangles and adding the areas together. 4.M.5 Understand that 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. Understand an angle that turns through 1/360 of a circle is called a one-degree angle, and can be used to measure other angles. Understand an angle that turns through n one-degree angles is said to have an angle measure of n degrees. 7 ft 22 ft 16 ft What is the area and perimeter of the figure? = n 12 ft 4.M.6 Measure angles in whole number degrees using appropriate tools. Sketch angles of specified measures. 7

8 Data Analysis 4.DA.1 Formulate questions that can be addressed with data. Use observations, surveys, and experiments to collect, represent, and interpret the data using tables (including frequency tables), line plots, and bar graphs. 4.DA.2 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using data displayed in line plots. Ten students measured their pencils to the nearest eighth-inch. They recorded their results as shown in the line plot (frequency table) What is the difference in length between the longest and shortest pencil? If you were to line up all 10 pencils, what would the total length be? n X X X X X x x x x x Add the whole numbers: = Add the numerators: = Simply the result : DA.3 Interpret data displayed in a circle graph. Based on the graph, which statements are true? About ¼ of the class chose blue as their favorite color. About ½ of the class chose blue as their favorite color. About ½ of the class chose green or orange as their favorite color. The color chosen most was blue. Orange and green were chosen the same amount. 8

10 Algebraic Thinking 4.AT.3 Interpret a multiplication equation as a comparison (e.g., interpret 35=5x7 as a statement that 35 is 5 times as many as 7, and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations. Write an equation that describes 4 times as many \$. 4 x 8 = n times 4.AT.4 Solve real-world problems with whole numbers involving multiplicative comparison (e.g., by using drawing and equations with a symbol for the unknown number to represent the problem), distinguishing multiplicative comparison from additive comparison. Sam has \$7.00. Amy has 4 times as much as Sam. How much does Amy have? Sam Amy \$7.00 \$7.00 \$7.00 \$7.00 \$7.00 x1 x2 x3 x4 n Algebraic Equation: 7 x 4 = n n = 28 Amy has \$ Riley has \$72.00 and that is 8 times as much as Nikolas. How much money does Nikolas have? Riley 72 Nikolas n 72 8 n Algebraic Equation: Nikolas has \$ 9.00 Madison has \$88 and Ben has \$22. How many times more does Madison have as compared to Ben? Madison 88 Ben 22 Algebraic Equation: 22n = 88 Ask yourself. How many times does 22 go into 88. Use repeated addition or division. Madison has 4 times as much money as Ben. 10

11 Algebraic Thinking 4.AT.5 Solve real-world problems involving addition and subtraction of fractions referring to the same whole and having common denominators (e.g., by using visual fraction models and equations to represent the problem). Josie and Ellie share a pizza. Josie ate 2/6 of the pizza and Ellie ate 2/6 of the pizza. How much did they eat altogether? Algebraic Equation: 2 2 n 6 6 They ate 4 pieces of pizza altogether. Kim has 3 3/8 pies left over from a party. After giving some to her dad, she has 1 1/8 pies left. How much pie did she give to her dad? Algebraic Equation: n n 2 8 Kim gave her dad 2 whole pies and 2/8 or 1/4 of another one. 4.AT.6 Understand that an equation, such as y=3x+5 is a rule to describe the relationship between two variables and can be used to find a second number when a first number is given. Generate a number pattern that follows a given rule. Heather makes a picture in art class. For every square she uses in her picture, she uses 5 triangles. The equation T = 5s represents the relationship where T represents the number of triangles and s represents the number of squares. How many triangles does Erin use if she uses 9 squares, 10 squares, 11 squares? Squares Rule Triangles 9 X X x5 55 x Rule y Multiply by 3, then subtract 2 Use the equation y = 3x 2 to determine the values of y for the given values of x. 1 (1 x 3) (2 x 3) (3 x 3) (4 x 3) (5 x 3)

12 Computation 4.C.1 Add and subtract multi-digit whole numbers fluently using a standard algorithmic approach. Evaluate each expression. 1. 3, ,079 = y 2. 4,006 1,248 = n 3. 85, ,009 = x ,492 36,195 = n 4.C.2 Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Describe the strategy and explain the reasoning. Evaluate each expression x 5 = n x 12 = n Lattice Multiplication 4.C.3 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Describe the strategy and explain the reasoning. Evaluate each expression n n 12

13 Fractions 4.NS.3 Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers. Name and write mixed numbers using objects or pictures. Name and write mixed numbers as improper fractions using objects and pictures. Write 8 as a fraction such that the numerator is 8. Which numbers are equivalent to 8? Draw a picture to represent Then write as an improper fraction NS.4 Explain why a fraction, a/b, is equivalent to a fraction, (nxa)/(nxb) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. [Denominators limited to 2, 3, 4, 5, 6, 8, 10, 25, 100] Which model shows that 3/4 is equivalent to 6/8? Name four fractions equivalent to 2 5 Whatever you do to the numerator, you must do to the denominator You can multiply top and bottom by two = 0.25 = = 13

14 Computation 4.C.4 Multiply fluently within 100. Evaluate each expression x 6 = n 2. 5 x 13 = n x 4 n x 2 = n 4.C.5 Add and subtract fractions with common denominators. Decompose a fraction into a sum of fractions with common denominators. Understand addition and subtraction of fractions as combining and separating parts referring to the same whole. A The fraction can be written as Write as a sum of two or more fractions in three different ways C.6 Add and subtract mixed numbers with common denominators (e.g. by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction) C.7 Show how the order in which two numbers are multiplied (commutative property) and how numbers are grouped in multiplication (associative property) will not change the product. Use these properties to show that numbers can be multiplied in any order. Understand and use the distributive property. One way to multiply 6x2x5 is to first multiply 6x2, then multiply the value by 5. Describe another way to multiply these three numbers (commutative property). What is 6x2x5? 1. (5 x 6) x 2 = n 30 x 2 = n n = Evaluate 7(3 + 2) Do the parentheses first (3 + 2) = 5 Multiply by 7...because SQUISHED TOGETHER MEANS MULTIPLY 7 x 5 = Evaluate 5(8-6) Do the parentheses first (8 6) = 2 Multiply by 7...because SQUISHED TOGETHER MEANS MULTIPLY 5 x 2 = 10 14

15 Vocabulary Expanded Form a number written as the sum of the values of its digits Models picture representation of a number Place Value the value of the place, or position of a digit in a number Standard Form a number written that shows only its digits Whole Numbers the set of numbers 0, 1, 2, 3, 4, 5 Word Form a number written in words Denominator the bottom number of a fraction that tells how many parts are in the whole Equivalent equal in value or meaning Fraction a number that names part of a whole Improper Fraction a fraction with a numerator than or equal to the denominator Mixed Numbers a number expressed as a whole number plus a fraction Numerator the top number of a fraction; the number that tells how many parts of a whole are counted Algorithmic approach using a list of well-defined instructions or a step-by-step procedure to solve a problem Decompose a Fraction find two (or more) fractions that when added together give you the fraction you started with. Fluently efficient and accurate Inverse Operation an operation that undoes another (multiplication is the inverse of division; addition is the inverse of subtraction) Quotient When one number (dividend) is divided by another number (divisor), the result is known as the quotient 15

16 Vocabulary Parallel lines lines that do not intersect Parallelogram a quadrilateral that has two pairs of parallel sides Perpendicular lines lines that intersect at right angles Quadrilateral a four-sided polygon Ray a part of a line that begins at a point and continues without end in one direction Rhombus a parallelogram with all four sides of equal length Triangle a three-side polygon Trapezoid a quadrilateral with exactly one pair of parallel sides Symmetry correspondence in size and shape on either side of a dividing line (like a mirror) Area the number of square units needed to cover a surface Mass the amount of matter an object contains Perimeter the distance around a closed twodimensional shape Volume the amount of 3-dimensional space an object occupies; capacity Circle Graph a graph made of a circle divided into sectors; also called a pie chart or pie graph- Line Plot data represented with check marks, X s, or other symbols above a number line to show the frequency of each value 16

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