Math

[[file:Weight Distribution for Grades 3-5.pages]]

 * Operations and Algebraic Thinking (4.OA)**

[|Representing Multiplicative Comparison Problems]
 * Use the four operations with whole numbers to solve problems**
 * 4.OA.1** Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 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.

[|Sample Multiplicative Comparison Problems]
 * 4.OA.2** Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.
 * Possible Activities:**

[|Multistep Word problems] [|Interpreting Remainders]
 * 4.OA.3** Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. 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.
 * Possible Activities:**

Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite. [|Choose a Number Project] [|Finding Multiples] [|Prime Number Hunt] [|Common Multiples] [|Least Common Multiple] [|Find the Factor] http://www.shodor.org/interactivate/activities/Factorize/
 * Gain familiarity with factors and multiples**
 * 4.OA.4**
 * Possible Activities:**

Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way. [|Square Numbers] [|Triangular Numbers]
 * Generate and analyze patterns**
 * 4.OA.5**


 * Number and Operations in Base Ten (4.NBT)**


 * Generalize place value understanding for multi-digit whole numbers**
 * 4.NBT.1** Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700÷70=10 by applying concepts of place value and division.

[|Numeral, Word and Expanded Form]
 * 4.NBT.2** Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

[|Round to the Nearest Ten] [|Round to the Nearest Hundred]
 * 4.NBT.3** Use place value understanding to round multi-digit whole numbers to any place.
 * Possible Activities:**

[|Addition and Subtraction Number Stories]
 * Use place value understanding and properties of operations to perform multi-digit arithmetic**
 * 4.NBT.4** Fluently add and subtract multi-digit whole numbers using the standard algorithm.

[|Multiplication Distributive Split] [|Multiplication Number Story] [|Breaking Apart a Factor] Multiplication Bump (x100) Make the Largest Product Make the Smallest Product
 * 4.NBT.5** 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. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models
 * Possible Activities:**

[|Division Split (1 digit divisor)] [|Remainders]
 * 4.NBT.6** 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
 * Possible Activities:**


 * Number and Operations - Fractions (4.NF)**

[|Creating Equivalent Fractions] [|Fraction Wall Game]
 * Extend understanding of fraction equivalence and ordering**
 * 4.NF.1** 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.
 * Possible Activities:**

[|Birthday Fractions] [|Pattern Block Fractions] [|Who Ate More?] Fraction Compare Fraction Cards http://www.shodor.org/interactivate/activities/FractionPointer/ http://www.shodor.org/interactivate/activities/FractionSorter/ http://www.mathplayground.com/Fraction_bars.html
 * 4.NF.2** Compare two fractions with different numerators and different denominators, e.g. by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with comparisons with symbols >, =, or <. and justify the conclusions, e.g., by using a visual fraction model.

a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. [|Adding Fractions with Like Denominators] [|Adding Fractions Using Pattern Blocks] - Ed Emberley's Picture Pie
 * Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers**
 * 4.NF.3** Understand a fraction a/b with a>1 as a sum of fractions 1/b.
 * Possible Activities:**
 * Possible Read Aloud:** (see task card in right hand column)

b. Decompose a fraction into a sum of fraction with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8 Decomposing Fractions http://www.mathplayground.com/Fraction_bars.html http://www.mathplayground.com/Scale_Fractions.html

c. Add and subtract mixed numbers with like 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. [|Mixed Number Word Problems (like denominators)] [|Adding Mixed Numbers] [|Subtracting Mixed Numbers]

d. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem. [|Fraction Word Problems (like denominator)] Addition Word Problem with Fractions Subtraction Word Problem with Fractions

a. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product of 5 x (1/4), recording the conclusion by the equation 5/4 = 5 x (1/4). [|Models for Fraction Multiplication]
 * 4.NF.4** Apply and extend previous understandings of multiplication to multiply a fraction by a whole number:

b. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 x (2/5) as 6 x (1/5), recognizing this product as 6/5. (In general, n x (a/b) = (nxa)/b).

c. Solve word problems involving multiplication of a fraction by a whole number, e.g. by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie? [|Whole Number x Fraction Word Problems] - Full House: An Invitation to Fractions
 * Possible Activities:**
 * Possible Read Aloud:** (see task card in right hand column)

[|Sums of 1] http://www.shodor.org/interactivate/activities/Converter/
 * Understand decimal notation for fractions, and compare decimal fractions**
 * 4.NF.5** Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.
 * Possible Activities:**

[|Decimals in Money] [|Representing Decimals with Base 10 Blocks] [|Decimal Riddles]
 * 4.NF.6** Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.
 * Possible Activities:**

[|Comparing Decimals] [|Decimal Sort]
 * 4.NF.7** Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.
 * Possible Activities:**


 * Measurement and Data (4.MD)**

[|Measurement Conversion Word Problems] [|Measurement Concentration]
 * Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit**
 * 4.MD.1** Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4ft snake as 48in. Generate a conversion table for feet and inches listing the number pairs (1,12), (2,24), (3,36)…

Measurement Word Problems Elapsed Time Ruler 1 Elapsed Time Ruler 2 24 hour number line (4 per page)
 * 4.MD.2** Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions of decimals, and problems that require expressing measurements given in a large unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

[|A Dinner Party] [|Fencing a Garden] [|Designing a Zoo Enclosure]
 * 4.MD.3** Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.

[|Length of Ants Line Plot] [|Objects in My Desk Line Plot]
 * Represent and interpret data**
 * 4.MD.4** Make a line plot to display a data set of measurements in fractions of a unit (1/2, ¼, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.

a. 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. An angle that turns 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. b. An angle that turns through n one-degree angles is said to have an angle measure of n degrees. [|Angles in Names]
 * Geometric measurement: understand concepts of angle and measure angles**
 * 4.MD.5** Recognize angles as geometric shapes that are formed whenever two rays share a common endpoint, and understand concepts of angle measurement:

[|Predicting and Measuring Angles] [|Angle Barrier Game] [|Angles in Triangles] [|Angles in Quadrilaterals]
 * 4.MD.6** Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.
 * Possible Activities:**

[|Unknown Angle Word Problems] [|How Many Degrees?] [|Angles in a Right Triangle]
 * 4.MD.7** Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.


 * Geometry (4.G)**

[|Geoboard Line Segments] ***new!** [|Angles on the Geoboard] [|Angle Barrier Game]
 * Draw and identify lines and angles, and classify shapes by properties of their lines and angles**
 * 4.G.1** Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.
 * Possible Activities:**

[|Right Triangles on the Geoboard] ***new!** [|Isosceles Triangles on the Geoboard] ***new!** [|Constructing Quadrilaterals] [|Quadrilateral Criteria] [|Classifying Triangles 1] [|Classifying Triangles 2] [|Triangles on the Geoboard]
 * 4.G.2** Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.
 * Possible Activities:**

[|Symmetry on the Geoboard] [|Symmetry in Shapes] [|Symmetry in Regular Polygons] [|Symmetrical Coin Designs] [|More Symmetrical Coin Designs]
 * 4.G.3** Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line symmetric figures and draw lines of symmetry.
 * Possible Activities:**



= Website links: =
 * [|MegaMath] **
 * [|First In Math] **
 * [|Math Chimp] **

= Math Articles: = ==== [|marilyn burns F93CDB2EF4A64EF783F00D0282EF123F.pdf] ====
 * [|Number Sense] **