Math

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

 * || **I Can . . .** ||
 * CCSS || **Operations and Algebraic Thinking (5.OA)** **Common Core Cluster:**
 * Write and interpret numerical expressions.** ||
 * 5.OA.1 || Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.


 * Unpacking: What does this standard mean that a student will know and be able to do?**

5.OA.1 calls for students to evaluate expressions with parentheses, brackets [ ] and braces { }. In upper levels of mathematics, evaluate means to substitute for a variable and simplify the expression. However at this level students are to only simplify the expressions because there are no variables.

Example: Evaluate the expression 2{ 5[12 + 5(500 ‐ 100) + 399]} Students should have experiences working with the order of first evaluating terms in parentheses, then brackets, and then braces. The first step would be to subtract 500 – 100 = 400. Then multiply 400 by 5 = 2,000. Inside the bracket, there is now [12 + 2,000 + 399]. That equals 2,411. Next multiply by the 5 outside of the bracket. 2,411 x 5 = 12,055. Next multiply by the 2 outside of the braces. 12,055 x 2= 24,110.

Mathematically, there cannot be brackets or braces in a problem that does not have parentheses. Likewise, there cannot be braces in a problem that does not have both parentheses and brackets.

Essential Vocabulary: (K) parentheses, brackets, braces, numerical expressions, order of operations || Activities: || __[|Target Number Dash]__ __[|Numerical Expressions Clock]__ || Activities: || __[|Verbal Expressions]__ || Activities: || __[|Function Table and Graph Template]__ __[|Function Table and Coordinate Plane Paper]__ __[|Addition on the Coordinate Plane]__ __[|Subtraction on the Coordinate Plane]__ || Activities: || __[|Multiplying a Whole Number by a Power of 10]__ __[|Multiplying a Decimal by a Power of 10]__ __[|Dividing a Whole Number by a Power of 10]__ __[|Dividing a Decimal by a Power of 10]__ || Activities: || __[|Representing Decimals with Base 10 Blocks]__ __[|Representing Decimals in Different Ways]__ __[|Hunt for Decimals]__ || Activities: || __[|Rounding Decimals to the Nearest Hundredth]__ || Activities: || __[|Make the Largest Product]__ __[|Make the Smallest Product]__ || Activities: || __[|Creating and Solving a Division Problem]__ || Activities: || __[|Base 10 Pictures with Decimals]__ __[|Base 10 Buildings with Decimals]__ __[|Decimal Cross Number Puzzles]__ __[|Base 10 Decimal Bag Addition]__ __[|Base 10 Decimal Bag Subtraction]__ __[|Total Ten]__ __[|Decimal Subtraction Spin]__ __[|Decimal Addition to 500]__ __[|Decimal Addition Bingo]__ __[|Decimal Race to Zero]__ __[|Decimal Magic Triangle]__ __[|Magic Squares (adding decimals)]__ || Activities: || __[|Fraction Word Problems (unlike denominator)]__ __[|Mixed Number Word Problems (unlike denominators)]__ __[|Closest to 25]__ __[|Magic Squares (adding fractions)]__ __[|Mixed Number Sum]__ __[|Mixed Number Difference]__ || Activities: || __[|Using Equivalent Fractions to Subtract Fractions]__ __[|Addition Word Problem with Fractions]__ __[|Subtraction Word Problem with Fractions]__ || a. Interpret the product (a/b) x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations axq÷b. For example, use a visual fraction model to show (2/3) x 4 = 8/3, and create a story context for this equation. Do the same with (2/3) x (4/5) = 8/15. (In general, (a/b) x (c/d) = ac/bd) || Activities: || __[|Multiplying Fractions by Dividing Rectangles]__ __[|Fraction x Fraction Word Problems]__ || Activities: || __[|Area Word Problems with Fractional Side Lengths]__ || a. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. || Activities: || __[|Fraction x Mixed Number Word Problems]__ || a. Interpret division of a unit fraction by a non-zero whole number and compute such quotients. For example, create a story context for (1/3)÷4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3)÷4 = 1/12 because (1/12) x 4 = 1/3. || Activities: || __[|Dividing a Whole Number by a Unit Fraction]__ || Activities: || __[|Division of Fractions Word Problems]__ || Activities: || __[|Comparing Units of Metric Linear Measure]__ __[|Metric Conversion Word Problems]__ || Activities: || __[|Fractions on a Line Plot]__ __[|Sacks of Flour]__ || a. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. || Activities: || __[|Exploring Volume]__ __[|Building Rectangular Prisms with a Given Volume]__ __[|Ordering Rectangular Prisms by Volume]__ || Activities: || __[|3D Structures]__***new!** __[|Build a Cubic Meter]__***new!** __[|Roll a Rectangular Prism]__ || a. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication. || Activities: || __[|Designing a Toy Box]__ __[|Designing a Cereal Box]__ || Activities: || __[|Coordinate Grid Geoboards]__ __[|Coordinate Shapes]__ __[|Coordinate Grid Swap]__ __[|Coordinate Grid Tangram]__ __[|Assorted Coordinate Grid Paper]__ || Activities: || __[|Identifying Quadrilaterals]__ __[|Quadrilateral Criteria]__ __[|Constructing Quadrilaterals]__ __[|Quadrilateral Tangram Challenge]__ __Properties of Quadrilaterals __ || Activities: || __[|Triangle Hierarchy Diagram]__ __[|Triangle Hierarchy Diagram 2]__ __[|Regular/Irregular Hierarchy Diagram]__ __[|Quadrilateral Hierarchy Diagram]__
 * Possible
 * 5.OA.2 || Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 //×// (8 + 7). Recognize that 3 //×// (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product. ||
 * Possible
 * 5.OA.3 || Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. ||
 * Possible
 * || **Number and Operations in Base Ten (2.NBT)** ||
 * 5.NBT.1 || Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. ||
 * 5.NBT.2 || Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. ||
 * Possible
 * 5.NBT.3 || Read, write and compare decimals to thousandths. ||
 * 5.NBT.3a || Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g. 347.392 = 3x100 + 4x10 + 7x1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000) ||
 * 5.NBT.3b || Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. ||
 * Possible
 * 5.NBT.4 || Use place value understanding to round decimals to any place. ||
 * Possible
 * 5.NBT.5 || Fluently multiply multi-digit whole numbers using the standard algorithm. ||
 * Possible
 * 5.NBT.6 || Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. ||
 * Possible
 * 5.NBT.7 || Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction, relate the strategy to a written method and explain the reasoning used. ||
 * Possible
 * || **Number and Operations - Fractions (5.NF)** ||
 * 5.NF.1 || Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or differences of fractions with like denominators. ||
 * Possible
 * 5.NF.2 || Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + ½ = 3/7 by observing that 3/7 < ½. ||
 * Possible
 * 5.NF.3 || Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g. by using visual fraction models or equations to represent the problem. ||
 * 5.NF.4 || Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
 * Possible
 * 5.NF.4b || b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. ||
 * Possible
 * 5.NF.5 || Interpret multiplication as scaling (resizing) by:
 * 5.NF.5b || b. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number; explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number, and relating the principle of fraction equivalence a/b= nxa)/(nxb) to the effect of multiplying a/b x 1 ||
 * 5.NF.6 || Solve real world problems involving multiplication of fractions and mixed numbers, e.g. by using visual fraction models or equations to represent the problem. ||
 * Possible
 * 5.NF.7 || Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.
 * 5.NF.7b || b. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4÷(1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) =20 because 20 x (1/5 )=4. ||
 * Possible
 * 5.NF.7c || c. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g. by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb. of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? ||
 * Possible
 * || __**Measurement and Data (5.MD)**__ ||
 * 5.MD.1 || Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5cm to 0.05m), and use these conversions in solving multi-step, real world problems. ||
 * Possible
 * 5.MD.2 || Make a line plot to display a set of measurements in fractions of a unit (1/2, ¼, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. ||
 * Possible
 * 5.MD.3 || Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
 * 5.MD.3b || b. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. ||
 * Possible
 * 5.MD.4 || Measure volume by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. ||
 * Possible
 * 5.MD.5 || Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
 * 5.MD.5b || b. Apply the formulas V= l x w x h and V = b x h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems. ||
 * Possible
 * 5.MD.5c || c. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems. ||
 * || **Geometry (5.G)** ||
 * 5.G.1 || Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the conventions that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). ||
 * Possible
 * 5.G.2 || Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. ||
 * || __[|Geometric Shapes on the Coordinate Grid]__ ||
 * 5.G.3 || Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. ||
 * Possible
 * 5.G.4 || Classify two-dimensional figures in a hierarchy based on properties. ||
 * Possible



= Website links: =


 * [|MegaMath] **
 * [|First In Math] **
 * [|Math Chimp] **

**[|Illuminations]**
= Math Articles: =


 * [|Number Sense] **

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