Unit 6: Fraction, Positive/Negative #'s, Algebra, and Inequalities

Dear 5V Math Families,

How are you? I hope you are well. I wanted to give you an update on our next unit of study. We will be moving into unit 6 upon our return to school on  April 1st. The unit will span from the 1st to the 16th. Standards of study include relevance to algebra, negative and positive numbers, fractions, and inequalities.

For more specifics please refer to the standards and skill acquisition below:

Standards

 

CC.6.NS.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?

CC.6.NS.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

CC.6.NS.5 Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, debits/credits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.

CC.6.NS.6 Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.

CC.6.NS.6a Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite.

CC.6.NS.7 Understand ordering and absolute value of rational numbers.

CC.6.NS.7a Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right.

CC.6.NS.7b Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write –3°C > –7°C to express the fact that –3°C is warmer than –7°C.

CC.6.NS.7c Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars.

CC.6.NS.7d Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars.

CC.6.EE.1 Write and evaluate numerical expressions involving whole-number exponents.

CC.6.EE.2 Write, read, and evaluate expressions in which letters stand for numbers.

CC.6.EE.2b Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2(8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.

CC.6.EE.2c Evaluate expressions at specific values for their variables. Include expressions that arise from formulas in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s^3 and A = 6 s^2 to find the volume and surface area of a cube with sides of length s = 1/2.

CC.6.EE.5 Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.

CC.6.EE.6 Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.

CC.6.EE.7 Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.

CC.6.EE.8 Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. ACQUISITION (Students will know):   • Vocabulary: absolute value, algebraic expression, coefficient, constant term, equation, evaluate, exponents, inequality, integers, inverse operations, open sentence, opposite of a number, order of operations, rational numbers, reciprocal, relation symbol, solution, solution set, solve, variable, variable term • Reciprocal fractions will have a product of one. • That (a/b)(c/d) is equal to ac/bd (algorithm). • To divide by any non-zero number (whole numbers or fractions) you can multiply by its reciprocal, including fraction. • The standard algorithm for addition, subtraction, multiplication (traditional) and division (long division) with multi-digit decimals. • Positive and negative numbers can be applied to real world examples. • Positive and negative numbers have a relationship with zero. • How integers fit on a number line or coordinate plane. • The opposite of the opposite of an integer is itself . • Inequalities are statements about positions on the number line. • That absolute value is the distance between any number and zero. • Exponents represent repeated multiplication of a given base. • Each part of an expression has a name and a purpose. • A given value for a variable can be used to solve a variable expression or formula. • An equation or an inequality can have an answer or set of answers that make the equation or inequality true. • A variable expression or equation can represent a real-world situation (word problem). • A variable can represent a real-world situation (word problem). • A variable is used to represent numbers and write expressions. • An inequality can represent a real-life situation. • Inequalities have an infinite number of solutions. • Inequalities can be graphed on a number line.

Unit 5 Begins!

Hello 5V Math Accel Families,

How are you? We are starting unit 5 on Monday, March 11th. I wanted to share with you the common core standards we are covering, the acquisition of knowledge, the learning the kids are doing, and the transfer of that learning: Please see the information below:

Math Accel. Grade 5

Vocabulary: absolute value, axis, coordinate, coordinate plane, midpoint, ordered (number) pair, origin, parallel, perpendicular, polygon, parallelogram, quadrant, quadrilateral, reflection, right angle, right triangle, sector, skewed, trapezoid, triangle, vertex/vertices.

·  CC.6.RP.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

·  CC.6.RP.3c Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole given a part and the percent.

·  CC.6.NS.6 Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.

·  CC.6.NS.6b Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.

·  CC.6.NS.6c Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.

·  CC.6.NS.7 Understand ordering and absolute value of rational numbers.

·  CC.6.NS.7b Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write –3°C > –7°C to express the fact that –3°C is warmer than –7°C.

·  CC.6.NS.8 Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

·  CC.6.G.3 Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.

ACQUISITION (Students will KNOW):

• Ratios can be represented as a percentage.
• How integers fit on a number line or coordinate plane.
• The opposite of the opposite of an integer is itself.
• That an ordered pair is the location of a point on a coordinate grid and how it is related to the x and y axis .
• That reflections across one or both axes are created by changing the signs of the x and/or y coordinate in an ordered pair.
• Positive and negative numbers have a relationship with zero .
• Positive and negative numbers can be applied to real world examples.
• How integers fit on a number line or coordinate plane.
• Students will understand there is a relationship among integers.
• That absolute value is the distance between any number and zero.
• Points on the coordinate plane can represent the vertices of a polygon.

ACQUISITION (Students will be able to):

• Determining a missing value in a percent proportion.
• Finding the opposite of a given number.
• Plotting rational numbers on a number line.
• Plotting ordered pairs on a coordinate plane.
• Graphing the reflection of a given ordered pair on a number line.
• Interpreting absolute value.
• Graphing points in all four quadrants of the coordinate plane.
• Using coordinates and absolute value to find distances between points with the same first coordinates or the same second coordinates.
• Determining the distance between two points on the coordinate plane given that the points have the same x or y value.
• Solving real-world problems using distances on the coordinate plane.