Grade 6Apply and also extend previous understandings of arithmetic to algebraic expressions.
CCSS.Math.Content.6.EE.A.1Write and evaluate number expressions including whole-number exponents.
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CCSS.Math.Content.6.EE.A.2.aWrite expressions that document operations v numbers and with letters standing because that numbers. Because that example, to express the calculation "Subtract y native 5" as 5 - y.
CCSS.Math.Content.6.EE.A.2.bIdentify parts of one expression making use of mathematical state (sum, term, product, factor, quotient, coefficient); watch one or an ext parts of an expression together a solitary entity. Because that example, explain the expression 2 (8 + 7) as a product of 2 factors; view (8 + 7) together both a solitary entity and a amount of two terms.
CCSS.Math.Content.6.EE.A.2.cEvaluate expression at specific values of your variables. Incorporate expressions that arise from formulas used in real-world problems. Carry out arithmetic operations, consisting of those including whole-number exponents, in the standard order as soon as there space no parentheses to specify a details order (Order that Operations). For example, use the formulas V = s3 and also A = 6 s2 to discover the volume and also surface area the a cube v sides of size s = 1/2.
CCSS.Math.Content.6.EE.A.3Apply the properties of operations come generate tantamount expressions. For example, apply the distributive residential property to the expression 3 (2 + x) to develop the tantamount expression 6 + 3x; use the distributive residential or commercial property to the expression 24x + 18y to produce the indistinguishable expression 6 (4x + 3y); apply properties the operations to y + y + y to produce the equivalent expression 3y.
CCSS.Math.Content.6.EE.A.4Identify once two expression are tantamount (i.e., as soon as the two expressions surname the very same number nevertheless of which worth is substituted into them). Because that example, the expressions y + y + y and also 3y are equivalent because they surname the very same number nevertheless of which number y was standing for..
CCSS.Math.Content.6.EE.B.5Understand fixing an equation or inequality together a process of comment a question: which values from a mentioned set, if any, do the equation or inequality true? usage substitution to identify whether a given number in a specified set makes an equation or inequality true.
CCSS.Math.Content.6.EE.B.6Use variables to stand for numbers and write expressions as soon as solving a real-world or mathematics problem; recognize that a variable deserve to represent an unknown number, or, depending upon the function at hand, any number in a stated set.
CCSS.Math.Content.6.EE.B.7Solve real-world and also mathematical difficulties by writing and solving equations that the kind x + ns = q and px = q for instances in which p, q and x space all nonnegative reasonable numbers.
CCSS.Math.Content.6.EE.B.8Write an inequality of the form x > c or x c to stand for a constraint or problem in a real-world or mathematics problem. Identify that inequalities the the form x > c or x Represent and analyze quantitative relationships between dependent and also independent variables.
CCSS.Math.Content.6.EE.C.9Use variables to stand for two quantities in a real-world difficulty that change in connection to one another; compose an equation to express one quantity, believed of as the dependent variable, in regards to the other quantity, believed of together the elevation variable. Analysis the relationship between the dependent and independent variables making use of graphs and also tables, and also relate these to the equation. Because that example, in a trouble involving motion at constant speed, list and also graph ordered bag of distances and times, and also write the equation d = 65t to stand for the relationship in between distance and also time.
CCSS.Math.Content.7.EE.A.1Apply nature of work as strategies to add, subtract, factor, and expand direct expressions with rational coefficients.
CCSS.Math.Content.7.EE.A.2Understand that rewriting one expression in different forms in a difficulty context can burned light on the problem and how the amounts in it are related. Because that example, a + 0.05a = 1.05a method that "increase by 5%" is the same as "multiply by 1.05."
CCSS.Math.Content.7.EE.B.3Solve multi-step real-life and also mathematical problems posed with positive and negative rational number in any type (whole numbers, fractions, and also decimals), using tools strategically. Apply properties the operations to calculate through numbers in any kind of form; convert in between forms together appropriate; and also assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will certainly make second 1/10 of her salary one hour, or $2.50, for a brand-new salary the $27.50. If you desire to place a bath towel bar 9 3/4 inches long in the center of a door the is 27 1/2 inch wide, you will require to ar the bar around 9 customs from each edge; this estimate can be provided as a check on the specific computation.
CCSS.Math.Content.7.EE.B.4Use variables to represent amounts in a real-world or mathematical problem, and also construct straightforward equations and also inequalities come solve difficulties by reasoning about the quantities.
CCSS.Math.Content.7.EE.B.4.aSolve word troubles leading to equations that the type px + q = r and also p(x + q) = r, where p, q, and also r are certain rational numbers. Solve equations the these forms fluently. To compare an algebraic solution to an arithmetic solution, identify the sequence of the operations provided in each approach. For example, the perimeter the a rectangle is 54 cm. Its length is 6 cm. What is that is width?
CCSS.Math.Content.7.EE.B.4.bSolve word troubles leading to inequalities that the kind px + q > r or px + q r, where p, q, and also r are certain rational numbers. Graph the solution set of the inequality and interpret it in the paper definition of the problem. For example: together a salesperson, you room paid $50 every week add to $3 per sale. This main you desire your pay to be at least $100. Create an inequality for the number of sales you must make, and describe the solutions.
CCSS.Math.Content.8.EE.A.1Know and apply the nature of integer index number to generate equivalent numerical expressions. Because that example, 32×3-5 = 3-3 = 1/33 = 1/27.
CCSS.Math.Content.8.EE.A.2Use square root and also cube root icons to stand for solutions to equations the the form x2 = p and x3 = p, wherein p is a optimistic rational number. Evaluate square root of tiny perfect squares and also cube root of little perfect cubes. Know that √2 is irrational.
CCSS.Math.Content.8.EE.A.3Use number expressed in the kind of a solitary digit times an integer power of 10 to estimate very huge or very little quantities, and to express how countless times as lot one is 보다 the other. For example, calculation the population of the United claims as 3 times 108 and also the populace of the people as 7 times 109, and determine that the world populace is an ext than 20 time larger.
CCSS.Math.Content.8.EE.A.4Perform operations v numbers expressed in scientific notation, including problems where both decimal and also scientific notation space used. Use clinical notation and also choose devices of proper size for dimensions of very huge or very tiny quantities (e.g., use millimeters per year for seafloor spreading). Analyze scientific notation that has been produced by technology
CCSS.Math.Content.8.EE.B.5Graph proportional relationships, interpreting the unit rate as the steep of the graph. Compare two different proportional relationships stood for in different ways. Because that example, compare a distance-time graph to a distance-time equation to recognize which of two moving objects has better speed.
CCSS.Math.Content.8.EE.B.6Use similar triangles to describe why the steep m is the same between any kind of two distinctive points top top a non-vertical heat in the coordinate plane; have the equation y = mx because that a line v the origin and also the equation y = mx + b for a heat intercepting the vertical axis at b.
CCSS.Math.Content.8.EE.C.7.aGive examples of straight equations in one variable with one solution, infinitely plenty of solutions, or no solutions. Display which of this possibilities is the case by successively transforming the offered equation into easier forms, until an equivalent equation the the kind x = a, a = a, or a = b results (where a and also b are various numbers).
CCSS.Math.Content.8.EE.C.7.bSolve direct equations with rational number coefficients, consisting of equations whose options require broadening expressions making use of the distributive property and collecting favor terms.
CCSS.Math.Content.8.EE.C.8.aUnderstand that solutions to a system of two linear equations in two variables exchange mail to points of intersection of your graphs, because points the intersection accomplish both equations simultaneously.
CCSS.Math.Content.8.EE.C.8.bSolve systems of two straight equations in 2 variables algebraically, and also estimate solutions by graphing the equations. Solve straightforward cases through inspection. For example, 3x + 2y = 5 and also 3x + 2y = 6 have actually no solution because 3x + 2y cannot concurrently be 5 and also 6.
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CCSS.Math.Content.8.EE.C.8.cSolve real-world and also mathematical troubles leading to two direct equations in 2 variables. Because that example, given works with for 2 pairs that points, determine whether the line through the an initial pair of clues intersects the line through the second pair.
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