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Identify and describe patterns by explaining its properties. Variable Constant Quantities whose values do not change. (ex: 2, 67) Numerical Expression Symbol, usually a letter, that represents one or more numbers. (ex: n, x) Mathematical phrase that contains numbers and operation symbols. (ex: 3+5) Algebraic Expression Mathematical phrase that contains one or more variables. (ex: 3n + 5) Look at the figures from left to right to determine which figure should come next. Try this: Tables are an easy way to organize data to recognize a pattern. Input/output Ex: how many toothpicks in the 20th figure? The following graph shows tank sizes in relation to the combined lengths of the fish it can hold. If you want five 2-in goldfish, four 1-in guppies, and a 3-in loach, what is the smallest capacity tank you can buy? What is the combined length? 17 inches Make a table using some points from the graph. The tank should be at least 19 gallons. Identify properties of real numbers by graphing and ordering. Numbers can be classified by their characteristics. Some can be represented on the number line. The opposite or additive inverse of any number a is –a. The sum of a number and its inverse is 0 Ex: 12 + (-12) = 0 The reciprocal or multiplicative inverse of any 1 nonzero number a is . 𝑎 The product of a number and its reciprocal is 1 Ex: 1 8( ) 8 =1 Numbers are classified using sets. Set- a well-defined collection of objects. Each object is an element of the set. Subset- consists of elements from the given set. Sets of Numbers natural numbers {1,2,3,…} 0 whole numbers {0,1,2,3,…} 0 Integers {…,-2,-1,0,1,2,…} 0 1 5 3 11 2 Sets of Numbers 5.75 3 4 5 6 7 𝑎 𝑏 • Rational numbers can be written in the form where a and b are integers. They can also be written in decimal form. • Decimals must be terminating or repeating. Sets of Numbers 15 3 4 5 6 • Irrational numbers cannot be written in as a quotient of two integers. • Decimals are non-terminating • Ex: 0.1010010001…, 3.141592… 7 #1 What kind of number is -5? integer, rational #2 What kind of number is 42? natural, whole, integer, rational #3 What kind of number is 4.5669? rational Rational numbers and irrational numbers form the set of real numbers. Subsets of real numbers: Natural Whole Integer Rational Irrational Inequalities An inequality is a mathematical sentence comparing the values of two expressions using an inequality symbol. -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 8 > -6 Inequalities -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 -7 < 7 #5 -7 < #6 -5 + 10 10 = 10 - 5 Odds p. 7 #13, 15, 23 p.15 #23-27, 35-39