MTE 280: Number Operations and Proportional Reasoning k-8 Teaching

Decimals☆ Base-10 system = Decimal System = 1-to-10 Relationship☆ Decimal separates the part form the whole☆ Decimal sits to the right of the unit

Addition:Subtraction:Multiplication:Division:

ConvertingDenominator is a multiple of 107/10=0.7 12/100=0.12 3/100=0.03 1.32=1 32/100 0.72=72/100Denominator is a factor of 10, 100, 1000, ect.2/5=(2x2)/(5x2)=4/10=0.4 7/20=(7x5)/(20x5)=35/100=0.35 Denominator is not 1 or 2Repeating VS Terminating☆ is not a decimal because it is not terminating or repeating - it is an irrational #

Integers☆ Integers: positive and negative numbers☆ "Chip Method": Best method for teaching integersCan be used for many lessonsUses two-color tokens to represent positive/negative numbers🟡 = Positive and 🔴 = Negative🟡🟡🟡 = 3 and 🔴🔴🔴 = -3

Addition W/Integers:🟡 = Positive and 🔴 = Negative+5 + +1= +6 🟡🟡🟡🟡🟡 + 🟡 = 🟡🟡🟡🟡🟡🟡 -5 + -1= -6 🔴🔴🔴🔴🔴 + 🔴 = 🔴🔴🔴🔴🔴🔴 +5 + -1= +4 🟡🟡🟡🟡🟡 + 🔴 = 🟡🟡🟡🟡-5 + +1= -4 🔴🔴🔴🔴🔴 + 🟡 = 🔴🔴🔴🔴☆ negative +/- positive = zero pair → 🔴 🟡 = 0 → cancel eachother outa) 3 + -2 = 1 🟡🟡🟡 + 🔴🔴 = 🟡 or 🟡🟡🟡 = 1 + 🔴🔴b) -6 + -2 = -8🔴🔴🔴🔴🔴🔴 + 🔴🔴 = 🔴🔴🔴🔴🔴🔴🔴🔴c) 3 + -4 = -1🟡🟡🟡 + 🔴🔴🔴🔴 = 🔴d) -2 + -1 = -3🔴🔴 + 🔴 = 🔴🔴🔴

Subtraction W/Integers:🟡 = Positive and 🔴 = Negative☆ negative +/- positive = zero pair → 🔴 🟡 = 0 → cancel eachother out+5 - +1 = +4 🟡🟡🟡🟡🟡 - 🟡 = 🟡🟡🟡🟡-5 - -1 = -4 🔴🔴🔴🔴🔴 - 🔴 = 🔴🔴🔴🔴+5 - -1 = +6 🟡🟡🟡🟡🟡 - 🔴 → 🟡🟡🟡🟡🟡 - 🔴 (+ 🔴 🟡) → 🟡🟡🟡🟡🟡🟡🔴 - 🔴 = 🟡🟡🟡🟡🟡🟡-5 + +1 = -6 🔴🔴🔴🔴🔴 + 🟡 → 🔴🔴🔴🔴🔴 + 🟡 (+ 🔴 🟡) → 🔴🔴🔴🔴🔴🔴🟡 - 🟡 = 🔴🔴🔴🔴🔴🔴a) 3 - -1 = 4 🟡🟡🟡 - 🔴 = 🟡🟡🟡🟡 🟡🟡🟡🟡🔴 - 🔴 = 🟡🟡🟡🟡b) -6 - -2 = -4 🔴🔴🔴🔴🔴🔴 - 🔴🔴 = 🔴🔴🔴🔴c) 3 - -4 = 7 🟡🟡🟡 - 🔴🔴🔴🔴 = 🟡🟡🟡🟡🟡🟡🟡 🟡🟡🟡🟡🟡🟡🟡🔴🔴🔴🔴 - 🔴🔴🔴🔴 = 🟡🟡🟡🟡🟡🟡🟡d) -2 - -3 = 1 🔴🔴 - 🔴🔴🔴 = 🟡 🔴🔴🔴🟡 - 🔴🔴🔴 = 🟡

Multiplication W/Integers:☆ Commutative: a x b = b x a3 x 2 = 63 groups of 2 = 6(++) (++) (++) = 6repeated addition → 2+2+2Commutative [property of multiplication: axb=bxa3 groups of 2 = 6 → (++) (++) (++) = 63 groups of -2 = 6 → (--) (--) (--) = -6-3 groups of 2 (-3x2) = -6 (same because of commutative property) 3 x -2 = -3 x 2 = -6 ⤴-Means "the opposite of" ⤵ -3 x -2 = the opposite of 3 x -2 = -6 → opposite of → = 6 → -3 x -2 = 6 🚫 -3 groupssomethinghing ⤴ Solve it this way because it is easier for students to understand ⤴ a) 2 x 5 = 2 groups of 5 = (+++++) (+++++) = 10b) 2 x -5 = 2 groups of -5 = (-----) (-----) = -10c) -2 x 5 = 5 x -2 = 5 groups of -2 = (--) (--) (--) (--) (--)d) -2 x -5 = the opposite of 2 x -5 = 2 groups of -5 = (-----) (-----) = -10 → opposite = 10

Division W/Integers:☆ Multiplication + Division = Inverse Operations

Percentages☆ % = percent☆ percent → per - cent → literally means out of 10025% = 25 out of 1003/100=0.03=3% 43/100=0.43=43%☆ 100 does not always = 100%9 people in a class everyone in there → 9=100%without context of the word problem 9=900%☆ can be > 100 → 1.25=125%

Problem Solving With Percentages3 Types of Problems with %'s:8 is what percent of 22? → answer will be a %8% of 22 is what #? → answer will be #8% of what # is 22?How to Solve: 8 = n x 22 → n = 8/22 → n = 36.6- → n = 37%0.08 x 22 = n → n = 1.760.08 x n = 22 → n = 22/0.08 → n = 275Essential Vocab:☆ "is" → = ☆ Change % into decimals☆ "of" → x ☆ "what percent" → write decimal as a percent ☆ "what" → variable n