1 Find the value of the expression. 1 2 4 Find the value of the expression. Base is 2 Exponent is 4 (how many times the base is multiplied by itself) 2 4 = 2 x 2 x 2 x 2 2 4 is not 2 x 4 = 8 3 3 = 4 x 2 x 2 2 4 = 16 = 8 x 2 = 16 NS 1.4 2 Find the prime factors of 24 and write as an expression in exponential form. When finding prime factors using a factor tree, circle a prime factor as soon as you write it so you don t forget to list it at the end. 2 Find the prime factors of 72 and write as an expression in exponential form. 24 Write the number. 8 x 3 Start with two factors for 24. Circle 3 because it is prime. 8 is composite, so factor it. 4 x 2 Circle 2 because it is prime. 4 is composite, so factor it. 2 x 2 Circle 2 s because they are prime. Since both factors are prime, you don t need to factor them. 2 x 2 x 2 x 3 List all circled prime factors in order from least to greatest. = 4 x 2 x 3 Check your work by multiplying. = 8 x 3 = 24 2 3 x 3 Write prime factors in exponential form. NS 1.4/5.OA.2.1 Page 1 of 14 MCC@WCCUSD 10/25/13
3 Decompose 176.842 to expanded form. 3 A number in expanded form is written as the sum of the values of each digit. Decompose 241.953 to expanded form. 1 7 6. 8 4 2 100 + 70 + 6 +.8 +.04 +.002 = 176.842 The sum written vertically: 100.000 70.000 6.000 0.800 0.040 + 0.002 176.842 NS 1.0/5.NBT.3.a 4 Round 335.687 to the nearest hundredth. 4 The digit 8 is in the hundredths place, so 335.687 will be rounded to 335.68 or 335.69. Round 687.456 to the nearest hundredth. Draw a number line starting with 335.680 (equivalent to 335.68) and ending with 335.690 (equivalent to 335.69). Add 335.685 as the midpoint between 335.680 and 335.690. 335.687 is closer to 335.690. Therefore, 335.687 rounded to the nearest hundredth is 335.69. 335.687 335.680 335.685 335.690 335.68 (midpoint) 335.69 NS1.1/5.NBT.4 Page 2 of 14 MCC@WCCUSD 10/25/13
5 Find the sum of 17.38 + 48.95 = 5 Decomposition 53.68 + 21.79 = 17.38 + 48.95 = Decompose each addend to expanded notation = (10 + 7 +.3 +.08) + (40 + 8 +.9 +.05) Group like terms (move tens with tens, etc.) = (10 + 40) + (7 + 8) + (.3 +.9) + (.08 +.05) Combine like terms = 50 + 15 + 1.2 +.13 Note:.3 +.9 = 1.2, not 0.12 Add terms = 66.33 Partial Sums (hundredths first) 17.38 + 48.95.13.08 +.05 1.20.3 +.9 Note:.3 +.9 = 1.2, not 0.12 15.00 7 + 8 + 50.00 10 + 40 66.33 Partial Sums (tens first) 17.38 + 48.95 50.00 10 + 40 15.00 7 + 8 1.20.3 +.9 Note:.3 +.9 = 1.2, not 0.12 +.13.08 +.05 66.33 NS 2.1/5.NBT.7 Page 3 of 14 MCC@WCCUSD 10/25/13
6 Find the difference between 4.73 and 2.36. 6 Open Number Line Find the difference between 6.14 and 3.57. The difference between two numbers is the distance between them (how far apart they are). Create a number line with the smallest number at the left end and the largest number at the right end. Jump using numbers that make it easy for you. Each person might jump differently. One way to jump: 2.0.04.33 2.36 4.36 4.4 4.73 Add the jumps to find the total distance: 2.00.04 +.33 2.37 Another way to jump (in opposite direction):.04.6 1.0.73 2.36 2.4 3.0 4.0 4.73 Add the jumps to find the total distance:.04.60 1.00 +.73 2.37 NS 2.1/5.NBT.7 Page 4 of 14 MCC@WCCUSD 10/25/13
7 D asia bought a sandwich for $3.50 and a milk for $1.25. How much change did she get if she gave the lunch clerk $5.00? Bar Model 7 Alberto had $10.00. He bought a pack of pencils for $1.50, a notebook for $1.25, and an eraser for $0.75. How much change did he get? Part Whole Part Bar models are used to find unknowns. Sometimes the unknown is the whole, and sometimes the unknown is a part. This word problem has two steps. Step 1 We know the parts: She spent $3.50 and $1.25. The whole is unknown: How much did D asia spend? We add the parts to find the unknown whole. Part: $3.50 Part: $1.25 Whole: $4.75 Part + Part = Unknown Whole $3.50 + $1.25 = $4.75 Step 2: We know the whole: She started with $5.00. We know one of the parts: She spent $4.75. The other part is unknown: How much change did she get? We know the whole and one of the parts, so we subtract the known part from the whole to find the unknown part. Whole: $5.00 Part: $4.75 Part: $0.25 Whole Known Part = Unknown Part $5.00 - $4.75 = $0.25 Words Math Spent $3.50 & $1.25 $3.50 + $1.25 = $4.75 How much change from $5.00 $5.00 - $4.75 = $0.25 D asia received $0.25 in change. NS 2.1/5.NBT.7 Page 5 of 14 MCC@WCCUSD 10/25/13
8 Find the product of 48 x 57 = Partial Products 48 x 57 56 (7 x 8) 280 (7 x 40) 400 (50 x 8) +2,000 (50 x 40) 2,736 8 Find the product of 98 x 36 = Generic Rectangle Decompose factors using expanded notation: (40 + 8) x (50 + 7) Draw a large rectangle. Write one of the expanded factors across the top and one down the side. Draw lines separating rows and columns at plus signs. Multiply expanded factors and write products in boxes. 40 8 50 7 50 x 40 = 2,000 7 x 40 = 280 50 x 8 = 400 7 x 8 = 56 Add the partial products from each box. 2,000 400 280 + 56 2,736 Traditional 48 x 57 336 +2,400 2,736 NS 2.1/5.NBT.5 Page 6 of 14 MCC@WCCUSD 10/25/13
9 Find the product of 2.3 x 3.2 = Partial Products 2.3 x 3.2.06 (.2 x.3) Does not equal 0.6. Think.40 (.2 x 2) about multiplying using.90 (3 x.3) fractions.!!"!!" =!!"" + 6.0 (3 x 2) =.06 7.36 9 Find the product of 4.2 x 3.4 = Generic Rectangle Decompose factors using expanded notation: (2 +.3) x (3 +.2) Draw a large rectangle with expanded notation factors. Include fraction equivalents to help place decimals correctly in partial products. 3 or!! 0.2 or!!" 2 or!! 3 x 2 = 6! x! =!!"!!" 0.4 0.3 or!!"! x! =!!!"!" 0.9! x! =!!"!"!"" 0.06 Add the partial products from each box. 6 0.9 0.4 +.06 7.36 Traditional 2.3 1 decimal place in factor tenth x 3.2 + 1 decimal place in factor x tenth 46 2 decimal places in product hundredth + 690 7.36 NS 2.1/5.NBT.7 Page 7 of 14 MCC@WCCUSD 10/25/13
10 Jada has 3 sticker books. Zarrie has 2 sticker books. Each sticker book has 50 stickers. How many stickers do they have in all? Bar Model Jada Zarrie 10 Each package of erasers has 20 erasers. Alonzo has 4 packages. Namon has 3 packages. How many erasers do they have in all? 50 50 50 50 50 150 100 250 (3 x 50) + (2 x 50) = 150 + 100 = 250 stickers Number Line Jada Zarrie +50 +50 +50 +50 +50 0 50 100 150 200 250 50 50 50 OR 5 x 50 = 250 stickers 50 + 50 250 stickers They have 250 stickers in all. AF 1.2 Page 8 of 14 MCC@WCCUSD 10/25/13
11 Find the quotient 8,588 38 = 11 Traditional Find the quotient of 9,342 27 = 226 38) 8,588-7 6 98-76 228-228 0 Partial Quotients Side Work: List some 38) 8,588 multiples of the divisor - 3,800 100 to help think about 4,788 quotient parts you - 3,800 100 want to use. Multiples 988 must be smaller than - 760 20 the dividend. 228 38 x 1 = 38-190 5 38 x 10 = 380 38 38 x 100 = 3,800-38 1 38 x 2 = 76 0 226 38 x 20 = 760 38 x 200 = 7,600 38 x 5 = 190 Stacking 6 10 10 200 38) 8,588-7,600 988-380 608-380 228-228 0 226 NS 2.2/5.NBT.6 Page 9 of 14 MCC@WCCUSD 10/25/13
12 Find the quotient of 75.25 3.5 = 12 Partial Quotients Side Work: List some 3.5) 75.25 multiples of the divisor - 35.00 10 to help think about 40.25 quotient parts you - 35.00 10 want to use. Multiples 5.25 must be smaller than - 3.50 1 than the dividend. 1.75 3.5 x 1 = 3. - 1.75 0.5 3.5 x 10 = 35 0 21.5 3.5 x.5 = 1.75 3.5 x 5 = 17.5 Find the quotient of 53.50 2.5 = Stacking 0.5 1 10 10 3.5) 75.25-35.00 40.25-35.00 5.25-3.50 1.75-1.75 0 21.5 NS 2.2/5.NBT.7 End of Study Guide Page 10 of 14 MCC@WCCUSD 10/25/13
1 2 3 You Try Solutions: Find the value of the expression. 3 3 = 3 x 3 x 3 = 9 x 3 = 27 Find the prime factors of 72 and write as an expression in exponential form. 72 2 x 2 x 2 x 3 x 3 = 2 3 x 3 2 = 72 8 x 9 2 x 4 x 3 x 3 2 x 2 Decompose 241.953 to expanded notation. 200 +40 + 1 +.9 +.05 +.003 = 241.953 5 53.68 + 21.79 = Decomposition: = (50 + 3 +.6 +.08) + (20 + 1 +.7 +.09) = (50 + 20) + (3 + 1) + (.6 +.7) + (.08 +.09) = 70 + 4 + 1.3 +.17 = 75.47 Partial Sums (hundredths first) 53.68 + 21.79.17.08 +.09 1.30.6 +.7 4.00 3 + 1 + 70.00 50 + 20 75.47 Partial Sums (tens first) 53.68 + 21.79 70.00 50 + 20 4.00 3 + 1 1.30.6 +.7 +.17.08 +.09 75.47 4 Round 687.456 to the nearest hundredth. 687.456 687.450 687.455 687.460 687.45 (midpoint) 687.46 687.456 rounded to the nearest hundredth is 687.46. Page 11 of 14 MCC@WCCUSD 10/25/13
6 7 Find the difference between 6.14 and 3.57. One way to jump on an open number line.03.4 2.0.14 3.57 3.6 4.0 6.0 6.14.03.40 2.00 +.14 2.57 Another way to jump (in opposite direction) 2.0.5.07 3.57 5.57 6.07 6.14 2.00.50 +.07 2.57 Alberto had $10.00. He bought a pack of pencils for $1.50, a notebook for $1.25, and an eraser for $0.75. How much change did he get? 8 Find the product of 98 x 36 = Partial Products 98 x 36 48 (6 x 8) 540 (6 x 90) 240 (30 x 8) +2,700 (30 x 90) 3,528 Generic Rectangle 30 6 90 8 30 x90 = 2,700 6 x 90 = 540 30 x 8 = 240 6 x 8 = 48 Add the partial products from each box. 2,700 240 540 + 48 3,528 Step 1 $1.50 $1.25 $0.75 $3.50 Step 2: $10.00 $3.50 $6.50 Words Math Spent $1.50, $1.25 $1.50 + $1.25 and $0.75 + 0.75 = $3.50 How much change from $10.00 $10.00 - $3.50 = $6.50 Alberto received $6.50 in change. Page 12 of 14 MCC@WCCUSD 10/25/13
9 10 Find the product of 4.2 x 3.4 = Partial Products Each package of erasers has 20 erasers. Alonzo has 4 packages. Namon has 3 packages. How many erasers do they have in all? 4.2 x 3.4.08 1.60.60 +12.00 14.28 Bar Model Alonzo Namon 20 20 20 20 20 20 20 80 60 140 Generic Rectangle 3 or!! 0.4 or!!" 12 0.6 1.6 +.08 14.28 Traditional 4.2 x 3.4 168 + 1260 14.28 4 or!! 3 x 4 = 12! x! =!"!"!!" 1.6 0.2 or!!"! x! =!!!"!" 0.6! x! =!!"!"!"" 0.08 (4 x 20) + (3 x 20) = 80 + 60 = 140 erasers Number Line Alonzo +20 +20 +20 +20 +20 +20 +20 0 20 40 60 80 100 120 140 20 20 20 20 OR 7 x 20 = 140 erasers 20 20 + 20 140 erasers They have 140 erasers in all. Namon Page 13 of 14 MCC@WCCUSD 10/25/13
11 12 Find the quotient of 9,342 27 = Find the quotient of 53.50 2.5 = Traditional 346 27) 9,342-8 1 1 24-1 08 162-162 0 Partial Quotients Side Work: List some 27) 9,342 multiples of the divisor - 5,400 200 to help think about 3,942 quotient parts you - 2,700 100 want to use. Multiples 1,242 must be smaller than - 540 20 the dividend. 702 27 x 1 = 27-540 20 27 x 10 = 270 162 27 x 100 = 2,700-162 6 27 x 2 = 54 0 346 27 x 20 = 540 27 x 200 = 5,400 27 x 5 = 135 Stacking 6 40 100 200 27) 9,342-5,400 3,942-2,700 1,242-1,080 162-162 0 346 Partial Quotients Side Work: List some 2.5) 53.50 multiples of the divisor - 25.00 10 to help think about 28.50 quotient parts you - 25.00 10 want to use. Multiples 3.50 must be smaller than - 2.50 1 the dividend. 1.00 2.5 x 1 = 2.5-1.00 0.4 2.5 x 10 = 25 0 21.4 2.5 x 2 = 5.0 2.5 x 20 = 50 2.5 x.4 = 1.0 2.5 x 4 = 10 Stacking 0.4 1 10 10 2.5) 53.50-25.00 28.50-25.00 3.50-2.50 1.00-1.00 0 21.4 Page 14 of 14 MCC@WCCUSD 10/25/13