Course Numbers and Patterns 1-1 Numbers and Patterns Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

Course Numbers and Patterns Warm Up Write a number in which no digit is repeated for each description digit number divisible by 5 and digit number divisible by 3 and digit number divisible by 2, 3 and 6. Possible answer 1,230 Possible answer 1,245 Possible answer 1,356

Course Numbers and Patterns Problem of the Day For each of the following, write the product of three and the number. –2, 3, 7, 12, 18 –6, 9, 21, 36, 54

Course Numbers and Patterns Learn to identify and extend patterns.

Course Numbers and Patterns Identify a possible pattern. Use it to write the next three numbers. Additional Example 1A: Identifying and Extending Number Patterns A pattern is to multiply each number by 4 to get the next number. 48  4 = 192, 192  4 = 768, 768  4 = 3072 So the next numbers will be 192, 768, and  4  4  4  4  4 3, 12, 48,,,,

Course Numbers and Patterns Additional Example 1B: Identifying and Extending Number Patterns 7, 12, 17,,,,... A pattern is to add each number by 5 to get the next number = 22, = 27, = 32 So the next numbers will be 22, 27, and Identify a possible pattern. Use it to write the next three numbers.

Course Numbers and Patterns Additional Example 1C: Identifying and Extending Number Patterns 20, 17, 14,,,,... A pattern is to subtract each number by 3 to get the next number. 14 – 3 = 11, 11 – 3 = 8, 8 – 3 = 5 So the next numbers will be 11, 8, and 5. – 3 – 3 – 3 – 3 – Identify a possible pattern. Use it to write the next three numbers.

Course Numbers and Patterns Check It Out: Example 1A 18, 25, 32,,,,... A pattern is to add each number by 7 to get the next number = 39, = 46, = 53 So the next numbers will be 39, 46, and Identify a possible pattern. Use it to write the next three numbers.

Course Numbers and Patterns Check It Out: Example 1B 45, 41, 37,,,,... A pattern is to subtract each number by 4 to get the next number. 37 – 4 = 33, 33 – 4 = 29, 29 – 4 = 25 So the next numbers will be 33, 29, and 25. – 4 – 4 – 4 – 4 – 4 Identify a possible pattern. Use it to write the next three numbers

Course Numbers and Patterns Check It Out: Example 1C 2, 6, 18,,,,... A pattern is to multiply each number by 3 to get the next number. 18  3 = 54, 54  3 = 162, 162  3 = 486 So the next numbers will be 54, 162, and 486.  3  3  3  3  3 Identify a possible pattern. Use it to write the next three numbers

Course Numbers and Patterns Identify a possible pattern. Use it to draw the next three figures. Additional Example 2: Identifying and Extending Geometric Patterns The pattern is to rotate the figure in a counterclockwise direction. So the next three figures will be.

Course Numbers and Patterns Check It Out: Example 2 The pattern is three triangular objects that repeat, while alternating between orange and green. So the next three figures will be Identify a possible pattern. Use it to draw the next three figures..

Course Numbers and Patterns Make a table that shows the number of triangles in each figure. Then tell how many triangles are in the seventh figure of the pattern. Use drawings to justify your answer. Additional Example 3: Using Tables to Identify and Extend Patterns Figure 2Figure 3 Figure 4 Figure 5 Figure 1

Course Numbers and Patterns Make a table that shows the number of Triangles in each figure. Then tell how many triangles are in the seventh figure of the pattern. Use drawings to justify your answer. Additional Example 3 Continued The table shows the numbers of triangles in each figure. The pattern is to add 2 triangles each time. Figure Number of Triangles Figure 6 Figure 7 Figure 6 has = 12 triangles Figure 7 has = 14 triangles

Course Numbers and Patterns Make a table that shows the number of squares in each figure. Then tell how many squares are in the seventh figure of the pattern. Use drawings to justify your answer. Check It Out: Additional Example 3 Figure 2Figure 3 Figure 4Figure 5 Figure 1

Course Numbers and Patterns Make a table that shows the number of Squares in each figure. Then tell how many squares are in the seventh figure of the pattern. Use drawings to justify your answer. Check It Out: Example 3 Continued The table shows the numbers of squares in each figure. The pattern is to add 4 squares each time. Figure Number of Triangles Figure 6 has = 24 squares Figure 7 has = 28 squares Figure 6Figure 7

Course Numbers and Patterns Identify a possible pattern. Use the pattern to write next three numbers. Lesson Quiz: Part I 1. –8, –6, –4,,,, … Add 2; -2, 0, 2 2. –3, 6, –12, 24,,,, … Multiply by -2; -48, 96, , 1, 3, 6, 10,,,, … Add 1 more than the number previously added; 15, 21, 28.

Course Numbers and Patterns Identify a possible pattern. Use the pattern to draw the next three figures Make a table that shows the number of dots in the figure. Then tell how many dots are in the seventh figure of the pattern. Use drawings to justify your answer. Lesson Quiz: Part II 14

Course Numbers and Patterns 1-2 Exponents Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

Course Numbers and Patterns Warm Up Simplify · 2 · · 3 · 3 · · 5 · · 4 · · 6 · 6 · 6 · ,776

Course Numbers and Patterns Problem of the Day You intend to place water lilies in the pond in your backyard. A water lily doubles in size every day. From the time you install the first lily until the entire surface of the pond is covered will take 20 days. how long will it take for the pond to be half covered? 19 days

Course Numbers and Patterns Learn to represent numbers by using exponents.

Course Numbers and Patterns Vocabulary power exponent base

Course Numbers and Patterns A DNA molecule makes a copy of itself by splitting in half. Each half becomes a molecule that is identical to the original. The molecules continue to split so that the two become four, the four become eight, and so on. Each time DNA copies itself, the number of molecules doubles. After four copies, the number of molecules is 2 · 2 · 2 · 2 = 16.

Course Numbers and Patterns This multiplication can also be written as a power, using a base and an exponent. The exponent tells how many times to use the base as a factor. Base Exponent Read 2 4 as “the fourth power of 2” or “2 to the fourth power.” Reading Math

Course Numbers and Patterns Find each value. Additional Example 1: Evaluating Powers A = 4 · 4 · 4 · 4 = 256 B = 7 · 7 · 7 = 343 Use 4 as a factor 4 times. Use 7 as a factor 3 times. C = 19Use 19 as a factor 1 time.

Course Numbers and Patterns Check It Out: Example 1 Find each value. A = 3 · 3 · 3 = 27 B = 6 · 6 = 36 Use 3 as a factor 3 times. Use 6 as a factor 2 times. B = 14 Use 14 as a factor 1 time.

Course Numbers and Patterns Any number to the zero power, except zero is equal to = = = 1 Zero to the zero power is undefined, meaning that it does not exist.

Course Numbers and Patterns To express a whole number as a power, write the number as a product of equal factors. Then write the product using the base and an exponent. For example, 10,000 = 10 · 10 · 10 · 10 = 10 4.

Course Numbers and Patterns Write each number using an exponent and the given base. Additional Example 2: Expressing Whole Numbers as Powers A. 625, base = 5 · 5 · 5 · 5 = is used as a factor 4 times. B. 64, base 2 64 = 2 · 2 · 2 · 2 · 2 · 2 = is used as a factor 6 times.

Course Numbers and Patterns Check It Out: Example 2 Write each number as an exponent and the given base. A. 2,401, base 7 2,401 = 7 · 7 · 7 · 7 = is used as a factor 4 times. B. 243, base = 3 · 3 · 3 · 3 · 3 = is used as a factor 5 times.

Course Numbers and Patterns On Monday, Erik tells 3 people a secret. The next day each of them tells 3 more people. If this pattern continues, how many people besides Erik will know the secret on Friday? Additional Example 3: Application On Monday, 3 people know the secret. On Tuesday, 3 times as many people know as those who knew on Monday. On Wednesday, 3 times as many people know as those who knew on Tuesday. On Thursday, 3 times as many people know as those who knew on Wednesday.

Course Numbers and Patterns Additional Example 3 Continued On Friday, 3 times as many people know as those who knew on Thursday. Each day the number of people is 3 times greater. 3 · 3 · 3 · 3 · 3 = 3 5 = 243 On Friday 243 people besides Erik will know the secret.

Course Numbers and Patterns Check It Out: Example 3 In a game, a contestant had a starting score of one point. She doubled her score every turn for four turns. Write her score after four turns as a power. Then find her score. After the first turn, she had 2 points. After the second turn, she would have 4 points. After the third turn, she would have 8 points. After each turn, her point total is 2 times greater. 2 · 2 · 2 · 2 = 2 4 = 16 points

Course Numbers and Patterns Lesson Quiz Find each value Write each number using an exponent and given base , base , base 2 7. Find the volume of a cube if each side is 12 inches long , ,728 in 3