Name Patterns on the Multiplication Table Essential Question How can you use properties to explain patterns on the multiplication table? Unlock the Problem ALGEBRA Lesson 4.7 Operations and Algebraic Thinking 3.OA.D.9 Also 3.OA.B. MATHEMATICAL PRACTICES MP1, MP3, MP7 You can use a multiplication table to explore number patterns. Activity 1 0 1 0 1 2 3 4 6 7 8 9 10 Materials MathBoard 2 Write the products for the green squares. What do you notice about the products? 3 4 6 7 8 Write the multiplication sentences for the products on your MathBoard. What do you notice about the factors? 9 10 Will this be true in the yellow squares? Explain using a property you know. Write the products for the yellow squares. Complete the columns for 1,, and 6. Look across each row and compare the products. What do you notice? What property does this show? Math Talk MATHEMATICAL PRACTICES 7 Look for a Pattern How can you use patterns on a multiplication chart to find other products? Chapter 4 229
Activity 2 Materials yellow and blue crayons Shade the rows for 0, 2, 4, 6, 8, and 10 yellow. What pattern do you notice about each shaded row? Compare the rows for 2 and 4. What do you notice about the products? Shade the columns for 1, 3,, 7, and 9 blue. What do you notice about the products for each shaded column? 0 1 2 3 4 6 7 8 9 10 0 1 2 3 4 6 7 8 9 10 0 0 0 0 0 0 0 0 0 0 0 0 1 2 3 4 6 7 8 9 10 0 2 4 6 8 10 12 14 16 18 20 0 3 6 9 12 1 18 21 24 27 30 0 4 8 12 16 20 24 28 32 36 40 0 10 1 20 2 30 3 40 4 0 0 6 12 18 24 30 36 42 48 4 60 0 7 14 21 28 3 42 49 6 63 70 0 8 16 24 32 40 48 6 64 72 80 0 9 18 27 36 4 4 63 72 81 90 0 10 20 30 40 0 60 70 80 90 100 Compare the products for the green squares. What do you notice? What do you notice about the factors? What other patterns do you see? Share and Show MATH BOARD 1. Use the table to write the products for the row for 2. _, _, _, _, _, _, _, _, _, _, _ Describe a pattern you see. Is the product even or odd? Write even or odd. Math Talk MATHEMATICAL PRACTICES 1 Analyze What do you notice about the product of any number and 2? 2. 8 _ 3. 6 3 _ 4. 3 _. 4 4 _ 230
Name Use the multiplication table. Describe a pattern you see. 6. in the column for 10 7. in the column for 8 On Your Own Is the product even or odd? Write even or odd. 8. 4 8 _ 9. _ 10. 7 4 _ 11. 2 9 _ 12. DEEPER Correct the pattern. Rewrite your pattern. 6, 12, 18, 22, 30, 36 Complete the table. Then describe a pattern you see in the products. 13. 14. 2 4 6 8 10 1 3 7 9 1. SMARTER Explain how patterns of the ones digits in the products relate to the factors in Exercises 13 and 14. Personal Math Trainer 16. SMARTER Helene selected an odd number to multiply by the factors in this table. Write even or odd to describe each product. 1 2 3 4 odd number Chapter 4 Lesson 7 231
MATHEMATICAL PRACTICES Sense or Nonsense? ANALYZE MATHEMATICAL 17. PRACTICE 3 Make Arguments Whose statement makes sense? Whose statement is nonsense? Explain your reasoning. The product of an odd number and an even number is even. The product of two even numbers is even. Gunter s Work odd even even 3 4 = 12 Giselle s Work even even even 2 6 = 12 I can circle 2 equal groups of 6 with no tiles left over. So, the product is even. I can circle 6 pairs with no tiles left over. So, the product is even. 18. DEEPER Write a statement about the product of two odd numbers. Give an example to show why your statement is true. 232
Name Patterns on the Multiplication Table Is the product even or odd? Write even or odd. Practice and Homework Lesson 4.7 COMMON CORE STANDARD 3.OA.D.9 Solve problems involving the four operations, and identify and explain patterns in arithmetic. 1. 2 7 = even Think: Products with 2 as a factor 2. 4 6 = 3. 8 3 = are even. Use the multiplication table. Describe a pattern you see. 4. in the column for. in the row for 10 6. in the rows for 3 and 6 Problem Solving 7. Carl shades a row in the multiplication table. The products in the row are all even. The ones digits in the products repeat 0, 4, 8, 2, 6. What row does Carl shade? 9. WRITE Math Draw a picture that shows an example of a product of two even numbers. Write the matching multiplication sentence. 8. Jenna says that no row or column contains products with only odd numbers. Do you agree? Explain. Chapter 4 233
Lesson Check (3.OA.D.9) 1. Is the product of 4 9 even or odd? 2. Describe a pattern you see. 10, 1, 20, 2, 30 Spiral Review (3.OA.A.3, 3.OA.B., 3.NBT.A.2, 3.MD.B.3) 3. Lexi has 2 cans of tennis balls. There are 3 tennis balls in each can. She buys 2 more cans. How many tennis balls does she now have? 4. Use the picture graph. Blue Green Brown Color of Eyes Key: Each = 4 students. How many students have green eyes?. Sasha bought 3 boxes of pencils. If each box has 6 pencils, how many pencils did Sasha buy? 234 6. Find the sum. 219 + 763 FOR MORE PRACTICE GO TO THE Personal Math Trainer