# 3rd Grade - Solve Patterns Using Rules

 Grade Level: 3rd Skill: Problem Solving Topic: Solve Patterns Using Rules Goal: Extend and recognize a linear pattern by its rules (e.g., the number of legs on a given number of horses may be calculated by counting by 4s or by multiplying the number of horses by 4). Skill Description: Algebra and Functions: Linear Patterns The ability to recognize that just as patterns exist in our everyday world they exist in mathematics too and this information can be used to correctly predict how numbers relate to each other.

### Sample Problems

 (1) Why are patterns important? Patterns are everywhere in the world around us. Understanding these patterns helps us understand math. (2) Are all patterns important? No, some patterns are better ignored or else they will confuse us as we look for an answer. (3) Can I glance at a word problem and solve it quickly? Maybe, but it is best to read a word problem all the way through to make sure you know what the problem is asking. (4) Do patterns only use numbers? No, patterns can use shapes, colors, solid objects and many other elements, even sounds. (5) What if I can’t solve a number problem? Try drawing a picture to help understand the patterns in the problem.

### Online Resources

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### Extra Help Problems

 (1) Two wagons. How many wheels altogether? (8) (2) Seven tricycles. How many wheels altogether? (21) (3) A yellow triangle. How many sides? (3 sides) How many angles? (3) (4) One closed box. How many sides on the box? (6: 4 sides, a top and a bottom) (5) Can you skip-count by 4s? Here are the first 4 numbers to get you started and you may stop at 40. 0, 4, 8, 12, ___, ____, ____, ____, _____, _____, 40. 0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40 (6) Can you skip-count by 6s, starting at 0? Stop when you get to 60. (0, 6, 12, 18, 24, 30, 36, 42, 48, 54, 60) (7) Can you skip-count by 9s, starting at 0? Stop when you get to 90. (0, 9, 18, 27, 36, 45, 54, 63, 72, 81, 90) (8) In addition, a “double” is the name for adding two numbers that are alike together. Can you make up 10 “doubles” problems? (Examples: 2+2=4; 3+3=6, 4+4=8, etc.) (9) Most children learn to count by 2s :2, 4, 6, etc. When you count this way are you naming even numbers or odd numbers? (Even) Can you count up to 21 just as quickly by odd numbers? (1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21) (10) One stop sign. How many sides on the polygon? (8) (11) A cookie recipe asks for 1 cup of sugar. How many ounces of sugar is that? (8) (12) What number comes next in this pattern? 0, 3, 6, 9, 12, ___ (15; this is the skip-counting pattern for the threes times-table) (13) What number comes next in this pattern? 1, 1, 2, 2, 3, 3, 4, 4, 5 ___ (5; the pattern is to repeat each number once and then add one (count) and repeat that number before stepping up again.) (14) At Liz’s school each third-grade classroom has 10 poster-paint sets. Each set has one bottle of each primary color and the class makes other colors using the colors in the paint set. How many bottles of paint does each class have altogether? (There are 3 primary colors—red, yellow, and blue. If there are 10 sets then there are 30 bottles altogether.) (15) What is the pattern in this sequence? Red, yellow, blue, blue, green, red, yellow, blue,blue, green, The pattern is made up of the colors red, yellow, blue, and green in that order, but when blue appears in the pattern it always appears twice. (16) What is the pattern in this sequence? What is the next color? Red, yellow, orange, blue, yellow, green, red, blue, ____ (The pattern: two primary colors are named and the next color is the name of the color created when those two are mixed. Then two more colors are named and the next color is again the created color. The final two colors are red and blue—both primary colors, so the next one is purple because when red and blue are mixed the result is purple) (17) My ruler is one foot long. How many inches are there? (18) What is the next number in this pattern? 0, 7, 14, 21, 28 ___ (This pattern is the skip-count pattern for the 7s table; the next number in this pattern is 35.) (19) What are the next three numbers in this pattern? 2, 4, 6, 8, 10, 12, 14 ______, ______ (This is the skip-count pattern for the 2s times-table or it is the pattern for counting by 2s. The next 2 numbers are 16 and 18) (20) What are the next 3 numbers in this pattern? 20, 18, 16, 14, 12, _____, _____, _____ (This is counting by 2s backwards, so the next 3 numbers are 10, 8, 6.) (21) Lyle’s teacher always says, “All eyes on me!” when she is ready to talk to her class. There are 20 children in Lyles’s class. If everyone follows this direction, how many eyes are looking at the teacher? (40 eyes) How many pairs of eyes are looking at the teacher? (20 pairs) (22) A pound of butter is often sold in a package with 4 sticks of butter, each wrapped separately. How much does each stick weigh? (A pound = 16 ounces. Each stick of butter is 4 ounces.) (23) At the circus we saw a parade of unicycles. If there were 20 unicycle riders, how many wheels did we see in the circus ring? (20; each unicycle has only 1 wheel) (24) A cake recipe calls for 1 tablespoon of vanilla. I only have a teaspoon to measure with. How many teaspoons of vanilla will equal 1 tablespoon? (3) (25) How many yards of cloth does Sue have if she has 6 feet of cloth? (There are 3 feet in one yard. She has 2 yards of cloth.)