3rd Grade - Solve Patterns Using Rules

Problem Solving
Solve Patterns Using Rules
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).
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


Why are patterns important? Patterns are everywhere in the world around us. Understanding these patterns helps us understand math.


Are all patterns important? No, some patterns are better ignored or else they will confuse us as we look for an answer.


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.


Do patterns only use numbers? No, patterns can use shapes, colors, solid objects and many other elements, even sounds.


What if I can’t solve a number problem? Try drawing a picture to help understand the patterns in the problem.

Learning Tips


Patterns are all around us and we often assume that our children are as aware of them as we are. Your child needs to be aware of many common patterns because knowledge of them is often assumed in mathematical word problems. Many patterns are familiar to your child, but he/she may not have thought about using information that is not specifically named. Ask your child, “If you were visiting a riding stable where horses were getting new shoes, and the owner asked you to bring over enough horseshoes for the next two horses, how many would you bring? (8; each horse will need 4) Listen to your child’s reasoning on how to solve such a problem. Help him/her think through where information that is not explicitly mentioned might come from.


There are instances where patterns can be, indeed, must be, ignored. Consider the horseshoe problem mentioned above. We read that there were two horses in need of new shoes, but suppose this statement was added to the problem: “The two horses are 3 years old and one of them is brown.” What would your child do with these extra numbers? The 3 is very obvious in the problem, and some children will recognize the word “one” as another number. But in this case, these numbers have nothing to do with the problem. They do not fit into any pattern that is essential to the calculations that are required. How can you help your child to recognize patterns that are needed to solve the problem and facts which are just there to distract or to add an interesting story to the problem?


Encourage your child to read all of a word problem before beginning to solve it. After he/she is sure that what the problem is asking for is understood, he can look for patterns that are necessary. For example, a problem that expresses its details in inches but then asks for the answer in feet will require an extra step to finish it, as well as the knowledge of how many inches are in a foot.


Sometimes we are asked to complete a number pattern that is already been started. This skill measures the student’s ability to analyze what rule(s) was/were followed to develop the pattern. Strategies you can suggest to your child: Look at the numbers from left to right. Do you recognize them as a skip-count that perhaps you’ve done in the past? If so, the next number will be the next number in that pattern. (Skip-counting is the same as saying the “answers” in a multiplication table; skip-counting by 3s begins 3, 6, 9, etc. Skip-count patterns are very common in third-grade math problems because these children are still learning their multiplication tables and there is much emphasis on different ways of accomplishing that.)

Are the numbers decreasing in value? If so, perhaps it is a skip-count in reverse. Look at the number sequence to see if there always the same difference between two adjoining numbers. If so, could the rule that formed the pattern be to “add the same number each time to the number that came before it”? Devise some patterns that use the math facts your child has been learning and see if he/she can solve the pattern mystery.


If number patterns are difficult for your child, try to approach the concepts above through the use of symbolic learning. If your child finds sequential number patterns challenging, start with patterns that involve color and/or shapes of graphic elements. Once a child sees how those patterns are formed, the bridge to number patterns may be more obvious to him/her. Another form of symbolic learning is to encourage your child to sketch the details in the problem. In the horseshoe problem above, where the pattern detail that had to be recalled in order to solve the problem was to remember how many legs each horse has, your child would probably realize immediately what information was missing if you asked him to draw the horses that will be getting new shoes. When two horses, each with 4 legs has been sketched, even if the drawing doesn’t look like horses to you, your child will likely see the legs and know what to do. If not, you could ask questions about the drawing until the child sees the connection.

It is also possible that problems such as these are challenging for your child because he lacks basic experience with numbers. If this seems the case, try to find more opportunities for your child to use numbers in daily living. Let him group your produce at the store in an attempt to figure out how best to choose the number of needed items and bag them. Let her count out the pieces of silverware needed to set the table and teach the skill of picking up the items in twos, counting 2, 4, 6 . . . and then challenge your child to pick up 3 at a time of items and count by 3s for a change. Give your child 10 pennies and encourage him to arrange them in as many designs as possible, noting the design with X’s on a piece of paper to make sure that each design is unique and not a repeat of an idea previously used. Work on the basic math facts with your child, if that seems to be a stumbling block, so that your child has the basic knowledge to allow the brain to concentrate on the challenging, or new, skills needed to complete a new style of problem. There are, it seems, children for whom “number sense” is a native skill, but far more children are math-competent because they have had much experience and practice in number manipulation and problem-solving.

Extra Help Problems


Two wagons. How many wheels altogether? (8)


Seven tricycles. How many wheels altogether? (21)


A yellow triangle. How many sides? (3 sides) How many angles? (3)


One closed box. How many sides on the box? (6: 4 sides, a top and a bottom)


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


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)


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)


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.)


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)


One stop sign. How many sides on the polygon? (8)


A cookie recipe asks for 1 cup of sugar. How many ounces of sugar is that? (8)


What number comes next in this pattern?
0, 3, 6, 9, 12, ___ (15; this is the skip-counting pattern for the threes times-table)


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.)


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.)


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.


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)


My ruler is one foot long. How many inches are there?


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.)


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)


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.)


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)


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.)


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)


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)


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.)


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