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**Helping Children Master the Basic Facts**

Addition

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Fall Open House Juan brought 2 pumpkins and Ingrid brought 4 pumpkins to the Fall open house at their school. How many pumpkins do they have together?

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**MENTAL MATH How would you solve this problem?**

Think about what strategies you used to solve this problem without counting on your fingers. Be prepared to share your thinking.

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Solve and Discuss Turn to a partner and discuss your answer and the strategies you used to solve the problem Be prepared to share your strategies with the class!

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Strategies Be sure to jot these down so that you will have them for future reference!

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**Addition Strategies One-More-Than and Two-More-Than Facts. + 1 2 3 4 5**

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Yardstick Activity Partner up; partner B take a yardstick and a disc marker. Partner A will call out a number and partner B will say what 1+ the number would be and what 2+ the number would be. If partner B gets stuck use the yardstick and number marker for help.

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Facts with Zero Zero is my Hero

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Doubles 0+0=0 1+1=2 2+2=4 3+3=6 4+4=8 5+5=10

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Near Doubles = 6 3+4= (3+3) +1=7 or (4+4) -1=7 +

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**Would this be a useful strategy for**

Make 10 Facts This strategy involves adding up to 10 and using it as a marker to finish the problem. 9+6= (9+1)=10+(6-1)=15 Would this be a useful strategy for 6+5 Why or Why not?

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**Other Strategies Doubles Plus 2 or 2 apart**

5+7=12 (5+5=10+2) or double the middle number 6+6=12 Make-10 Extended 8+3=11 (8+2=10+1=11) Counting On 6+3=9 (6+1=7+1=8+1=9) or 7,8,9 10 Frame Facts

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10 Frame Activity NIFTY NINES / EXCELLENT EIGHTS / FANTASTIC FIVES Played like Terrific Tens except that each player removes a “9”, “8” or “5” card from the deck to use as an addend for each face off. Then each player turns over a 10 frame and adds this number to the 9,8,or 5. The child with the highest number keeps the card. This is an excellent way for children to practice addition facts using a visual model. Encourage your child to use thinking and visual strategies rather than counting strategies. Have her explain how she knows her answer. For example, for a child might say “The eight has two empty spaces, so two of the dots from the four could slide over and fill up the ten and then it would be which is 12.” (Cheval, 2004)

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**Helping Children Master the Basic Facts**

Subtraction

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Fall Open House Juan brought 2 pumpkins and Ingrid brought 4 pumpkins to the Fall open house at their school. How many pumpkins do they have together?

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Pumpkin Pies Their teacher, Ms. Ricardo, decided to use three pumpkins to make pumpkin pies for the class. If she took away three pumpkins, how many of Juan and Ingrid’s pumpkins are left?

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**THINK!!!! How would you solve this?**

Think about the strategies you used to solve the problem without counting on your fingers. Write these down. Be prepared to share your thinking.

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Solve and Discuss Turn to a partner and discuss your answer and the strategies you used to solve the problem Be prepared to share your strategies with the class!

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Strategies Be sure to jot these down so that you will have them for future reference!

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Old School Teach your kids different methods of subtraction instead of JUST the old, “count-count-count method!” Ex: 13-5 - Count 13, count off 5, count what’s left. This is boring. ZZZZzzzzzzzz…..

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**Subtraction as Think-Addition**

In this strategy, children are encouraged to think, “What goes with this part to make the total?” Students use addition facts to produce the unknown quantity or part. Think addition problems sound like addition but have a missing addend. Walle, Teaching Student Centered Mathematics (K-3) Pages

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**Example 1 Think-Addition Word Problem**

Juan brought two pumpkins to the Fall open house. Ingrid brought pumpkins too. Together, they had six pumpkins. How many pumpkins did Ingrid bring? 2 + ? = 6??????? … = 6! 6-4=2!! Ingrid brought 4 pumpkins!!!!

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**Tips for Think-Addition**

Children need to have mastered numbers 1 through 10 before moving on to higher numbers. Some students will struggle with this strategy. Work with them.

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**Subtraction Facts with Sums to 10**

Before children can master subtraction facts, they will need to know the accompanying addition facts. Before students can learn 6-2? They need to know that 4+2=6. Explore and assess your students’ number concepts to find out what they do and do not understand. An assessment idea is found on page of the K-3 Volume.

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**The 36 “Hard” Subtraction Facts: Sums Greater Than 10**

Look at these problems. Take a couple of minutes to solve them. Use any strategy you can think of to solve them. When you’ve finished turned to another person who is done and discuss your strategies. Be prepared to share them with the class.

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Build Up Through 10 “This group includes all facts where the part or subtracted number is either 8 or 9.” Examples: 13-9 15-8 “For 14-9, it is easy to start with 9 and work up through 10: 9 and 1 more is 10, and 4 more makes 5.” Page 108

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Back Down Through 10 This strategy more “take-away” than think-addition. This is helpful when the ones digit of the first number is close to the one being subtracted. “For example, with 15-6, you start with the total of 15 and take off 5. That gets you down to 10. Then take off 1 more to get 9. For 14-6, just take off 4 and then take off 2 more to get 8.” Page 109

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**Extending Think-Addition**

Think-Addition can be used for many, if not all subtraction problems. It should not be limited to these 36 problems.

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**Activity 1: Lady Bug Subtraction**

Use counters to solve the problem When you are done, quietly talk with a neighbor about your answer. When your whole table is done raise your hands. Materials needed: Counters, computer (s) Address:

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**Activity 2: Building Up & Down with Ten Frames**

Take out 2 sheets of paper and draw a ten-frame on each sheet like the one drawn on the board. Use your counters to help you solve the problems. You may work with a partner, but each person needs to work with their own counters.

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**Building Up Let’s start with 8. How much do we need to get to 10? 2**

How much MORE to 14? 4 So 14 take away 8 is...? 6!!!! Good job!

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**Building Up Let’s Start with 9 this time. How many more to get to 10?**

5 So 15 take away 9 is…??? 6!!!!

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**Back Down Let’s start with 16 How could we take off 7 counters?**

What happen if we take off 6 counters? How many are left? What if we take off 1 more counter? How many counters have we taken off? So what do you think 16 take away 7 is? 9! Good job!

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**Reflection What strategies did you like best? Least?**

What are the benefits of knowing these strategies? Is it still ok to know the “old school” way? Any further comments on subtraction?

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**Helping Children Master the Basic Facts**

Multiplication

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Fall Open House Ingrid brought 8 pumpkins to the Fall open house at their school. Juan brought 4 times more pumpkins than Ingrid. How many pumpkins did Juan bring?

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**THINK!!!! How would you solve this?**

Think of a few strategies you could use to solve the problem without counting on your fingers. Write these down. Be prepared to share your reasoning. Is it possible to solve without a working knowledge of addition?

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Solve and Discuss Turn to a partner and discuss your answer and the strategies you used to solve the problem Be prepared to share your strategies with the class!

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Strategies Be sure to jot these down so that you will have them for future reference!

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**Multiplication Concepts**

Factor x Factor= Product ex: 8 x 4= 32 8 and 4 are factors of the product 32 Commutative property: 8 x 4 = 4 x 8 Practical use in area models.

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**Multiplication as Repeated Addition**

The basic idea of multiplication is repeated addition For example: 8 × 4 = = 32 But as well as multiplying by whole numbers, you can also multiply by fractions or decimals. For example 8 × 3½ = (half of 8) = 28

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**Multiplication Strategies**

Zeros and Ones- be clear in distinguishing the multiplication rule from the addition does not equal 8 x 1. In other words if: a) Juan had 8 apples and Ingrid gave him 1 of hers is not the same number as; b) each bag contains 8 apples, Juan bought one bag- how apples does Juan have? The same is true with zero.

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Doubles Building on the students awareness of addition doubles, we show the fact in a multiplication format. 8+8= 16 is the same as 2 x 8 or 8 x 2.

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Five Facts When at least one factor is 5. Essentially counting by fives. On pp88-89 of 3-5 book there is an activity correlating these facts to the minute hand of a clock 1-9.

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Nifty Nines Time to see who read. Discovery activity (found on p90 of 3-5 book). Write out a nines table, and look for patterns.

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Nifty Nines In the product, the digit in the 10s place is always 1 less than the “other” factor (the one other than 9). 9 X 8 = is one less than 8 The digits in the product add up to = 9 Can also be looked at as 10 times the other factor minus the other factor- or 10 x 8= 80 80 – 8= 72

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“Helping” Facts In the event that a student is a wiz at addition, but is having difficulty with multiplication concepts; or you’d like to dig deeper into multiplication concepts, there are a few more strategies.

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“Helping” Facts- 4s 4s can be looked at as double and double again. 4 x 8= (8 x 2) + (8 x 2) or 16+16= 32

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“Helping” Facts- 3s 3s can be looked at as doubles plus 1 more set. 8 x 3= (8 x 2) + 8= 24

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**“Helping” Facts- either factor is even**

If either factor is even then you can half that number than double the answer. 7 x 8 = (7 x 4) + (7 x 4)= 28+28=56

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**“Helping” Facts- Get close than add one more set**

8 x 6? I know 8 x 5= 40 plus one more set of 8 equals 48.

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**Using Music and Rhyming**

A more fun way to memorize, but it is still memorizing. 7 x 8 = 56 Five - six - seven - eight, Fifty-six is seven times eight. 8 x 8 = 64 Eight times eight is sixty-four, close your mouth and shut the door!

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**Helping Children Master the Basic Facts**

Division

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Fall Open House A local farm donated 32 pumpkins to the elementary school. There are 4 classrooms in the school. How many pumpkins would each classroom get if they were handed out evenly?

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Solve and Discuss Turn to a partner and discuss your answer and the strategies you used to solve the problem Be prepared to share your strategies with the class!

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Division Strategies Thought of as a missing factor. 4 times what equals 32? Understanding multiplication facts goes hand in hand with division proficiency.

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Division Strategies Estimation and near facts- getting students in the habit of finding the closest missing factor allowing for a remainder less than the known factor. Activity 3.10 p93 in 3-5 book.

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Sources Van de Walle, John, & Lovin, LouAnn. (2006). Teaching Student-Centered Mathematics Volumes 1 & 2. Boston,MA: Pearson. BBC. The Little Animals Learning Activity Learning Center <http://www.bbc.co.uk/schools/laac/numbers/ch2.shtml>. Cheval, Kathy. (2004). Activities that Build Number Sense. Retrieved from Adetula, L. (1996). Effects of Counting and Thinking Strategies in Teaching Addition and Subtraction Problems. Educational Research, 38(2), Retrieved from ERIC database. (2009). Rhyming to teach times tables. Kimstem publishing. [Online]. Available: [October 2, 2010]

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