super strategies for addition super strategies for addition · lesson plan: the moving counter what...

Super Strategies

for Addition

Super

Strategies for Addition

Copyright © 2019 St. Jude Children’s Research Hospital. All rights reserved.

Dear Teacher,One of the biggest goals for elementary teachers (and parents) is for students to develop fluency in the 100 Basic Addition Facts. This is, in large part, a memorization process for most students, but to help build understanding, number sense, and a support system, it is a good idea to teach students helpful addition strategies. This is particularly helpful as students begin to learn the facts and for anyone who struggles with memorization.

On the front of this poster, we have seven addition fact strategies with examples for students. Below are short, simple lesson plans you can use that feature hands-on activities to help your students understand,

apply, and practice these useful strategies.

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STANDARDS: CCSS for Mathematics 1.OA.6

Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

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Add anything to 0 or add 0 to anything, and the other

addend stays the same. 0 + 9 = 9 and 9 + 0 = 9

Zero

Herothe


FACT STRATEGY:

Zero the Hero (aka: The Identity Property or Zero Property of Addition)

Adding anything to 0 or adding 0 to anything leaves the other addend unchanged. 0 + 4 = 4 and 4 + 0 = 4. (This actually covers 19 of the 100 basic facts.)

LESSON PLAN:

Empty-HandedWHAT YOU NEED: • Small manipulatives such as marbles, paper clips, or buttons• Paper and pencil

WHAT TO DO:Explain to students that you are going to demonstrate some math facts and you would like them to write the facts down. Reach into your set of marbles, pull out three, and close your hand. Reach into your set of marbles again, this time with your other hand, do not pull out any, but close your hand. Display your closed hands in front of the class. Open your hand with the three marbles and ask students to write what they see (3). Now open your other hand and ask students to write what they see. (0) Ask students to write the complete addition fact that they see (3 + 0 = 3). Discuss how “when adding zero” to another number, the first number does not increase or decrease. Demonstrate this several times, sometimes having zero as your first selection and sometimes as your second selection.

Now give students a set of small manipulatives and ask them to try the same thing and write down as many +0 facts as they can find.


EasyDoubles

Doubles facts are the easiest to remember. They go up by 2 each time.


FACT STRATEGY:

Easy Doubles The nine Doubles facts are perhaps the easiest to memorize. Children will happily recite 1 + 1 = 2, 2 + 2 = 4, 3 + 3 = 6, 4 + 4 = 8, etc. Challenge students to observe the pattern of the sum increasing by two each time.

LESSON PLAN:

Mirror, MirrorWHAT YOU NEED: • Drawing paper• Crayons or markers

WHAT TO DO:Give each student a piece of drawing paper. Have them fold it down the middle and draw a line down the fold. Ask students to imagine that the piece of paper is a mirror, with one side reflecting the other: anything drawn on one side of the fold will be drawn on the other side of the fold. Demonstrate by making one color dot on one side of the fold. Now on the other side of the fold, draw one color dot. Ask students what math fact would match that picture (1 + 1 = 2). Demonstrate again by drawing two color dots on one side and two more on the other side. Ask again what math fact would match the picture (2 + 2 = 4). Explain that these special math facts are called Doubles because the first number is doubled. Give students the materials and ask them to use the Mirror idea to create as many Doubles pictures as they can and to write an addition fact that goes with each.

Don’t forget to have a picture for 0 + 0 = 0! Also, ask students to see if they can find a pattern with the sums that result: 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20. (The sums increase by two each time. This is handy to know in case students forget a Doubles fact. They can always go back one fact and just add two to the sum. For example, if I can’t remember 7 + 7, but I do remember 6 + 6 = 12, I know that 7 + 7 is just two more than 12, or 14!)


Knowing Easy Doubles helps us know other facts that are near them.

If I see 5 + 6, I think about what Easy Double could be a part of it.

NearDoubles


FACT STRATEGY:

Near Doubles Knowing Doubles helps us figure out a lot of other facts. For example, if I encounter 5 + 6, I think about what Doubles fact might be a part of it. I know 5 + 5 = 10, so 5 + 6 must be one more, or 11. If I see 6 + 7, and I know the Double 6 + 6 = 12, I know one more makes it 13. This strategy can be used with 18 basic facts, including many children find difficult.

LESSON PLAN:

Tower PowerWHAT YOU NEED:• Set of cubes or blocks• Paper and pencil

WHAT TO DO:Build a tower of two cubes or blocks. Build an identical one right next to it. Ask students to tell you what addition fact matches the model (2 + 2 = 4). Ask what kind of addition fact that is (a Doubles fact). Now tell the class that the second tower needs one more floor. Add one more cube. Ask students what addition fact the tower shows now (2 + 3 = 5). Repeat with two towers of three cubes. Ask students what addition fact matches the model and what type of fact it is. (3 + 3 = 6, a Doubles fact). Now add the top floor to the second tower. Ask what the new fact is (3 + 4 = 7).

Ask students what they notice about these facts. (When we add one to a Doubles fact, the sum is one more than “the Doubles fact sum.”) Explain that if we encounter a fact, like 3 + 4, and we are unsure of the sum, if we recognize a Doubles fact within it (like 3 + 3 = 6), we will know that adding one will help us get the answer (like 3 + 4 is only one more than 3 + 3, or 7)!

Give students blocks or cubes, paper, and pencils. Ask them to create doubles towers, write the fact, then add a top floor and write the resulting Near Doubles facts.


When we add 1, or 2, or 3 to another addend,

we can just count up. So 8 + 1 = 9, because if I count up from 8,

one more is 9.

CountingUp


FACT STRATEGY:

Counting UpAnytime we are adding 1, 2, or 3 to another addend, a quick strategy is to just count up. So 5 + 1 is 6 because if I count up from 5, one more is 6. This is easy to do with + 2 as well. 5 + 2 is 5, 6, 7! Some teachers will take this strategy as far as +3, anything higher, and it just takes too long.

LESSON PLAN:

Spin to WinWHAT YOU NEED:• Spin to Win spinner• Paper clip, dice• 0–20 number line• Penny or button to mark position on number line• Paper and pencil

WHAT TO DO:Make a simple Spin to Win spinner like the one in the picture here.

Give, or have each student draw, a simple 0–20 number line, a Spin to Win spinner, a button or penny to mark their position on the number line, and a pair of dice to roll. Players begin by rolling one die. This is their first addend. They write this number down. They then spin the spinner. The paper clip will either point to + 1, + 2, or + 3. This is the second addend. The player writes this down to complete a number sentence. For example, if I roll a 5 and then spin a + 3, my addition fact is 5 + 3. While looking at the number line, the student should mentally count up, write the sum down, and then check their work by moving their button or penny on the number line the appropriate number of spaces.

Students repeat this procedure, trying to find as many different addition facts as they are able. Then allow students to use both dice to create the first addend. Have students try to mentally move up the number line after they spin but before checking with their button or penny. The first person to get ten different facts correct wins.


If we have a fact with 9 as an addend, take away one

from the other addend and add it to the 9.

NiftyNines


FACT STRATEGY:

Nifty NinesNines facts can be difficult for students. This strategy helps retrieve Nines facts or check them. When you have a 9 as one addend, take one away from the second addend and add it to the 9 to make a 10. Adding on from 10 is always easy. So, if you have 9 + 8, take one from 8 to get 7. Add the one to the 9 to make 10. Now you have 10 + 7, which equals 17. Super easy!

LESSON PLAN:

The Moving CounterWHAT YOU NEED:• Any kind of small counters• Tens frame for each student• Paper and pencil

WHAT TO DO:Provide each student with a tens frame, 20 counters, paper, and a pencil. Explain that you will be focusing on addition facts with nines. Start with 9 + 5 as an example. Put nine counters in the tens frame with the last square of the bottom row empty. Put five counters in a row outside the tens frame, lined up with the bottom row of the tens frame. Say, “I have nine counters in the tens frame and five outside the tens frame. This is a model of the problem 9 + 5.” Write 9 + 5 near your model. Continue, “Now, I am going to move one counter from outside into the tens frame. How many counters are in the tens frame now (10)? How many are outside the tens frame (4)?” Ask, “What is our new problem shown here (10 + 4)? Write the new problem you see. What does it equal (14)?”

Model a few nines problems together with students as they move their counters and record the two facts that result. Explain to students, “We can model this with counters, but we can also do it easily in our heads. If you have an addend that is a 9, just take one away from your second addend and make the 9 a 10. Now add the two addends just like you did with your tens frame.” Have students practice doing a few mentally.


You can use your fingers to check all of the facts that add up to 10.

MakeTen

For example, 7 + 3 = 10.


FACT STRATEGY:

Make TenMake Ten facts are very “handy.” We can use our hands to check. These are all the facts that add up to 10. For example, 8 + 2 = 10 and 4 + 6 = 10. If we put the number of fingers down on the first addend (say 8), the number of fingers still up (2) is the second addend.

LESSON PLAN:

I Was (Ten) FramedWHAT YOU NEED:• Tens frame for each student• 10 cubes or counters• Paper and pencil

WHAT TO DO:Give or have each student draw a tens frame, which is just two rows of five boxes, one row on top of the other. Provide 10 cubes or counters for each student. Demonstrate by placing two cubes in the first two spaces on a tens frame. Ask students how many spaces are filled (2). Ask students how many spaces are not filled (8). Ask students how many spaces there are all together (10). Ask students to write an addition fact that matches the model (2 + 8 = 10). Tell students to use their tens frames to find all of the different ways to make a sum of 10 using two addends. Remind them to make sure they get all of the Turnaround facts and the Zero facts as well.


Turnaround Facts

If I know 4 + 3 = 7, then I also know

that 3 + 4 = 7. Any two addends added

together always equal that same sum,

no matter what order they are in.


FACT STRATEGY:

Turn-around FactsThis addition fact strategy is also a property of addition, the Commutative or Order Property. If I know 4 + 3 = 7, I also know that 3 + 4 = 7. If a student encounters 3 + 4 and doesn’t automatically know it, they can flip it and see if they know the answer 4 + 3. They will find that it is usually easier to have a larger first addend. This makes counting up simpler.

LESSON PLAN:

Turnaround TrainsWHAT YOU NEED: • Linking cubes of two different colors• Paper and pencil

WHAT TO DO: Give each student a set of 20 linking cubes, 10 of one color and 10 of another. Next, create a train of four cubes, with three cubes of one color at the beginning of the train and one cube of the other color at the end. Ask students to write a math fact that matches the cube train you have made (3 + 1 = 4). Now, rearrange the train so students see the one cube that was at the end first. Ask students to write the fact they see now (1 + 3 = 4). Explain how these are called Turnaround facts. The order of the addends doesn’t matter; the sum will be the same. Have students use their cubes to write as many Turnaround facts as they can. This example of an addition fact strategy is also a property of addition, the Commutative or Order Property. If a student encounters 3 + 4 and doesn’t automatically know it, they can flip it and see if they know 4 + 3. They will find that it is usually easier to have a larger first addend. This makes counting up simpler.


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