Four Square Addition3.Your students will likely be surprised and will wonder if that always works. That’s an invitation to try another one. Try one with four new numbers like the

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OVERVIEW

PROCEDURE

Materials: % paper Optional: & activity master

Skills: • Addition and

subtraction of whole numbers, integers, and decimals

• Finding patterns

Foursquare Addition The commutative property is the foundation of these creative practice problems. Because students are solving each problem two ways, their matching answers allow them to self-assess their work. Vocabulary: commutative property, sum, addend, integer

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1. Write four numbers in the cells of a foursquare box. Add the six and the eight in the top row and write the sum to the right of the row. Repeat this for the two and the five in the second row. Add these two sums on the right and write the answer in the upper right triangle of the lower box as shown.

2. Now add the six and the two in the first column and write the sum in the blank below. Repeat this for the eight and the five in the second column. Add these two sums and write the answer in the lower left triangle of the lower box as shown. Voilá, the answers match!

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3. Your students will likely be surprised and will wonder if that always works. That’s an invitation to try another one. Try one with four new numbers like the sample on the left. Your students will see that it works again.

4. Now try a third problem that uses the same numbers as the previous problem, but in a different arrangement. Not only do the numbers match, but you still get an answer of 36.

5. Ask your students to try to explain this mystery. It may occur to them that each triangle is the sum of the four numbers in the original four squares. This is a good time to introduce the commutative property. This property states that a + b = b + a.

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It stands to reason that this will give the same sum.

6. Design further problems that challenge your students. You may wish to use two-digit numbers, decimals, or integers. Fractions can also be used, but since they are harder, you should assign fewer problems.

7. To introduce subtraction, put some numbers in the blanks and some in the cells like in the example on the right. Students must subtract to work backward and solve the puzzle. In most cases, only four numbers need to be given to solve the puzzle.

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Journal Prompts: ) Why does the same answer always appear in the two triangles?

What effect will switching the three and four have in the problem on the right? Will this always occur? Why or why not?

Homework: *

Assign one of the activity masters included or create your own using a blank master. You may wish to have students make up problems of their own which they write on the board for others to copy onto a blank master.

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12 30

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a+c+b+d

a b

c d

a+b

c+d

b+d a+c a+b+c+d

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48

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480

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Taking a Closer Look:

Algebra students may wonder why these drills always produce matching answers. Substituting variables for the numbers shows that it is simply a matter of using the commutative property.

You may also wish that the students try multiplying the number pairs instead of adding. Since the commutative property also works for multiplication, matching answers will occur. However, multiplying the products in the blanks can be tedious, so assign fewer


Good Tip! + To develop number sense, select number pairs that compliment one another. For example, pick pairs that add to 100, decimals that add to one, or integers that are opposites.

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problems. Oddly, this process also works for subtraction. Assessment: , Since students should get matching answers in the two triangles, these drills are self-assessing for the most part. To be more certain, you may wish to write the answers to each worksheet randomly at the bottom of each page. Students can cross off answers as they find them to verify that they are doing the problems correctly.

Answer Key (The answers in the lower triangles are given.)

Foursquare Addition Worksheet Number 1 2 3 4 5 6 Problem 1 86 -34 6.5 47 31 1.4 2 135 8 1.63 given given given 3 121 -4 5.49 79 42 4.7 4 200 -16 99.99 given given given 5 89 -3 108.99 139 196 6.49 6 183 -21 22.2 given given given 7 163 0 55.09 97 97 3 8 163 0 9.26 given given given 9 145 -12 2.25 64 -10 2.89 10 180 15 7.2 43 26 .26 11 159 0 61.08 72 49 7.39 12 242 -1 9.03 given given given 13 100 13 24.6 given given given 14 258 -23 100.01 given given given 15 209 -63 20 94 -78 9.89


Teaching master Foursquare Addition Add across and write the sums in the blanks on the right. Add down and write the sums in the blanks below. Add the side blanks and write the answer in the top triangle. Add the bottom blanks and write the answer in the lower triangle. What do you notice?


Name______________________________

Foursquare Addition

Find the missing addends to solve each problem as in the example. You will need to work backwards to be successful.

Activity master 1


Name______________________________

Foursquare Addition


Activity master 2


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9 12

Name______________________________

Foursquare Addition 1

Add across as in the example. Then add downward. Add the sums on the right side and write the answer in the upper triangle. Then add the lower sums and right the sum in the lower triangle. Do your answers match? Congratulations!

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Activity master


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Name______________________________



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Name______________________________ Foursquare Addition 3


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Activity master


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Activity master


Name______________________________ Foursquare Addition 6


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Activity master


If you liked this activity, you might also like some of the other character education lessons available in my TeachersPayTeachers store. Simply search for “Brad Fulton”.

You can also find many free and inexpensive resources on my personal website, www.tttpress.com. Be sure to subscribe to receive monthly newsletters, blogs, and activities.

Similar activities include: • Pyramid Math: Developing the Mathematical

Practices • Take Your Places: Activities 1–6 (Covering addition,

subtraction, multiplication, and division of whole numbers, and addition and subtraction of fractions

• Math Maps: Developing the Mathematical Practices • Sum Thing Interesting: Finding Amazing Patterns in

Addition • Array We Go: Building: An Engaging and Visual

Representation of Factors, Multiples, Primes, and Composites, and More

• Developing Number Sense

Feel free to contact me if you have questions or comments or would like to discuss a training or keynote address at your site.

Happy teaching, Brad

Documents

Four Square Addition3.Your students will likely be surprised and will wonder if that always works. That’s an invitation to try another one. Try one with four new numbers like the