1. Conceptual Mathematics How does it all work together? Lincoln County Schools Alycen Wilson Math Lead Teacher K-8

2. Addition 25 +43 68 20 + 5 40 + 3 60 + 8 It is important to understand the place value of each digit. The value of 25 is 2 tens and 5 ones. The value of 43 is 4 tens and 3 ones. Tens are added to tens and ones are added to ones.

3. Addition with regrouping 48 +34 82 40 + 8 + 30 + 4 When 8 ones and 4 ones are added together, there are 12 ones. We can decompose 12 and make a new ten out of the 12 ones. The new 10 will be moved to the ten’s place. The two ones will remain in the one’s place. Compose the tens and ones place. 10 + 2 80 + 2 = 82 10 12 2 80 +

4. Subtraction 243 - 122 200 + 40 + 3 100 + 20 + 2 100 + 20 + 1 Each number is decomposed into place values. Subtract each place value Compose the difference = 121

5. Subtraction using regrouping 242 - 127 200 + 40 + 2 100 + 20 + 7 100 + 10 + = 115 Each number is decomposed into place values. There are 2 ones in the first number. Are there enough ones to take away 7 ones? No. Make an equal exchange of one ten into ten ones. Move ten ones into the ones place to create 12 ones. 12 ones is enough to subtract 7 ones. 4 tens-1 ten = 3 tens = 30 10 ones +2 ones = 12 ones 5

6. Multiplication as repeated addition 3 x 7 = 3 x 7 can be seen as 3 groups of 7 7 + 7 + 7 = 21 Or 7 groups of 3 3+3+3+3+3+3+3 = 21 21 is the product, no matter how they are added or multiplied.

7. Area Model of Multiplication 24 x 15 = Decompose each number and represent the value with lines. Multiply each of the area sections. Add each product to determine the final product. Each product represents the area of the square that it is in. Add all of the products together to get the final product of 24 and 15. 20 + 4 10 + 5 20 x 10 = 200 4 x 10 = 40 4 x 5 = 20 20 x 5 = 100 200 + 100 + 40 + 20 = 360

8. Multiplication as Partial Products 24 x 36 Decompose each number in to tens and ones.(As students get comfortable with this method they will begin to do this step in their head.) 20 + 4 x 30 + 6 Multiply by each place value, then add each product. 6 x 4 = 24 6 x 20 = 120 30 x 4 = 120 30 x 20 = 600 864

9. Division as Repeated Subtraction 35 ÷ 7 = Dividing means splitting into equal parts. How many groups of 7 can be made from 35. 35 – 7 = 28 28 – 7 = 21 21 – 7 = 14 14 – 7 = 7 7 – 7 = 0 There are 5 groups of 7 in 35, so 35 ÷ 7 = 5

10. Division as “Giving out” into equal Groups Division can also be worked through the “giving out equal shares” method. 84 ÷ 4 = 84 is given out into 4 equal groups. This can be done in a variety of ways. Counting by 10 is a friendly way to give 84 out. 10 + 1 10 + 1 21 84 is put into 4 equal groups, with 21 in each group. 21

11. Division as partial products. (Box Method) 147 ÷ 6 = 1476 10 - 60 87 6 10 - 60 27 6 4 - 24 3 10 + 4 24 r. 3 There is not enough in the dividend to pull out another group of ten, I was able to use 4. I pulled out 6 groups of 4. I have a remainder of 3. Divide with friendly numbers to make the math easier to manage. I used groups of 10 because I can easily multiply and divide by 10. I subtracted 6 groups of 10 from my total. Always circle the number divided by to total in the end. Move the remaining dividend to a new box and divided by 10 again

12. Division as Partial Products 276 14 10 -140 136 5 - 70 66 4 - 56 10 Add the partial quotients to find the final quotient. 19 r. 10 Subtract 14 groups of ten because 10 is easy for me to calculate. I don’t have enough to subtract another group of ten so I will subtract 5 groups of 14. I know 5 is half of ten so I can calculate that easily. I do not have enough to subtract another group of 5 so I will subtract a group of 4. I have 10 left and that is not enough to subtract another group of 14 so 10 is my remainder