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

Addition It is important to understand the place value of each digit. The values 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.

Addition with regrouping 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. Add the tens place =

Subtraction Each number is decomposed into place values. Subtract each place value Compose the difference = 121

Subtraction using regrouping = 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. Change the form 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. 40 tens-1 ten = 30 tens 10 ones +2 ones = 12 ones 5

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

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 x 10 = x 10 = 40 4 x 5 = x 5 = = 360

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.) x Multiply by each place value, then add each product. 6 x 4 = 24 6 x 20 = x 4 = x 20 =

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

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 is put into 4 equal groups, with 21 in each group. 21

Division as partial products. (Box Method) 147 ÷ 6 = 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