Lesson: Divide by Friends

What are we really doing when we are dividing? Can anyone explain what it actually means to divide? (probably not)

Input                                          
When we divide, we are asking what happens when we take a number and split it into a certain number of equal pieces. THere is an easy way to imagine and draw most division problems. We can imagine that we have a certain amount of money, and that we have to give it to our friends. We have to be equal with our friends or they will fight with us. We need to know how much each friend can have in order to be fair. 

Guided Practice or Coaching + Checking for understanding

 Provide students with division problems written in all four formats. Ask them which number is the money we have, and which is the friends who want money. (This is best done with positive-solution problems until completely mastered.)Students rewrite division problems in algebraic form (10 over 2.etc)

Second input:
When problems are rewritten, explain that the top number is the money we have and the bottom is our friends who want money. Students translate problems into sentences as such. 

Explain that you have to give away all your money and everybody has to get the same amount. Everybody gets first before anybody gets second. Represent the friends with circles and the increments of money with numbers inside the circles. Students practice with simple, single-digit problems. 

Subsequent days: 
Challenge students with larger numbers and use guided practice to encourage them to distribute money in different denominations. (For 100/5, students could "pass out" 10s or 20s rather than 1s or 5s).

Introduce the idea of dividing with remainders. Help students drill on the simple procedure that when we can not give out equal money to each friend, we give as much as we can equally, write that amount as the whole number, and the amount that is left over is the top of the fraction. The bottom of the fraction stays the same as the problem.

(A subsequent unit on equivalent fractions will be needed, but most division students will encounter in the course of Algebra I will be without remainders.)