3rd grade math

[Thirdgradermom]

This is my sons problem:
Bella is planning to write in a journal. Some pages will have 1 journal entry on them, and other pages will have 2 journal entry on them. If Bella wants to make 10 entries how many different ways can she write them in her journal?
I'm looking for a formula to show him how to get this answer. Thank you for any help!

 

[stapel]

This is my sons problem:
Bella is planning to write in a journal. Some pages will have 1 journal entry on them, and other pages will have 2 journal entry on them. If Bella wants to make 10 entries how many different ways can she write them in her journal?
I'm looking for a formula to show him how to get this answer. Thank you for any help!

I'm assuming that, being in third grade, your son is not expected to use combinatorial methods. However, that fact does not tell us what method(s) he is expected to use. Kindly please provide that information. Thank you!

 

[soroban]

Hello, Thirdgradermom!

This is my son's problem:

Bella is planning to write in a journal.
Some pages will have 1 journal entry on them,
and other pages will have 2 journal entry on them.
If Bella wants to make 10 entries,
how many different ways can she write them in her journal?

I'm looking for a formula to show him how to get this answer.

A formula?
Can your 8-year-old handle Algebra?


I made an exhaustive list and counted the ways.

\(\displaystyle 2\,2\,2\,2\,2:\;\text{1 way}\)

\(\displaystyle 2\,2\,2\,2\,1\,1:\;{6\choose4,2}= 15\text{ ways}\)

\(\displaystyle 2\,2\,2\,1\,1\,1\,1:\;{7\choose3,4} = 35\text{ ways}\)

\(\displaystyle 2\,2\,1\,1\,1\,1\,1\,1: \;{8\choose2,6} = 28\text{ ways}\)

\(\displaystyle 2\,1\,1\,1\,1\,1\,1\,1\,1:\;{9\choose1,8} = 9\text{ ways}\)

\(\displaystyle 1\,1\,1\,1\,1\,1\,1\,1\,1\,1:\;\text{1 way}\)


Therefore: \(\displaystyle \;1+15+35+28+9+1\:=\:89\text{ ways.}\)