# Cupcakes of Good Measure: Another look into Counting, Division, and Fractions.

The kids are getting older to the point of doing more things to help out in the kitchen.  This has given them a sense of empowerment and joy in cooking and baking.  For this baking experience, one needed to distribute 24 baking cups into the cupcake baking tins. This task was for my little one to do, to give her a chance to practice on her counting.  The other child was given the responsibility of measuring the ingredients and placing them in the bowl.  Then there was mixing and distributing the mixture into the cupcake holders, my other child. 🙂

When it was time to distribute the mixture into the cupcake holders, we needed to talk about how much to fill the holder.  If it was filled to the top, the cupcake would overflow when baking.  If filled to little, then it might over baker, or burn.  So we decided to fill it up about halfway.  That worked. 🙂 We also filled some a third of the way and that worked as well, but we needed to keep an eye on them to prevent over baking.

After putting everything into the oven, waiting for them to bake, and letting them cool, it was time to decorate.  Each child was able to decorate given the icing, sprinkles, and their own different piping tips with icing bags to use too! Before they were able to begin decorating, they needed to figure out how many cupcakes each would have equally if there are 24 to distribute.  To help my little one figure it out, the two older ones distributed one cupcake at a time to each other until there were no more to distribute.  So the result was that each have 8 cupcakes to decorate any way they wanted.  We did this outside to make clean up easier.  🙂 It was a good day!

Giving each child a task to do for a single project, like baking, gives them an opportunity to contribute.  The task does not need to be daunting, or feel like they are in a lecture about Mathematics.  When you cook, bake, or do a project together, point out the math they are doing and ask them if they were having fun doing it!  For a bit of advice, do no more than pointing out three to four things they are doing in math.  For kids, they want to experience things too. 🙂

In baking, I point out the importance of following the directions because it is an exact science.  Baking, in my opinion, does not have many allowances to veer off the path because you are working in an area of chemistry.  There are substitutions, but you need to research those substitutions, or you may get goop or a something as hard as a rock for your result.

The ingredients, whether dry, or wet, need to be added a certain way in order to react properly.  Over mixing can cause too much air to be added to the batter and may not come out right in the oven.  There is a difference between baking powder and baking soda, but both are chemical agents to help the batter to rise.

There also is working with expansion when heat, from the oven, is applied to the mixture.  That is why it is so important to talk to the children about how much mixture should be put into the cupcake holder.  Describe how much batter should be added by using what fraction of the cupcake holder should be filled.

Baking might be looked at such a trivial task to do and not so complicated, but it is really a great math and science project talking about how each ingredient plays an important part.  As always, enjoy what you are doing so that the children enjoy also.  The more experiences we are given in working with mathematics, the less intimidating it will become in the future.  My goal is to create a space where mathematics is not for the chosen few to understand, but to make it accessible for all to be successful in because it is that important and beautiful!  :). Enjoy!

This particular batch of cookies are shortbread cookies and the filling is from using the last bit of jams that we had in the our kitchen. 🙂

The weather is finally getting cooler and we can begin using the oven for baking!  Baking is a great time to learn about mathematics!  The best part of it is making arrays with the cookies.   An array is an arrangement of objects, pictures, or numbers in columns and rows.  An array is especially easy to make when we place the cookie dough onto the cookie sheet.  The reason for me even doing this is because I am working with my oldest son on how to think about multiplication in several different ways.  One way to think about multiplication is by making arrays of columns by rows to find the total product.  The most important part of multiplication, for me, is also learning how to apply the multiplication to everyday things in his life.

Before baking the cookies, the instructions on the box/recipe will tell you how many cookies the mixture will make.  Ask the question out loud about how many dollops of cookie dough can fit onto one oven sheet.  For this particular batch, we were able to make 30 cookies.

After the cookies are baked, the next question I ask my oldest is how many rows do we have on the cookie and how many columns.  For this particular one, we have six columns and five rows.  How many cookies do we can by multiplying 6 and 5?  To get this answer he can count out the total cookies that are on the cookie sheet, or have a chance to figure it out in a different way.

Here comes another situation with having more than one child in the family, how to distribute/divide the cookies equally?  We have three kids in our household who have three different tastes.  One would like to have strawberry jam as a filling.  The second child does not like anything on the cookie.  The third child likes apple butter as a filling.  The conversation is now about division and distribution.  The kids then need to decide how many cookies each of them will have and if it needs to be the same number of cookies.  They need to figure out how to divide thirty cookies by three kids equally.  So they did!  The results are the pictures below. 🙂

With your child, you may want to do fewer columns and rows. You can point out small arrays within the bigger array of cookies.  For example, you can make ask how many cookies are in a 2 by 3 array.  How about a 3 by 3 array?  Look at the shapes of these arrays too!  When you make a 2 by 3 array, is this a rectangle, or a square?  When you make a 3 by 3 array, is this a rectangle, or a square?  The answer is that a 3 by 3 array will make a square and visually will make the square number of 9!  Check out a 4 by 4 array on the cookie sheet, is this also a square?  So is 16 a square number, which is 4 multiplied by 4?  How cool is that!

In any case, make this a fun and tasty mathematical exploration.  Always remember that this is not only a time to learn about math, but a time to get together and make something of love! Enjoy!

# Picking Summer Squash: Learning that Sharing is Caring and So Is Division

The summer of 2015 was the first time we planted a garden as a family. Of course we talked about how long it takes to start growing vegetables from seed and even read a bedtime story about it. ( Planting and Time ). It was still a long wait for them, but it was worth it. Even through our scorching desert heat, the summer squash grew.

It was time to pick and eat the squash and, yes, there was a math problem here. What if there are three kids and six squash? How many will each of them get, if each person gets the same number of squash?  – That was the question I asked my two older kids.

The boys were able to use the squash, fingers, and whatever else it took to figure this out. They took a few moments and they figured it out.  We have done something similar while grocery shopping for lettuce(Lettuce Division ). But what if they needed more help?

If they needed help with how to start, I would have taken three squash and handed one to each of the three. I would then ask them how they would share the rest amongst themselves. This was basically, in just a few moments, their math problem at home.

What math concepts are learned for 3-5 years of age?

1. Division
2. Numbers (counting)
3. Problem Solving
4. Quantity

What if we had twelve squash to share amongst the three kids? Now, what if we have sixteen squash to share amongst three? What do we do with the extra? These are questions that we can also ask, depending on when the children are ready to explore.  But was is really important here, is that the kids were solving a problem in context, or in the real world.

Funny how we all want to understand how to use math in the real world. That is why I post ideas for you to try with yourself, or with your children. 🙂 Remember, math is everywhere, including the garden.

copyright 2015 learning math with mom

# Tortoises, Greens, and Grocery Shopping. Division is There Somewhere!

We are guardians of tortoises during Spring and Summer. They love their greens, which means frequent trips for lettuce and greens. Each time we go to buy lettuce at the grocery, I know there must be a division problem somewhere. I then grab three bags and ask, “If we need six lettuce and I have three bags, how many heads of lettuce do we put in each bag?”

The boys think it over and for the first time, they needed help. So I tell them that each bag needs to have the same number of heads of lettuce. I give them time to think. Then I grab two heads of lettuce and place it on one bag. “Now tell me what to do next?” The boys get it that we need to put two heads of lettuce in each of three bags. Great! We move on.

The next few times, I do not need to give hints because they go and put the lettuce in the bags automatically. Sometimes we need four, sometimes we need six, and sometimes we need eight. Then the number of bags changes and so does the number in each bag. This takes five minutes at the maximum and we continue on. Division in context 🙂

Where is this in the math concepts for ages 3-5 years?