# Pizza Creations: Thinking About Ingredients, Combinations, and Sequencing

On the Mountain, it is cool enough to bake in the oven during the Summer months.  This is also a great time to make something together as a family, like pizza.   In our family, we have many different preferences when it comes to toppings.  Some of us like a plain cheese, some of us like pepperoni, and some of us like to put everything on it to jazz it up. This gives our family an opportunity to talk about the different combinations of pizza we can create, if you have a finite number of ingredients.

Let’s say you have cheese, pepperoni, olives, chicken, and tomatoes to choose from for toppings. You can easily make a cheese pizza, or a cheese and pepperoni pizza, or a cheese and pepperoni and olive pizza, or even a cheese and pepperoni and olive and tomato pizza.  How many different varieties can you make?

Thinking about the different varieties, or combinations, you can make is actually preparing the child to think and do the Mathematics.  At this point, you can just ask them to think, estimate, and calculate the number of combinations you can make.  They can draw pictures, or write each combination out.  For this age, I would suggest talking it out and creating some of those combinations with the kids.  What you are giving them is experience in working this out.  Be mindful of how many ingredients you work with though.  Start simple and then add more ingredients to choose from at another time.  Most importantly, have fun!

When making pizza and talking about the number of pizzas you can make, just take about five minutes with your child.  You can take more time if you want, but make it enjoyable, not like a quiz.  There will be a question on whether or not double toppings count as a different pizza.  The question is, by adding double toppings does this create a different tasting pizza?  This is a great question to discuss with the kids!

Keep in mind that you may have a child who can think this all in her/his head.  You may have a child who enjoys drawing out the pictures, or listing the combinations.  You may have the child who wants you to buy lots of pizza dough so that she/he can actually create all those pizzas to find out.  For this child, keep the number of ingredients to three!  We all learn differently and we all must honor the child on her/his learning.

Think about sequencing. What do you do first when making a pizza?  What do you do next? When do you add the cheese, or other toppings? This is another great way to have the little ones work on their sequencing and critical thinking.  Make this experience fun.  The end result is to create a great pizza, memories, and learn about Math!

# 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!

# Critical Thinking and Sledding: How to Get the Most Fun Out of Snow.

On Mount Lemmon, the kids are understanding that there are different stages of snow, or forms of snow.  Lightly dusted snow can melt quickly once the sun comes up.  Snow that has been there for a while can be hard as a rock.  They must waste no time when the snow is just perfect because it might not be like that the next day, or even later in the day.

For this particular day, we were going to check out a favorite area to go sledding.  They had full faith that there was the perfect snow for sledding and they were right!  The rest of the afternoon was filled with pure blissful fun!  However, it was the next morning that would prove to be the challenge.

The next morning, the kids wanted to try sledding again, but there was not any “new” snow. It was the same patch that was used the previous day.  It was also windy the previous night which moved a lot of debris.  As usual, the kids went to the top of the path to sled down and it was a disappointment.  So I began asking them some questions to help in their thinking of what was potentially slowing them down.  Here is a list of things we came up with:

1.  Pinecones, pine needles, and rocks were on the path, which slowed them down.
2. A smoother surface would help them sled down faster
3. The layer of snow was not as thick as the previous day because it was pressed down from yesterday’s sledding and no new snow had fallen.
4. To sled down, someone had to push the person on the sled for a bit to get going, or having mom pull them down worked too!

The kids still had fun and they helped each other out with getting all the debris out of the way, taking turns pushing each other, and tried to lay flat on the snow board sometimes to go faster.  It was their second time sledding and I think they understand how to think critically to get the most fun out of snow.  I also did my own turn in sledding down the incline to show them what I can do to sled faster to see if that would work for them too!  So where is the math in all of this?

In Mathematics, critical thinking is really important.  When you come up with a problem that has a lot of “problems” in it, trying to look at what is keeping you from solving it out is important!  When you can critically look at a situation, without getting upset or feeling frustrated, to see what is slowing you down in solving the problem in the first place, you will become more successful.  It also takes practice.

Since sledding is not intimidating to the kids, it was easier for them to think critically and not give up so quickly.  The more times the kids can do this for things that are “no big deals” to them, the easier it will be to show them how to apply this for any sort of math problem.  It is also important to purposefully tell them that these are the same tools of thinking to apply in any math problem they encounter.

Here are a few questions to ask your child when they are having trouble with solving a math problem:

1. What is the word problem asking you to do?
2. Have you done this type of math problem before? If you have, how did you solve that one? (this is like thinking back to when the snow was perfect for sledding the day before)
3. What is slowing you down? Is there too much information given to you?  What do you really need to solve this problem? (this is like the pinecones and rocks in the path)
4. Would you like me to help you, or have your brother or sister help you? (this is like me showing them how I sled down the incline to show them what could work)
5. What if I showed you how to do a similar problem and then you can see if what I did would help you solve the next one?

In reality, the first time we directly apply critical thinking to a situation may not mean that they will be able to transfer that when working with math problems.  It takes time, practice, and directly referring back to a situation in context.  Be patient, everyone learns differently, and most of all, have fun!  Mathematics really should not be presented as something difficult to learn. It was not made to be that way.  Have fun with it!  Enjoy!

# Pi Day is Today!!!! Let’s Celebrate Another Year of Pi

Today is Pi Day again!  This post you will see each year because it is just that important 🙂  To learn more for yourself about Pi, or for your older children, try http://www.piday.org

What about for our younger children?  We can:

1. Begin experimenting with measuring different circles with a piece of string and then taking that against a ruler to figure out length, which leads to,

2.  Talking about circumference (which is really finding the perimeter of the circle, or length

3. Looking at diameter (the length or distance across the circle),

4. Looking at Radius, which is half the length of a diameter of a circle, and

5. Compare! Get the circumference of any circle you are measuring and divide that by the measurement of its diameter. What number do you get? Get another circle and take its circumference and diameter and compare. What number do you get? How does that compare with the other circle?

6. This item can be either you number one choice to do before choices 1-5, or you can save this best for last. Read story books about Pi! This one is really fun and doesn’t take a whole lot of planning.

Where is this in the schedule of Activities of 3-5?

1. Monday- Reading a Math Story

2. Tuesday- Math under Numbers

http://www.learningmathwithmom.com/sites/default/files/CALENDAR3yearsto5yearsofagePDF_0.pdf

For yourself, search through the internet on Pi.  Go to the library and look for books about Pi and read them for yourself and for your children.  For Pi, it is not just about that one day our of the year to learn about it, it is most importantly about seeing how this relates to the world around you and your children.

The more you and your children can see how you interact and deal with mathematics in everyday life and in nature, the more comfortable you will become in learning mathematics.  Learning about math is for everyone.  Mathematics is not just for the ones who go to college, or because they are a certain gender, mathematics is something that is all around us and everyone can study it.

So we can we celebrate Pi Day? Of course! Celebrate math everyday! 🙂

# Learning About Red, Green, Black, and Time. What’s in Your Garden?

A garden is just a garden, right?  What is so interesting about a garden?  Well, what you grow in the garden can teach your children many things like the fact that colors can have flavor, texture, and smell.  A garden can teach you about how time can be measured more than with days, weeks, and months.  So what’s in the garden?

For my current little one in the house, we were fortunate to pick some tomatoes and watermelon from a garden that we help at once a week during late summer and fall.  This was a perfect opportunity to teach my daughter about the color red, green, black.

Before giving the fruit, or vegetable to your child, describe the color.  Not all watermelons are red inside.  Not all tomatoes are red either.  Even on the same fruit, or vegetable there can be multiple colors.  Point those out 🙂

Learning about a color of a fruit, or vegetable is very important because they learn when it is ripe to eat, or best to eat it.  Talking about when a tomato gets red and what color is it when it begins to grow is very important to learn and it gives them the opportunity to understand why certain colors of food is so important to know before eating it.  Why do we not eat the tomato when it is green?  We eat celery when it is green, why not tomatoes?

To learn about flavor of a fruit or vegetable, it is easy to just have the child eat it.  For smell, have the child smell it and ask it the smell and taste are the same, or different.  For example, some people can tell if they are smelling cilantro, but the taste to them is like eating grass.

On another thought, what does the rind, which is green, taste like when you take a bite of it?  What anything green taste like and smell like?  How about the color black?  Black berries and black cherries are great examples of black fruit!  What about a banana that goes from green, to yellow, to brown, to black?  What does a banana taste like and smell like when it is those colors and when would we eat them, or use them to cook with?  In other words, give your child the experience to find out these certain characteristics of food that we sometimes take for granted.

For texture, I know people who might describe a tomato has mushy, slimy, or juicy.  It just depends on the person who is tasting that tomato at that moment.  The same can go for a the texture of watermelon.  🙂

So what does color, smell, texture, and taste have to do with learning about math?  When we take the little moments to help our children understand the relevance of color, smell, texture, and taste of what we eat, we are giving our children an opportunity to understand the world they are living in.  By also taking the time to explore the characteristics of fruit and vegetables we prepare the child to use more vocabulary in describing something.  In mathematics, exploration, understanding relevance, finding more ways to describe something, and looking for patterns is very important.

Think about time for a moment, time can be measured by seconds, minutes, hours, days, months, and years.  But when we look at vegetables and fruit, time can also be measured in the color that a vegetable turns.  Time can also be measured in terms of the texture and smell that a certain vegetable and fruit produces.  It is very important to understand time this way because it teaches us to understand when a certain vegetable, or fruit from our garden is ready to eat.

When we can think of different ways to describe what goes on in our world, like produce from the garden, the more interested we might become in exploring other situations around us.  The more different ways we can see a garden, the deeper the understanding we can develop about how a garden works and what goes on in a garden and this can all start with your little one.

Mathematics becomes more interesting when we think it is connected to things in our life because it really is.  When we give our children the opportunity to see it in their early years, the less of a struggle it will be when they get older.  We all, at some point, need to know why we need to learn something and that, my friend, is called relevance.

I have come across this need for relevance many times when I taught students in the classroom, also other teachers in mathematics, with my own learning, and with my children. We all want to know why we need to learn something and that is a good thing.   When we see that it is part of our everyday life, then we are more open to learning about it.  All this, from a garden.  So what’s in your garden?

copyright 2016 learning math with mom

# 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?

1. Division
2. Problem Solving
3. Quantity

I do not quiz my kids on math concepts. I find things about math to get them thinking. It really is not a lesson where they sit in front of the chalk board because at home, they cannot sit for that long. So I find moments where even getting lettuce can be a math learning experience. I could have easily made this into an addition problem by asking them, “what is 2 heads of lettuce plus two heads of lettuce, plus two more?” For multiplication, I could have easily asked them, “what is 2 heads of lettuce times 3 bags of them ?”

The more your children interact with the world mathematically, the less hesitation they will have in working with it at school and in life. Just remember this, it is not about getting to the finish line of learning first that is important, it is actually about getting there in the first place.

copyright 2015 learning math with mom

# Do You want a Half of a Banana, or a Whole Banana? Starting Fractions Early

When it is time for a snack or dessert, a banana is so nice and sweet for the little ones.  At first, when I have asked each of my kids whether they want a half of a banana, or a whole banana, they look at me like I am crazy.  So I take out a banana and show them a whole banana, then I take that banana and show them half.  Usually, they will say that they want a whole banana and then go eat because of course they want a whole banana.  It was not to test them on the idea of whole, or half.  It was giving them the vocabulary to use to describe how much of something they wanted.

Why would anyone want half a banana?

With my two boys being so little and close in age, sometimes there would be only one banana left.  If both were to get a banana, we would need to cut this in half.  This is the moment to now see half as equal parts because for kids, each person should get the same as the other, right?

Taking the knife to cut the banana, I placed the knife at different parts of the banana, asking them each time if this was cutting the banana in half.  “Would the both of you get the same amount if I cut it here?” “Would he get more or less of the banana, if I cut it here?” “Where would I cut the banana so that both of you get the same amount?”

After cutting the banana in half, I put the two pieces, one over the other, to have the boys see if both pieces were equal.

So, there it is.  It took me longer to type this out, than it did to show my kids in real time about half and whole.

Where is this in the Schedule of Activities for ages 18 months to 3 years?

Click to access ScheduleofActivitiesfor18mosto3yrsofage_0.pdf

1. Tuesday-Numbers

2. Wednesday-Big and Small

3. Thursday- More and Less

Start asking your little one about whole and half. This does not need to happen each and every time someone asks for a banana because then it starts to sound scripted. Once in a while, bring it up as this lesson should only take no more than five minutes.

Teaching math to the little ones should be a part of life so that they can see early on how math relates to their world. The more we do this, the less foreign it will be when they begin school. Math is a part of life, just as it is with sharing a banana.

copyright 2015 learning math with mom

# Helping Around the House: Teaching About Money, Charts, and More

For this learning activity, the kids and I have been working on creating and modifying our own chore charts for three summers now.  The first summer, I needed the boys to work on certain skills around the house. So the first set of skills I focused on were:

1. Eating  all their food for each meal

2. Water plants

3. Pick up their toys and games when done playing

4. Lessons at home

5. Mommy’s helper

At the same time, I wanted my sons to become more comfortable in counting higher than 20 and 30.  At the beginning of this project, boys are about 4 and 3 years old, just about.

To create this, I went to the local dollar store, purchased some poster board and stickers, and it grew from there.  The idea behind it was for them to work in increments of 40 stickers.  I wanted them to understand how to count to 40.  For every 40 stickers, they were able to have the buying power of a certain dollar amount to use when we went out to the store.  However, there was no purchasing power until they earned an increment of 40 stickers.  This was to prevent them from spending a dollar here, or five dollars there, and just focusing on buying stuff.

Every time they finished their food, or at least ate until they were really full, they would get a sticker.  Each time they watered plants, they earned a sticker.  Every time they picked up after themselves, they earned a sticker.  The lessons were things like playing dominoes to learn adding, doing an art project, learning our shapes outside, and so on.  For “mommy’s helper”, I might need help with doing something that is not on the chart.  This gave me the flexibility to change that chore a bit now and then.  It could be helping me put their dirty dishes in the sink, or to help me put the laundry into the dryer.

The reason behind the “mommy’s helper” was so that the chore list was not 20 items or more long.  For small kids, that is intimidating.  So there were about five to start with from the very beginning.  The kids were also encouraged to decorate their charts.  After another summer, they wanted to choose their own stickers to use.  At our house, we do not use those stickers for anything else because they are considered money for our kids.

For the second summer, the 40 stickers are now worth 25 cents a piece.  This helped them now with understanding money.  We talked about how 4 stickers are worth \$1, just like you need four quarters (25 cents) to make a dollar.  We played with real money, as now it was not a choking hazard for their ages anymore.  We talked about dimes and pennies and half dollars too.  We still continue talking and learning about this as it comes up in our day.  Then we figured out that 40 stickers are worth \$10 now.

As they get closer and closer to the full amount of 40 stickers, they need to find out how many stickers they need to earn the full forty.  At that time, they thought of different things they could do around the house to earn it.

Chore List for Second Summer

1. Clean up toys and games after playing

2. Mommy’s helper

3. Help with sorting laundry (math lesson)

4. Put away your dishes (plasticware)

5. Water plants 6. Lessons at home

Chore List for Third Summer: (used this during the school year too)

1. Clean up toys and games after playing

2. Laundry (folding and sorting)

3. Getting yourself dressed and brushing teeth (morning and night)

4. Lessons

5 Mommy’s helper

Since this was the third new list for chores, they boys and I discussed what was placed on there.  It was not just me telling them on things to work on.  They had a say and I knew that would work better, now that they wanted to become more independent.

Logistics:

1.  We started with both boys on one poster board, now they each have their own.

2. Explain to the grandparents what stickers are worth and such, so that you do not come home with kids saying that they were promised 200 stickers for cleaning up.  🙂 (This actually happened)

3. I grouped the 40 stickers in increments of 4 stickers each by circling them.  The boys were there to learn that 4 stickers/quarters equal \$1 and 40 stickers/ 40 quarters equal \$10.  Then, the stickers were crossed out with marker.

4.  I tried looking for actual stickers of quarters and thought about using a stamp that was a quarter, but that will be after the school year starts.

5. Be patient.  This is a work in progress for us, still to this day.  It takes a lot of communication as well.

6. Use the chart as a way to show your child the areas they might need to work on more based on showing them how many stickers they have in that area.  (compare and contrast)

Where is this in the Schedule of Activities for ages 3-5?

Click to access CALENDAR3yearsto5yearsofagePDF_0.pdf

1. Tuesday-Numbers, Quantity

2. Monday-Patterns (showing them areas they do more often and less often, what pattern do they see?)

3. Not posted -Money

In looking back at all of this, one child is now making better choices in spending money.  The lesson learn is not to spend for the sake of spending, but use your money wisely, especially on something that will not break after one day of use.  The other son has really learned about saving money and choosing not to spend the \$10 dollars just yet.  He waits until he earns another increment of 40 for something that costs more and can be used for a longer period of time.

No, we are not crazy for setting up the bar for \$10.  It is still a work in progress for the kids, so they do not earn \$10 each week or month.  They also understand how much work it takes to earn their money too.  There is also no exchanges after purchasing something either because we need to make things count.

You do not need to set the amount to 25 cents a sticker, nor set it to \$10.  You make the decision based on what works.  We have also chosen projects to work for donations and such.  They are reminded of how we need to share and give to others.

Their purchasing choices were more toys at the beginning.  Now, the purchases go toward kits of building robots, learning games, and books.  This was my goal because the main point was teaching them mathematics and also to invest in their learning. This post was a long one. If you have any questions, comment, or email me at mom at learningmathwithmom dot com.

# Pi Has Passed, but Can We Still Celebrate?

The biggest Pi Day ever has since passed. It was celebrated on 3/14/15 at 9:26 am and 53 seconds, so that we had 3.141592653…! We will not be seeing this for about another hundred years, but we still get to celebrate Pi Day every year on March 14th! To learn more for yourself, or for your older children, try http://www.piday.org

What about for our younger children?  We can:

1. Begin experimenting with measuring different circles with a piece of string and then taking that against a ruler to figure out length, which leads to,

2.  Talking about circumference (which is really finding the perimeter of the circle, or length

3. Looking at diameter (the length or distance across the circle),

4. Looking at Radius, which is half the length of a diameter of a circle, and

5. Compare! Get the circumference of any circle you are measuring and divide that by the measurement of its diameter. What number do you get? Get another circle and take its circumference and diameter and compare. What number do you get? How does that compare with the other circle?

6. This item can be either you number one choice to do before choices 1-5, or you can save this best for last. Read story books about Pi! This one is really fun and doesn’t take a whole lot of planning.

Where is this in the schedule of Activities of 3-5?

1. Monday- Reading a Math Story

2. Tuesday- Math under Numbers

http://www.learningmathwithmom.com/sites/default/files/CALENDAR3yearsto5yearsofagePDF_0.pdf