# 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!

# When Temperatures Rise, It is Time to Make Sugar Water for the Hummingbirds: Measuring with the Help of Little Hands!

This is not a new concept, but it is new for my child and that is what counts!  We love seeing our Hummingbird friends and they do remind us that the sugar-water is getting low.  For this activity, it takes just a smidge of time with your child and it is just right for the little hands to measure.

Materials:

1. A pot to hold at least 4 cups of water
2. Distilled, or Spring Water
3. 1 cup of raw sugar
4. A measuring cup, be it a 1/2 cup, whole cup, or 1/3 cup
5. Humming bird feeder

With those little hands, count out 1 cup of sugar and pour into the pot. If you are using a 1 cup measuring cup, then counting is easy.  If you are using a 1/2 cup, then you are counting to two.  If you are using a 1/3 cup, then you are counting to 3.  This would be a great time to show your child how two half cups of sugar equal into 1 cup and how three 1/3 cups of sugar equal 1 cup too!

Now count out 4 cups of water and pour it into the pot as well.  If you are using a 1 cup measuring cup, then count to 4.  Using a 1/2 cup will have you counting to 8 and using a 1/3 cup will have them counting to 12.  Then get a spoon to stir it up before putting this on the stove.

This is also a great time to tell your kids about the rules of the house with a stove.  To make sure my little one can still pour and scoop, the pot is first placed on the table and then transferred over to the stove.  Turn on the stove and let the mixture boil.  Once it is boiling, turn it off right away and let cool.

For us, we make this in the mid-morning and it cools off completely after lunch to be able to pour into the humming-bird feeder.

Now you can enjoy the Hummingbird friends coming over to your yard and take notice of the sounds they make when they call each other, fight over the feeder, or the different colors and sizes of the Hummingbirds.

Purchasing sugar-water at the store can be expensive over time and it also contains a lot of additives that the Hummingbirds should not consume in the first place.  This activity is much about being responsible to our animal visitors, as well as a mathematics lesson.  Planting flowering plants in your yard, that do not contain any pesticides, are also a wonderful addition to your yard.  There is plenty of measuring in that activity too!

Do not be surprised if you see a Woodpecker enjoying the sugar-water as well.  It is really fascinating to see them hang on to it to drink the water 🙂  If you also encounter a lot of Bees drinking the Sugar Water, do not be surprised either.  If this is a problem for you, then wait until the sun sets, or gets dark to remove the feeder, as Bees always go back to the hive at night.

The most important thought to keep with you, after reading this, is that you had a great time with your child that included mathematics and nature!  Enjoy!

# Preparing for the Winged Visitors Coming Back from the Winter: Pouring, Measuring, Classifying, and Counting.

At this time of year, it might be snowing where you live, but not here.  The weather is slowly getting warmer and the birds are coming back from homes during the Winter time and they are hungry!  So why not prepare something for them and turn it into a mathematics lesson?

You can either make your own bird feeder and bird seed mix or purchase them from the store.  Get some measuring cups, a ruler/measuring tape, and go outside to have some fun!

First, take a look at the bird seed mix.  What shapes do you see?  Do you see some circles and ovals?  Do you see some triangles, spheres, or curvilinear triangles?  What colors do you see?  How many different types of seeds do you see?  Could you sort them out if I gave you a cup of that bird seed?  How would you sort them?

Next, have your child look at the measuring cup and estimate how many cups of bird seed it will take to fill up the feeder. Remember what your estimate is and now begin to count how many cups of birdseed it takes to fill up the feeder.

Then,  how many inches, or rulers tall, or building bricks tall, or hands tall is the bird feeder?  Where are we putting the feeder and how long of a string do we need?

Once you have your feeder up, let the fun begin by observing what birds come to use it.  It might take a day, or two before the birds come, but it will be a great experience to see how many birds a day visit the feeder.  What colors do the birds have?  How big are the birds?  How many different birds come visit the feeder?

This whole math lesson may take 5 to 15 minutes from start to finish and it is worth it.  Something very simple and so many mathematical ideas to explore!  Have fun with this and with your child(ren)!

This activity can be adapted for any age of child and learning stage for the child.  You know your child(ren) better than I do 🙂  So, you may want to not ask so many questions, maybe use three.  If you have older children, they can make charts to categorize and keep track of the kinds of birds they see.  They can also name the types of seeds and birds as well.

Whether or not the weather is right at the moment, the birds will still be hungry and you are inviting the birds to come to you 🙂  The kids and you can even practice different bird calls and whistles by listening to them as well!  Get yourself and your child(ren) outside to explore the Mathematics around you and have fun!

Enjoy!

# What Books Does Mom Have About Math? Here are just a few….

At our home, we have a lot of books about math.  I have been asked what books I have read or the kids used since they were little ones and even to this present day.  The best way I can do this is through photos and there will be repeats as I have taken these photos at different times.

As a note, none of the publishers, nor the authors have paid me or asked me to post these books on this blog.  These are books that we actually own, or have owned.  You do not need to get all of these books, just choose a one or a few and go from there.  Remember, checking them out in the library, borrowing them from a friend, or buying them are options.  The important thing to remember is to begin reading to your child, especially in mathematics. 🙂

copyright 2015 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

# 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.

# Math That You Can Eat: Quantity with Chopsticks, Cereal, and Number Cards

This is certainly not a new idea, but one that I changed according to what I had in the house.  Basically, you want to have a set of number cards 1 through 10, chopsticks or dividers, and cereal.  My second oldest was about 2 ½ to 3 years old.  He really was showing signs of how much he liked to count things, so I wanted to give him a learning activity to help build on his sense of quantity.

First, everything was set up just as you see in the picture above, but without the cereal.  The cereal is in a bowl for my son to grab and use.  I showed him the name of the game by saying that I have the number one, so I need to put one piece of cereal in the spot.  I then said that now I have the number two, so I need to put two pieces of cereal in the spot.  I then said that I now have the number three and asked him how many pieces of cereal I need to put in the spot.  He told me I had to put three pieces of cereal there, so I knew he got it.  I told him that I would like him to finish it all the way to the number 10; once he finished, he can eat all that cereal up as a treat.

This did not take very long for him to finish.  It took about ten to 15 minutes.   Because this was the first time for this learning, I sat there to see what he was doing to check his quantities for each number.  If he miscounted or forgot what number he was on when counting, I was there to help him.  If I had left him by himself this very first time, he would have eaten all the cereal after doing four and five on the numbers cards because he loves his cereal! 🙂  When I am with him, though, we are learning together and it is a great mommy and son time to have in the morning.  The photo below is the rest of the activity set up with his completed work with the cereal before he ate it all 🙂

Where is this on the Schedule of Activities from 18 months to 3 years of age?

1. Tuesday on Numbers, especially in quantity

http://www.learningmathwithmom.com/sites/default/files/ScheduleofActivitiesfor18mosto3yrsofage_0.pdf

Where is this on the Schedule of Activities for 3 to 5 years of age?

1. Tuesday for Numbers (specifically counting), Quantity, and Measurement

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

Once my son learned how to do this, he wanted to work on this over and over again.  It was about the third time that I did not need to be with him sitting next to him or looking over his shoulder.  He wanted to do this by himself and then I would check his quantities when he was done.  The big treat was that he was doing something by himself and got to eat the cereal 🙂

My oldest was watching him do this and also wanted to work on it.  He already knew his numbers 1 through 10, but I am not one to get in the way of any of my kids when it comes to doing a learning activity.  After the first try, I changed the quantities from 1 through 10 to 11 through 15.  You can change the quantities to whatever you want, depending on the age of your child.  If you want to do numbers 1, 2, and 3, then do that.  If you want to just do the first five numbers, go for it!  If you want to do this in tens, or in any other quantity for your multiple age kids, this is a great idea!  This learning activity is so easy to set up and flexible to be adapted for any quantity, that I do hope you take advantage of this one and try it out.

Materials:

Number cards (you can make your own)

Chopsticks (you can use forks, pencils, breadsticks, straws, string, etc.)

Cereal (you can use crackers, green peas, corn kernels, or whatever you have in the kitchen)

Again, as a parent, we might think we need to hurry up on teaching certain things to our children so that they won’t fall behind. This allows us to become more stressed or pressured if our children are not learning at the rate we think they should. No worries…just breathe. Because even reading this blog and finding out how to help your child become more successful in math should tell you that you are a wonderful and caring parent. If your child takes more time to learn concepts, it is okay. We all learn at different times. I will say this over and over again because it is that important to know that you are doing a great job! 🙂

copyright 2014 learning math with mom

# Stop and Notice How the Day is Changing

What is day? What is morning? What is afternoon? What is evening? What is night? What is dawn?  There is a cycle that is being repeated by nature every time the sun comes up and goes down and the moon joins in at night.  Your baby, or itty bitty one can listen to you as you describe the day or night.  It is about being deliberate about what we already know about the parts of the day and to say it out loud so that our child can listen and observe.  Just like we sometimes point out that this is a yellow banana and the grass is green, and the sky is blue, so do we need to point out change in the day to our child.

Once your child is old enough to notice the clock or begin to talk, start talking about what time it is during the day.  When you are waiting to go out of the house to run an errand, or go visit someone, let your child know what time it is that all of you or both of you will be leaving?  Either write down the time and have it next to the digital clock, or have their toy clock set to the time of departure and have it near the analog clock.  Start talking about what time it is when it is breakfast time, lunch time, nap time, getting ready for bedtime, and time to go to sleep.  This routine you have set for them is associated with the time of day.  Beginning to point out what time opens the child’s world to taking note to time.

This piece of time is not about learning how to tell time by reading a clock, but the beginnings of doing so.  To learn about something, it is better to have a purpose or meaning connected to it.  By beginning the phases of time for day, you are establishing meaning.  The child will begin to notice that the sun is rising or setting.  The child can see that the moon is there in the sky at night.

Where is this on the Schedule of Activities 0-18 months?

1. Saturday and Sunday for Go outside and Explore it).

This is a bit of a stretch, but to really understand what is day, what is night, what is morning, and so forth, the baby needs to see it outside.

http://www.learningmathwithmom.com/sites/default/files/Schedule%20for%20the%20Week_zerotoeighteenmonths.pdf

Where is this on the Schedule of Activities 18 months-3 years?

1. Tuesday for Numbers
2. Saturday and Sunday for Go Outside and Explore It.  The child must know what day, night, morning, afternoon, evening, and night look like.  Go out and see the sunset or the stars!

http://www.learningmathwithmom.com/sites/default/files/ScheduleofActivitiesfor18mosto3yrsofage_0.pdf

Where is this on the Schedule of Activities for 3 to 5 years of age?

1. Tuesday for Numbers (specifically counting), Quantity, and Measurement
2. Fridays for Numbers (specifically counting and sequence)
3. Every day for Play Time.  Go see the stars and the moon, the sun and the sunsets!

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