# 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!

# Diversity Exists in Nature To Teach Us a Lesson: Counting, Pattern Finding, and More!

I could not resist in getting our home a bunch of beautiful red Tulips.  If you have read the other posts about looking at flowers in Nature to look for patterns, well this one is not any different.  Tulips taught me a lesson about diversity.

Fascinated about the black and yellow six-pointed star, I counted the points on the Stigma of the flower.  Three points on the Stigma, then six Stamen, then six red petals on the Tulip.

In Nature, there are flowers demonstrating these patterns of either doubling the original number from the Stigma, or simply repeating the original number from the Stigma.  However, this second Tulip (pictured below) surprised me because this Tulip demonstrated the same doubling pattern, but a different original number.

Looking at this particular Tulip, the Stigma has four points, not three points.  Then that quantity of four is doubled to eight Stamen and eight petals!  Wow!  I love Nature!!!! Yes, I realize that these Tulips were not cultivated in the wild, but this one grew to be much different then the other red Tulips.  So this hit me with a great example of showing kids and ourselves as to how Nature and Mathematics shows us that Diversity still exists even when we think we are all the same.

These two Tulips have the same color pattern, have the same green stem, and are both called Tulips.  However, both are still different and unique from each other, which is beautiful!

So how is this important with Mathematics?  Well, just by understanding how to count, how to compare and contrast, and how to find patterns, that can simply take you to a lesson of learning and appreciating Diversity.  Yes, Nature has an abundance of beautiful flowers of different shapes, sizes, and colors!  Each of them have their own purpose of making the world function and be beautiful! How exciting it is to further see that even when we think a bunch of flowers look the same, Diversity still exists!

This is why Mathematics is so very important and near and dear to my heart.  Mathematics is not just solely about numbers, but extends to our very own life and life lessons that we might encounter from day to day.  What a wonderful way to introduce this particular lesson to your child about how Nature can beautifully teach us about the importance of Diversity and celebrating the Diversity!  🙂

The world of Mathematics is in your home and outside, so go explore what new lessons are out there!  Always remember that it does not matter who crosses the finish line first, it is actually getting there that is more important!

If you would like to see the article describing number patterns on flowers, go to

https://learningmathwithmom.wordpress.com/2016/07/01/theres-math-in-them-there-mountains-spending-time-outside-exploring-math-and-building-vocabulary/

# 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! 🙂

# 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!

# Math on the Mountain: The Geometry of Streams, Bubbles, and Chocolate Milk

Mount Lemmon has been getting a lot of rain. With rain, comes running streams. Running streams bring a great lesson in geometry…..bubbles!

Take a walk and listen to the running water. Ask the kids to go find the water and see if there are any bubbles forming. Look at the bubbles and ask the kids to name the shapes they see. Do they see Spheres? Do they see Circles? What happens when the Spheres get pushed together, what other shapes do they form? Do they see Pentagons, or Hexagons (five-sided or six-sided shapes)? How would you be able to recreate these shapes at home? How about with milk?

If it raining outside, or you need to take a snack break, give the kids some milk….chocolate milk if you have it.  Get a straw and have them blow bubbles in the milk.  What happens?  Do Spheres take shape? What happens if they get pushed together?  Do you see the same shapes as from the stream?  Do you see a rounded triangle?  Well, that is called a curvilinear triangle!

Look Closer.  You will see a Curvilinear Triangle to the left of the center of the picture.  Copyright 2016 Christina Grossman All Rights Reserved

Take a look at the size of the shapes when looking at the bubbles in streams, or in the milk.  Are all the bubbles the same size?  What do you notice when big bubbles are pushed together?  Do you notice a pattern in the bubble formations?  These are great questions to ask, even if asking just one or two of these questions.  It creates another way of looking at something that we might have taken for granted, especially up on the mountain. For instance, blowing bubbles and why are they always spherical….this is something to think about.

The next time you have some bubble solution, bubble wands, and/or a bubble machine, ask this question:  Does the bubble always come out as a sphere regardless of the shape of the bubble wand?  Why do think that happens?

Here is a website that has a brief description about that:  http://bubbles.org/html/questions/round.htm

Remember, these small lessons are to help the child and ourselves to begin seeing and thinking about the world for what it is.  The mathematics is there, it is free for everyone to learn, and there is an abundance of math to explore inside your home and outside, on the mountain, on a desert, and everywhere else.  🙂

If you would like a recipe to make bubble solution, here is a link for you (I am not paid to show support for this site, as well as the one above regarding the spherical shape of bubbles).  Enjoy!

http://www.wikihow.com/Make-Bubble-Solution

# There’s Math in Them There Mountains!  Spending Time Outside, Exploring Math, and Building Vocabulary

(On Mount Lemmon, Arizona )

Summer brings grandkids, our own kids, nieces, and nephews up to the mountain.  This is the greatest time for kids to explore and enjoy the mountain life. Even we can be kids at heart and enjoy what the mountain has to offer! But what’s that you say? There is math on these mountains?  Of course!

As a mother and a mathematics teacher, I take every opportunity to teach my children about math, even on Mount Lemmon.   Here are a few ideas of how to look at the natural landscape of our beloved sanctuary for the little ones:

Shape Watching on a Nature Walk

1. Small Pine trees are growing all over and some are the right height for young children to see the top of them.  Have them look at the top, looking down, and ask them what they see?  Do they see baby pine cones growing, they are called cones for a reason because cones are shapes.  Also, look at the way the needles are growing, they form a spiral!

2. While you are looking at the Pines, look down below because the Ferns are growing.  Did you know that they grow from unraveling from a spiral? When the leaves stretch out, they are little triangles too!

3. There are many tree stumps around, so take a closer look.  What shape do you see?  We see circles, tree rings. Together, they are concentric circles, like a bullseye.  What if you dropped a rock in the stream, would that make “tree rings”, or concentric circles in the water too?

4. What about when the Common Dandelions (Taraxacum officinale)come out?  The parts that we like to call Dandelion wishes are small spheres.  If you look closer, each little part of the white “Dandelion wish” are little parabolas.

Counting on Nature to Teach Us Numbers

1. Let us look at the Richard’s Geraniums (Geranium richardsonii) and Cranesbill (Geranium caespitosum) that will be growing soon.  Count the number of stamen of the flower and count the number of petals on the flower.  Is one double of the other? Is one half of the other? Are they the same?

2. Take a look at the Big Leaf Periwinkle (Vinca major).  Looking at the center, you see a pentagon, then out of that, another pentagon, and then the five petals.  This flower is all about the number five 🙂

3. When the Common Sunflowers (Helianthus annuus) start growing, count the number of petals they have.  Do you get an odd or even number of petals?  How many?  What about the flowers on the Common Mullein (Verbascum thapsus), count the number of petals on one little flower.  Do you get an odd or even number of petals?  How many?

These are simple things to open the mind of the child, and the child-like hearted ones we all are, to seeing the mathematics out in Nature.  Even if this takes five minutes to the whole entire day, everyone went outside, explored mathematics, and learned and used new vocabulary. This is a great way to show relevance of learning shapes and numbers because it is out there in our world.  🙂

Also, a many thanks to Frank S. Rose’s work on Mountain Wildflowers of Southern Arizona as it was a great resource to me to finally learn the names of the wonderful plant life we see on Mount Lemmon, AZ.

# 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

# 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.

# Fruity Fractions are Healthy and Delicious!

Why not learn fractions with watermelon as well!  Watermelon is a great snack for kids and an opportunity for learning about fractions. With the last fraction activity using oranges, the whole was the whole orange.  In this case, I use a circular slice of the watermelon as a whole.  Why?  All of us need to see the whole in different ways and its parts.

At this time, my oldest was 5, second oldest was about to turn 4, and my youngest was too young to notice what we were doing, nor could eat watermelon.  Taking a slice of watermelon, I told them that this slice is the whole.  Cutting in half, I then said that this is now cut in half.  “What do you notice about the two pieces that came from the whole slice of watermelon?” “Are they the same, or different?” If cut this slice of watermelon into two pieces and give it to the both of you, would you want them to be the same or different?” “Why?”

Those are the questions, I asked and still ask when the moment presents itself.  When asking the kids questions, ask both questions that will result in a yes or no, and ask them questions that they need to explain more.  The most important thing to remember is just to ask your child questions to find out what they are thinking.

Now cut the two equal parts in half again.  How many slices of watermelon was the whole cut into?  What are they called now? Are they called halves, or something else?  Answer:  they are called fourths.  Cut each of those fourths in half and what do you get?  Answer: they are called eighths.  Why are they called eighths?  Are each of these eighths the same/equal to the other eighths?  If we put all of these eight eighths together, what do they make?  These are just a sample of questions to ask your kids.  Just be mindful of how many questions you ask before the kids’ attention span is gone.  🙂

Now eat and enjoy so they can taste the delicious mathematics they just learned!  🙂

Here are more pictures for you to use.  Print them out and use them for later to help your kids learn their fractions again.  The kids can also use the pictures to help them cut the fruit in equal pieces.

Whole- One Whole

Half- Two Halves

Fourths- Four Fourths

Eighths- Eight Eighths

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

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

1. Tuesday-Numbers

2. Wednesday-Big and Small

3. Thursday- More and Less

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

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