Are You Taller Than a Cow Parsnip?: Measuring in Units of Nature

Cow Parsnip (Heracleum lanatum)

I am so grateful for such a wonderful paradise on Mount Lemmon, being so close to the desert, and being surrounded by a beautiful community.  What a better place to go learn mathematics because there is math everywhere on the mountain.  What a great time to be up on Mount Lemmon and go exploring!

One of my favorite plants on the mountain is the Cow Parsnip.  These are my favorite wonders of the area!  Cow Parsnips remind me of a child where they begin as small little ones and grow above and beyond 5 feet tall, or close to it.  So I guess the big question is, are you taller than a Cow Parsnip?

What is great about being outdoors is that plants do not know what inches, centimeters, or feet are.  In Nature, there is an abundance of resources use to measure and one of these can be the Cow Parsnip of course! So go for a wonderful walk and look for one of these beauties.  Stand up next to one and measure yourself.  Who is taller, you or the Cow Parsnip?

Take the kids out for a walk and see how they measure against these wonderful giants.  Start using the words of comparison like, “shorter than”, or “taller than”.  How many of you would take to be as tall as the Cow Parsnip?  What about the blossoms?  How many blossoms would it take to be the length of your hand?  How about the width of your hand?  Take a look at those leaves!  How many of your hands would it take to be the same length, or width of those leaves?

Something to Think About:

This is cute and all, but how does learning Mathematics really measure up to the “real” world?  Take a child, for instance, maybe that child is sad because he/she hasn’t grown as tall as everyone else, but take a look at the Cow Parsnip with how small the Cow Parsnip began.  The Cow Parsnip starts out tiny and then shoots up to be taller than any other flowering plant I know.

Success can be measured using blossoms and stalks of plants, or the number of tree rings a tree can have in a lifetime.  Nature has so many opportunities where we can learn and explore in Mathematics.  What I would like everyone to get out of these posts is that the world of Mathematics encompasses more than what we can imagine.  The earlier we start our kids and grandkids in interacting and learning from Nature, the more they will have more reason to protect what is treasured by the rest of us.

copyright 2017 Christina Grossman. All Rights Reserved

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Getting Our Child Ready for Kindergarten: The Count Down Begins

Copyright 2017 Christina Grossman. All Rights Reserved

 

If you need some ideas of what math activities to do with your child(ren) at home, go to the header above on this blog and select an age, or topic!  If you have any questions, feel free to contact me on the comment section or email me at momatlearningmathwithmomdotcom (spelling this all out because of spammers).

If you would like to have a checklist handy for the summer, here are two resources for you to use:

1.  Summertime Tips for Preparing Kids to Enter Kindergarten from AZ First Thing First http://www.azftf.gov/WhatWeDo/Impacting/Documents/Preparing%20Kids%20to%20Enter%20Kindergarten.pdf
2. Getting Kids Ready For School With PBS KIDS from PBS.org http://www.pbs.org/parents/education/going-to-school/starting-school/getting-kids-ready-for-school/

Do you also want a chart, or schedule, as a friendly reminder during the summer?  Go to this link to see charts to set up your day by topic for different age ranges!

https://learningmathwithmom.wordpress.com/category/schedule-of-activities/

Something To Think About:  

There are plenty of things at the stores and online that you can buy and do with your child at home.  This blog focuses on things that you might already have at home that you can use, so learning at home does not need to be expensive. From the checklists though, I hope you see that just talking to your children and pointing things out to them about numbers, colors, shapes, letters, and reading to them are just the fundamentals of getting your child(ren) ready for learning.

Remember, learning should not be a race to see who gets there first, it is actually about getting there.  Learning should be enjoyable and relevant to the child’s world.  Once the child sees how math is a part of his/her world, the mathematics becomes that more interesting to learn.

Copyright 2017 Christina Grossman. All Rights Reserved

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!  🙂

 

Something To Think About:

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/

copyright 2017 Christina Grossman. All Rights Reserved

Whether Freshly Collected in Your Basket, Hard-Boiled, Scrambled, or Colored, Eggs Teach Us About Equality: Making Division “Egg”citing!

We just colored these hard-boiled eggs that you see in the picture above.  Each child wants to make sure that he/she has the same number of eggs, so I took this opportunity to explore division and practice it too! Regardless if we were going to color the eggs, or eat them, everyone wants to have their equal share, so distributing the eggs equally was a good way to show how division works.  This goes for eating the eggs for breakfast, as a snack, or with any food item, the concept of equality is always there.

After boiling the eggs, we needed to let them cool off.  Afterwards, each child was handed their plate for their eggs they were going to color.  We started with 15 eggs and I asked the older ones how many eggs each of us should get if there are three of us.  Then I did the distribution of the eggs one at a time.  Each of the three plates received one egg at first, then two, then three, checking each time if each plate has the same number of eggs. We checked back to see how were left and if we could still distribute those eggs.  We did this until all eggs were equally distributed.

Each plate now had 5 eggs for each of the 3 plates.  This makes 15 eggs divided by 3 plates to equal 5 eggs each.  But what if we had one egg leftover, or two eggs leftover? We could divide each egg into three equal parts and distribute those equally, but we face the concept of context.

Something to Think About:

In this context of coloring eggs, it does not make sense to divide a hard-boiled egg into three equal parts because who wants to color a third of an egg?  This is a wonderful conversation to have with your child.

In this “egg”citing activity, this is about starting with a quantity of eggs that will result in everyone having an equal number of whole eggs.  If you scramble your eggs, then it might not matter about everyone each getting and egg and a third of an egg because the context is different.  Sometimes, mathematics is all about the context of it all.

Another important piece is talking about what other contexts hold division in distributing everything equally?  What cultures and communities share all their food equally with everyone?  How does this relate to using division and how important is it to divide equally?  What are some other examples where things need to be divided equally and why is that important?  Asking ourselves and our children these questions places the mathematics of division in a contextual situation, something more real to us in life than what is on paper.

Trust me, Mathematics is really “egg”citing!  So get to exploring and think back to how you practice Mathematics in your life!  Enjoy!

 

Copyright 2017 Christina Grossman. All Rights Reserved

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.

Something to Think About:

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!

Copyright 2017 Christina Grossman. All Rights Reserved

 

 

 

 

 

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?

Answer:

1. Monday- Reading a Math Story

2. Tuesday- Math under Numbers

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

Something to Think About:

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)!

Something to Think About:  

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!

 

copyright 2017 Christina Grossman. All Rights Reserved

 

Math, It’s What Soup is Made Of: Counting, Measuring, and Shapes.

It’s now beginning to look and feel like winter for us. My youngest and I made soup together and like so many times, I squeeze in a math moment.

Before we get to wash our vegetables, we count how many stalks of celery we have, how many carrots, potatoes, and zucchini we have. Then it is time for washing.

When we cut our vegetables, what shape does celery look like when we chop it this way? Crescents? How about the carrots? Circles? What about the zucchini? Don’t forget the garlic and onions too!

What about the potatoes? What types of shapes do you see? Why is it important to make sure we cut the potatoes the same way and size? Would it take longer or shorter to cook small pieces?

Then put the vegetables in a pot and start measuring. How many cups of water, or cups ofchicken/vegetable broth do we add to the soup? How long do you think it will take to cook? These are are great questions to ask. Even if your child says, “it will take a billion years to cook,” that might just be accurate for them because in their world, a few minutes feels like a million years anyway . 😊😊

Something To Think About:

Making soup is not a new concept, but it is one of those moments to ask them to count, or identify shapes, or measure out in cups. At least do one of those things and you have placed math in your child’s environment. Most importantly, you spent some time together, made a mess, and had fun. 😊

Enjoy!

copyright 2017 Christina Grossman. All Rights Reserved

Concentricity: Triangles, Circles, and Even More Shapes in Our Food, Life, and in Nature

Mount Lemmon, AZ

 

Concentricity is something that others would say is too early to teach the little ones about.  I strongly disagree on this note.  Basically, Concentricity happens when there is a common center shared among other circles or spheres.  What I have found are some other examples that go outside of the rule of circles.  With the kids, we have found examples with triangles and ovals.

So by trying to keep this short and sweet for this month’s post, look at the examples below.  When Concentricity happens out in Nature, it is so easy to just point that moment out to our children, regardless of age.  This happens outside our home, inside the home, and in our food.  I hope this encourages you to go find more examples where you live. 🙂

Concentric Circles: 

Tree rings are about the most common one that all of us can identify as they are concentric circles.  The sliced beets you see below are candy-striped beets and they taste delicious!

 

Concentric Triangles:

This Pine is a wonderful example of concentric triangles. So go out to the forest and see what the trees can teach you! 🙂 Let us not forget the strawberries too!

Palisades on Mount Lemmon, AZ

Strawberries 🙂

 

Concentric Ovals and More: 

Kiwi is just as delicious and a great tool to show Concentricity.  This beautiful Agate can be debated on whether this shape is an oval, or an ellipse, or a five-sided figure.  Either way, I see the Concentricity here too 🙂 Do you?

 

 

Something To Think About:

How about squares? When do concentric squares happen?  How about other shapes? Where do you see them?  Think about it and start exploring!  That is the beauty about Mathematics as it is out there and there are so many opportunities for more than one answer because that is just how it is.  Just because a definition of Concentricity only includes circles, or spheres does not mean that there is no likelihood of an exception for that definition.  When we are able to discover and see the exceptions when they happen, that is where the heart and beauty of Mathematics exists.  These interesting surprises are the most important to point out to the children!  and to you!

Learning about Geometry, especially Concentricity, at such an early stage in life gives them the opportunity to see it everywhere.  Once a child, or any person of any age, is able to see the Geometry, it becomes more tangible when it is time to learn more in the classroom.  It then becomes more relevant and more important to them to learn because Mathematics is even more interesting than rules and procedures, it is about exploring and experiencing what happens outside your door.

Have fun learning and exploring together! 🙂

copyright 2016 Christina Grossman. All Rights Reserved

Stars in the Forest, Not Just in the Sky: Geometric Stars in Plant Life.

 

Scarlet Gilia (Ipomopsis aggregata)                                                                                                                                           Copyright 2016 Christina Grossman. All Rights Reserved

On Mount Lemmon, this is the first time I have seen a Scarlet Gilia.  It is so beautiful and unlike any flower that I have seen on the mountain.  This particular Scarlet Gilia was located on Turkey Run across from the community center.  After having the gift of encountering this, it encouraged me to share this out with the rest of you and your kids that Stars do exist in our world, not just in the sky.

For the little ones, stars just may be the easiest shape to learn because they are so special looking.  So why not begin with teaching them about things that are shaped like stars and point them out in the plant life and in food!

Up on Mount Lemmon, you have the beautiful Scarlet Gilia that is a five-pointed star.  The Cow Parsnips that bloom earlier in the summer look like spheres from far away, but look closer and you see little individual blossoms that are five-pointed stars!  As these bloom until October, Richardson’s geraniums on the mountain are these beautiful dark lavender blossoms that are also five pointed stars.  So go take a walk with the kids, or even for yourself and go find these beautiful stars during the day.

For other plants, it depends on where you live.  If you live in cooler areas, you may be able to look at the Lilies of the area and notice that their blooms are six-pointed stars.  Take the Hollyhock.  Look from within the bloom and you will see this beautiful green five-pointed star in the center.  In the desert, look for the Aloe Vera plants and look from above to see the star.

In food, we have stars that form on the top tomato plants (five-pointed stars), onion blossoms (six-pointed stars), and on the pomegranate fruit (six-pointed stars).  If you cut an apple horizontally, you get to see a star there as well (five pointed star)! So get the kids in the kitchen and explore which fruits and veggies have stars in them, or cut them into stars.

Hollyhock (Alcea rosea) Ft.Ticonderoga, NY                                                                                  Copyright 2016 Christina Grossman All Rights Reserved

 

Aloe (Aloe vera) Tucson , AZ                                                                                                                 Copyright 2016 Christina Grossman All Rights Reserved

Cow parsnip (Heracleum lanatum) Mount Lemmon, AZ                                                           Copyright 2016 Christina Grossman All Rights Reserved

Tomato Plant Tucson, AZ   Corpus Christi Catholic Church Garden                                                                                                                         Copyright 2016 Christina Grossman All Rights Reserved

Richardson’s geranium (Geranium richardsonii) Mount Lemmon, AZ                                 Copyright 2016 Christina Grossman All Rights Reserved

Wood Lily (Lilium philadelphicum) Queensbury, NY                                                                   Copyright 2016 Christina Grossman All Rights Reserved

 

Pomegranate Fruit Tucson, AZ                                                                                                            Copyright 2016 Christina Grossman All Rights Reserved

Onion Blossom Queensbury, NY                                                                                                          Copyright 2016 Christina Grossman All Rights Reserved

 

Something To Think About:

To learn about shapes and to teach them to your young child, it really is not difficult.  You either need to look at the food you eat, or look at the plants outside.  Begin with teaching them about stars because they are everywhere you are,  up in the sky or growing out of the ground.  It just takes a moment to open your eyes and the eyes of your children so that you get to see and enjoy the beautiful geometries, the beautiful shapes that are already around you.  🙂

Learning about geometry at such an early stage in life gives them the opportunity to see it everywhere.  Once a child, or any person of any age, is able to see the geometry, it becomes more tangible when it is time to learn more about geometry in the classroom.  Geometry then becomes more relevant and more important to them to learn.

Have a wonderful time searching for the stars!

copyright 2016 Christina Grossman. All Rights Reserved