# Making Math Hands On: Adding With Math Bears

Once your child has developed one to one correspondence, he or she can begin to understand addition.  There are many ways to incorporate adding into your day.  When you are playing with cars, for example, count how many cars you have.  Ask your child, “How many cars would you have if I added two more?”  Add two more cars and count them all together.  This is how I introduce the concept of adding, in the context of play with real objects.

After the child seems comfortable with the concept, I would add the number representation of the problem along with the manipulatives.   Eventually, after a lot of practice, the child can add without the aid of objects.  But there is no rush!  You want your child to add in a hands-on fashion enough times so that he or she can form mental representations in their minds.  Until then, they need the physical representation of the problem. This takes time and practice and it is very necessary.

## How to show the physical representation of an addition problem:

The set up:

• Tray
• Math bears on the right side
• Foam numbers 0-9 on top
• A couple of addition problems (based on child’s level) on the left

Numbers 0-9

Step 1:  Draw a card with an addition problem.

Step 2:  Have the child put the corresponding number of bears for the top number and the bottom number. These two numbers are called addends.

Step 3:  Explain that the (+) plus sign tells us that we are to count the bears all together.  So if we have one bear and we add five more bears, how many do we have all together?  The child may begin to count all the bears.  If not, show the child how to count them all together.  Sometimes moving them together helps:

Putting them all together

I put them all together under the equal sign so that the child gets a visual image of where the answer goes.

Step 4:  Have the child find the number that corresponds to the quantity.

Teaching Tip:  As your child learns the concept of addition, he or she is also learning math vocabulary.  Words like, “plus”, “all together”, “equals”, “sum”, and “addend” are great words to include in your explanation.

The more hands on practice your child has with the concept the better!  Often times, we jump too fast into paper and pencil before the child was able to form a solid foundation of the concept.  If your child comes home with addition homework and needs your help- break out the math bears!

Linked to: Montessori Monday on Living Montessori Now

# Math Connections: Ten Little Caterpillars by Bill Martin Jr.

Aside from learning cardinal numbers (our counting numbers), such as one, two, three, etc., kids also learn to use ordinal numbers such as first, second, third, and so on. Bill Martin Jr.’s book Ten Little Caterpillars is the perfect book to introduce ordinal numbers to your child!

In this book, we meet ten caterpillars. Each caterpillar is introduced one at a time and referred to by it’s position or ordinal number. For example, we meet the first caterpillar, then the second caterpillar, all the way until the tenth caterpillar who eventually turns into a butterfly. The sentences are very short and have a rhyming pattern. This makes the book easy to read and allows you focus on the new concept of ordinal numbers. If your child already knows ordinal numbers have your child predict what will come next in the pattern. This book is a great resource to reinforce the idea for your child!

#### How to extend this:

• When you are walking up the stairs, have your child say out loud, “First step, second step, third step…” until you reach the top.
• Line up a group of toys (cars, action figures, blocks, dolls,) and ask your child questions such as, “Which car is third in line?”. If your child needs help, show him or her how we start on the left for the first car, the next one is second, the next one is the third car.

You can use cars in a line.

• When you are playing a game, state who is going first, second, third, etc.
• If you are playing baseball outside, for example, you may keep track of the pitches you threw- first pitch, second pitch, third pitch, and on.
• Making a salad? Tell your child, the first step is wash the lettuce, the second step is slice the tomato, third step is cut the carrots, etc. Or, use ordinal numbers when you are following a recipe.
• Toys around the house:

Melissa & Doug Caterpillar Gear Toy  (Bonus: This toy also practices motor skills, color recognition, and spacial skills)

• There are so many possible ways to use ordinal numbers. Anything in order can be identified with an ordinal number. Keep your eye out for those opportunities and include your children. It won’t take them long to catch on!

Teaching Tip: These activities show children how ordinal numbers are used in everyday life. It puts the skill in context of how it is actually used, versus a contrived experience or worksheet. Real life application gives the child a better understanding of the concept and allows the child to later extend that knowledge to new situations.

#### In the book we also see:

• The caterpillars eat leaves, flowers, and vegetables.
• One caterpillar build a chrysalis.
• The caterpillar becomes a butterfly.
• The end of the book shows art work of different kinds of caterpillars and what they look like when they become a butterfly or moth.

All of these things can spark conversation about the life cycle of caterpillars!

Enjoy the story!

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Ten Little Caterpillars by Bill Martin Jr.

# What Makes a Good Math Word Problem?

Our son was showing signs of interest in finance, business, and investing so we wanted to provide him with a good, practical, mathematical word problem.  We started a series of problems that focus on finance and the first one we gave him was a basic lesson in income and expenses.   This problem is a great exercise for a number of reasons.  First, it teaches fiscal responsibility and gives the student an idea of what certain essentials actually cost, something that is not highly focused on in most elementary education and perhaps should be.  Second, it causes the student to keep track of the information in the problem, perhaps by use of a table with two columns:  income and expenses (our son used a separate sheet of paper).   Third, it empowers the student to help the character described in the narrative (Jimmy in this case) and provides relevance as the student is applying skills relative to a job they have been hired for.  Fourth, it asks practical questions that force the student to think, generate original ideas, and compare or test those ideas.  The first question doesn’t simply ask a rote math question such as “What is the sum?” or “How much is left?”  It asks the student if Jimmy can afford something which forces a comparison of numbers that are found only after a number of proper calculations.  The second question is great because it forces the student to think critically, gives them freedom to decide, and causes a change in the outcome.  Additionally, there is no wrong answer.  In this case, our son advises that Jimmy forgot to include “food and water” in his calculations and assumes it will cost \$250 per month, which is reasonable.  This problem can extend to other mathematical applications as well—use your imagination!  From this exercise and more like it, a student can practice basic math, but also keep track of information, make needed comparisons, and provide empowering advice!

# Math and Science Connections: One Watermelon Seed by Celia Barker Lottridge

#### Math: Counting up to 10, Counting by tens, Counting to 100 Science: Plants, Seeds, Ecosystems

Just a few days ago on one of our trips to the library my son really wanted the book The Watermelon Seed by Greg Pizzoli, but after searching the library’s catalog we realized the book was checked out.  That’s when we came across the book One Watermelon Seed by Celia Barker Lottridge.  He really enjoyed this new book and it was a great book to use to support math knowledge.  I’m glad we found it!

Math Connections:

Counting up to 10- The story has 2 children planting a garden. First they add 1 seed, then 2, then 3, and so on.  Underneath the text the author writes the numbers in order so they kids see each number being added on sequentially.  We pointed to each number as we read them. Since it builds and repeats, it gives a lot of practice saying each number.

Counting by tens- After the children count up to 10 and the seeds grow into a bountiful harvest, the book continues on counting the fruits and vegetables by tens. Once again, the author adds on sequentially. First you see 10, then 10 and 20, then 10, 20, 30 until they reach 100. The numbers are bright and colorful. But, even better, when they reach 80 the author clearly groups the vegetables into groups of 10. For example, when they reach 80 the main character picked eighty string beans. The illustrator clearly shows 8 groups of 10 string beans.  You can show your child how this grouping allows to quickly count. They visually see what counting by tens is all about! There is a visual connection to the skill of counting by tens.  The numbers 90 and 100 are also clearly grouped by tens.

Counting up to 100- There are like a gazillion books that count from 1 to 10. But it is always nice to find books that count higher. This book does count up to 100 however, after 10 it does not count every single number up to 100. As mentioned, it begins counting by tens after it reaches 10.  If you wanted to count the ears of the corn at the end of the book, there are 100 of them! You could have them count the corn to practice their numbers up to 100.

Teaching tip:  If you are counting the objects in the picture with your child, encourage them to point to each object as they count or if they are very young you can point and count.  One of the earliest math skills kids learn is “one to one correspondence”.  One to one correspondence is the understanding that you only count an object one time.  This takes time to learn.   Have you ever seen a child count three objects and say there are five because s/he counted two things more than once?  That child is learning one to one correspondence.  Keep practicing pointing and counting an object only one time when your child is interested and they will pick up this skill.

Science Connections
:

Seed and Plants:  When the children plant the seeds and the plants begin to grow, the illustrator shows the roots growing in the ground and the sprouts growing up.  It’s a very good visual for seeing the parts of the plant. In the book, we also see the children watering the plants and weeding the garden. This can create discussion on what plants need to live and how to care for them. You can ask the child, “Why do we weed the garden?”

Ecosystems: There are great illustrations that can spark discussion. You also see worms digging tunnels in the dirt, a bird with a worm in its mouth, bugs in the air and on the ground, etc. Encourage your child to think about how the living and non living elements help each other.

Looking for another great book that counts to 100?

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1 2 3 Peas by Keith Baker is incredible!

You can count each and every pea individually. And when you are on the final page, each pea holds up its number so you can count and see each number from 1 to 100 also! This is one of my new favorite books!

Check your local library for this book. It is also available on Amazon (just click on the picture)

Another great book to try for fun: