Shopping for toys & Adding Double Digits

We happen to have a little board book that has various shops with prices. It is wonderful addition and subtraction practice. You could use a toy catalog, a supermarket flyer or make one up yourself.

Using this sheet helps young children keep place value. Have them write the name of the item on the blank and the amount to the right. They can then add the ones and tens columns separately  as the tens are shaded. Be careful to put low numerals in the ones place if you have not covered "carrying" yet.

source:

• Math Their Way

Estimating & Counting on the Counting Board

How many marshmallows are in a bag?
You could choose anything to count. Use a board that has 10 spaces in each section: ones, tens and hundreds, and once they have ten, they move one over to the next section and start over in the ones column.

Guesstimation and Place Value

Present to your students the task of estimating how many objects are in any empty container you have. You can use any math manipulative for this activity, but I like to use snacks, such as these gummy frogs because it interests children. In my family, Quentin guessed "21"; Sam guessed "26" and James guessed "25."

Then ask one student to take the counters out of the container and put one on each small circle of a place value board. A place value board has 10 small circles in one section for the ones, ten larger circles for the tens. If you make the circles the same size as the bottom of a bathroom paper cup, you can use those to hold ten of any item you are counting. In the next section have circles large enough for a bowl or coffee can. This container needs to be large enough to hold ten of the bathroom cups, or 100 items per circle.

Once all the circles on the ones section are filled then have your student take them off the ones circles and put them in a bathroom cup and put the cup on the tens side.

For this example, Quentin filled the ones section twice and had three frogs left over. It was easy for them to see that there were 23 in the jar. This is a pleasureable way to learn estimating skills if you do this regularly with different counters and different containers of all sorts of shapes and sizes.

After you have done this several times, you can increase the amount of counters you are usings as well. Initially their estimates will not be so accurate this time, as the numbers you work with are higher. Give your students chances to change their estimates as they go along because the object is for them to get better at estimating, not winning against each other. Once you have completed your estimating exercise and are ready to hand out the counters for a snack, first have them figure out the quickest and easiest way to divide the crackers equally.

For the benefit of Sam and James, I followed along with on the white board, writing down everything they did. In the end Quentin said, "That sure is a lot of numbers!"

Making Designs and Learning About Numbers of Things

Make various shapes of various sizes and colors. Using a pre-determined number of shapes, have your students make pictures out of them. Once they have their pictures as they want them, have them glue them to paper.

Remember, they are only allowed to have a certain number -whatever you choose. For example, here is James' picture for the number 8. They can play this game over and over, with different amounts of shapes. This gives them an idea of the amount of various numbers of objects. They learn, for example, what 8 looks like. It also increases their estimating skills.

Math Games: Handfuls

In advance, print out these cards or make up cards that say "more' and "less."

Using a large pile of counters of two colors (we used chips), have your students each take a group of them. Flip over a card and have them estimate which color matches the card. Then let them prove it by counting, if they need to. 

Number Stations: Using Anything for Math Manipulatives to Explore Patterns

In this game students use two colors (to begin with, but you can increase this amount later) of any kind of math manipulative. In this case we are using Unifix cubes to make different patterns with the number of the day. They make their own discoveries with patterns, in-variance of number, counting and thinking logically.

On another day, they wanted to explore the number "5," and they wanted to use goldfish, but we only had one color of them, so instead of arranging patterns, their task was to arrange 5 goldfish in various different ways. In this way they can get an idea of what 5 looks like in various arrangements.

It is interesting to see how this game can continue to keep interest as they make new discoveries with different amounts of materials. We vary the types of materials as well.

Sam and James showed the concept that 7 is an odd number by showing two sets of 3, with the odd man out in the middle.

James showed the concept that we naturally can only mentally conceive of 5 and then after that branch off to adding more to 5. He had a row of 5 with 2 branching off, or 5 +2=7

Quentin is most comfortable with the number 4. Even though often he can successfully count to 10, he still becomes unsure after 4, so he split his 7 in 4+3=7

Math Games: Handfuls

In this game, it is best to have four players. Two players take handfuls of something in which there are a lot of similar items like blocks or stones. The third player will choose more or less. The fourth player decides which of the two handfuls matches the request of the third player. For example, if the third player chooses more, then the fourth player has to decide which of the handfuls has more. I was very surprised at how accurately Quentin could guess. He determined that one handful, in which we later counted had 19 in it had less than the other handful which contained 22!

source: 

• Mathematics Their Way, Mary Baratta-Lorton

Measuring with Jars

Measuring with Jars allows students to estimate how many of any type of measuring cups full of water will fill a particular jar. Estimating gets better with practice until they get to unusually shaped jars. James was surprised to find out that this jar held one measuring cup full of water.