Form I Number: Place Value: Application and Extension of Place Value (PreK-2)

"There is a fundamental discrepancy between the names of the numbers and the numbers themselves. This causes children great difficulty in trying to make sense out of large numbers." 

-Mary Baratta-Lorton, Math Their Way

 All of the following activities are in base ten. It is critical that both you and your students use the same terminology for base 10 that was used for the other bases. In this way, the earlier grouping games are linked to base ten and students receive the full benefit from the earlier games. It is fine for students to say "twelve" but reinforce the concepts by saying, "and that means one ten and two." Encourage your students to say this whenever they say or write a numeral. Without this, students rely on their memory and the skill is quickly lost through disuse.

Measuring

Have your student pick out at least 3-5 things around the house to measure with trains of Unifix cubes.

Then have him break the trains into groups of ten.

If he needs to, he can then put them on a place value board.

Have him record the total for each measurement.

Estimating and Checking

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 or goldfish crackers because it interests children. I 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 can simply be pieces of cardstock or construcion paper of various colors taped together, each color signifying a different place value. If your student has difficulty with math, is very young or just has difficulty noticing when they have collected ten, you can make the place value columns more clear by putting ten small circles in one section for the ones, ten larger circles for the tens, etc. 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 pleasurable 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 using 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. 

Counting Jars of Objects

Each student counts the number of objects in a jar onto their place value board. When he has finished, he writes the total on a piece of paper and places it in a designated place. We use a bulletin board. Other students check this total by recounting and writing on the previous piece of paper "agree" or "disagree with the  amount that the student that disagrees believes is in the jar. Have the whole family participate, even if the other members of the family are beyond this skill.

Peas in a Pod

Dump a bag of unshelled peas onto a table. First, ask them how many peas on the average are in each pea pod. Record their guesses.

Now open the pea pods and have them count how many peas are on each side, counting one side at a time and recording the numbers as an addition problem. (Number of peas on left side plus number of peas on the right side equals how many peas altogether.) Have them put each pea pod's contents in a cup and have the students place their cups on a graph according to the number of peas inside.

Base Ten Unifix Patterns

We had fun with Base Ten Unifix patterns.

He explored the number six this day.

He just picks a number to explore and adds the cubes to the place value board in groups of that number. Once he reaches ten cubes on the right-hand side, he snaps them together and puts them on the left-hand side.

Here is his cubes once he had added 6 five times.

He makes a record as he works independently, adding one group at a time.

Perimeters

For this activity, you will need records of tile and geoboard designs from exploring numbers at the number stations.

The student places Unifix cubes around the perimeter of the base design, snaps the cubes together into sticks of tens, counts them and records the total. He may repeat this many times for the various designs of six to ten.

Geoboard Design

The student makes a shape on the geoboard using one large band. At first students can cover the pegs inside the one shape with one color of Unifix cubes and the pegs on the outside with a second color Unifix cubes. They then take the Unifix cubes off and record each number and the total number of pegs on their paper.

 (Worksheet for this can be found here.)

After they have become more accomplished with counting, they can just count the pegs and record their numbers as addition problems of their own making.

The Store

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 catalogue, a supermarket flyer or make one up yourself. Begin by having students use the place value board at first and then progress to their using this sheet . 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.

Recording Number Patterns from Row, Column and Diagonal Patterns with Unifix Cubes

After exploring Row, Column and Diagonal Patterns with Unifix Cubes, you can take the same numbers to explore in a different way. This time the student records these numbers in a stair-step method on graph paper. Set up the graph paper by putting a thick black line down the middle of the paper and have ones on the right side of the line, and tens on the left.

Can you see where he made a mistake, and then tried to erase it?
It is easy to see when you make a mistake when you look at the patterns.

This picture actually shows the patterns found in base 6,
but any base can be done in this way, including base 10.
Can your student predict the continuation of the number sequence?

Recording Number Patterns from Surrounding Patterns

For this activity, you will need your student first to make some Surrounding Pattern pages.

We didn't have enough cubes of any one color, so he had to combine colors to equal  each row. This is fine as long as he doesn't get the colors confused.

Students then put the Unifix cubes back on the graph paper on top of the patterns. They then take the cubes for each row and snap the cubes together and compare the number of cubes with those used in the previous surrounding.

Student breaks the rods into rows of ten and whatever is left over.

source: 

• Mathematics Their Way, Mary Baratta-Lorton