Home School Life Journal From Preschool to High School

Home School Life Journal ........... Ceramics by Katie Bergenholtz
"Let us strive to make each moment beautiful."
Saint Francis DeSales

Decimals (3-6)

If you get students to search problems and answers for patterns leading to rules for the correct placement of the decimal point in decimal problems and they are allowed to discover the rules for themselves, their learning will be a product of understanding, not memorization.
In the past we have assigned values to our counting board and coordinated amounts and colors.
At first we used beans and grouped them in cup, bowls and large #20 tin cans to represents ones, tens, hundreds and thousands. We next made bean sticks and rafts so we didn't have to always count out the beans. We then matched them to Math-U-See blocks, matching the colors of the counting board to the block amounts.
Now we are taking this one step further and assigning fractional values to the beans, cups and bowls on the bean trading board in  preparation for using it to represent decimal fractions.

Beans, Cups, Bowls and Cans

James has begun to learn about decimals. We began by assigning values to beans, cups and bowls on a bean trading board in preparation for using it to represent decimal fractions. When we were working with fractions, we made up different Unifix cube sticks and called them one. We now did the same thing with beans on the trading board. If one cup on the trading board is now one, instead of ten, then one bean is 1/10. We thought of it as if the cup represented a class at co-op which had 10 students in it. The class would be one, and each student would be 1/10 of the class. If we decided that the bowl represented one (instead of 100 as it had in the past), then we could look at it as one co-op school, in which each class was 1/10 of the co-op (assuming that the co-op had 10 classes in it) and each student was 1/100 of the co-op students. After this introduction, we practiced ways of writing fractions whose denominators are powers of ten. We wrote them as fractions and we wrote them as decimals.


We then practiced the same concept using different materials. We assigned fractional values using plastic colored chips on the counting/trading board. We then created decimal problems for addition and subtraction using the counting/trading board by rolling a die for each column. Since he already knows how to create addition and subtraction problems in this way, the only difficulty he might encounter is where to place the decimal. Some students may find placing the decimal point correctly is obvious, but others might need to be asked questions to come to this understanding.

"How can you tell where the decimal point goes? Could you make up a rule to predict where it goes for addition and subtraction problems?"


Today we got out a piece of 10 x 10 graph paper to make a matrix.
Just like when we played with fractions and worked with Unifix cube sticks, and called them one, we used Math-U-See blocks today, and called them one. You could use Unifix cube sticks, bean sticks or whatever you have as a base-10 manipulative, since we are working with decimals, which are all working with divisions of ten. We then chose the blue ten rod and called it one.
"What is the fraction of one division of this rod?"
"Since the fraction has ten as a denominator, you can write it as a decimal. Let's write it along the side beside the first block on this graph paper."
"What fraction would two spaces or divisions be?"
"Two tenths."
"Let's write that next to the second block on our matrix."
We continued on, filling in the whole side. He especially enjoyed writing in the last square (1.0) because we called the whole rod one, and he found delight in ending up with both a numeral which represented one and .9 +.1 =1.0, or 10 tenths.
 We then completed the same notations on top of the blocks along the row of spaces at the top of the graph.
Now we looked at the whole graph paper as a multiplication matrix, and began the multiplication of decimals.
"How many squares are there altogether on the matrix?"
"If I say the whole matrix is one big square, what fraction of the big square be to the little square?"
"How would you write that as a decimal?"
"Put that in the first square."
"Can you fill out other squares in the matrix?"
He picked out a few and added their numbers into the matrix. We shall work on this again, until it is all filled in, but I don't anticipate that being too hard for him at this point.
Then I will give him a new matrix of 100 x100, but it won't be necessary for him to completely fill this one too. I will give him a few problems to work out on it instead such as
.01 x .01= or .12 x .12=
He will be able to learn how to add, subtract and multiply decimals, not because he was told how, but because he was directed where to look and saw for himself what needed to be done.


  1. What a neat idea! Love anything to do with Math for little ones!

  2. I'm bookmarking this one! Great idea!

  3. Fantastic way to introduce decimals! I like the new photos in the header too. :-)


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