Ordering decimals in a real world context!

Students worked in the media center with decimals today! After learning about the Dewey Decimal system from LMS, Cary Hanson, students put their ordering decimal skills to work!

Decimals to Fractions!

After working our way through Mystery of the Meter, a Cathy Fosnot context for learning, students are working with base-ten blocks, Cuisenaire rods, and area models to make sense of decimals.

Students were provided with a series of problems and through analysis, problem-solving and talk, were able to further develop their understanding of decimals and multiplication.

Up until now, students have believed that when we "multiply" the numbers get bigger. However, this does not hold true when we multiply decimals.  Another big takeaway is that we can operate with whole numbers and then place the decimals where it would be reasonable.

It was a huge day in math today!

After a variety of "tests" to see if we can multiply decimals like we add decimals, students were able to make some sturdy generalizations. And let me say, we tried many problems when "bringing down the decimal" worked-- just like it did when we were doing addition with decimals. But there were always some counter examples that we had to test, retest, reflect, and analyze with other problems.  

We were able to see that when we multiply a decimal with another decimal, we are creating a smaller value. We observed that there is a relationship with the number of places after the decimal and the place of the value in the product. 

     We continued to work with decimals as fractions. We discovered that, unlike adding fractions, when we multiply fractions we multiply the numerators but have to also multiply the denominators!  Whew! So many great connections today. Too many to jot down here! I can say with joy that many students had many "aha" moments today!

Making sense of multiplication and decimals

Here are some links to support our math understanding for Topic 7
Start with the first link and work your way down as you gain a greater understanding.

Learn Zillion Area Model w/ Multiplying decimals

Learn Zillion Multiplying a whole number and a decimal

Traditional Algorithm for Multiplying Decimals

Students continue to build their understanding of place value

Students continue to grapple with the relationship between the tenths, hundredths, and thousandths place. It is an abstract concept and one that many students struggle with.

When thinking of a number that is greater than 0.23 but less than 0.24 prompted further practice.  

Using a number line is one visual that may support students when developing their understanding of how these quantities are related.  We will keep working on developing this concept in our next unit!

Place Value and Decimals

Students were challenged to represent 0.001 using Base Ten Blocks and a model.  Working in small groups, students worked to share their thinking.

                                 
Students present their models to show what the "whole" is. Then, they label 0.1, 0.01, and 0.001. I learned a lot from their work and where their current understanding is with decimals!

Mystery of the Meter

Students learn that they are going to do an investigation!

What are these dials? What do they mean?

Students discussed their observations.

Students make posters to explain their thinking.

         

        

Students then shared their posters and thinking with the class. Tomorrow, we will

continue the Mystery of the Meter!