(1) developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions)
(2) extending division to 2-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations
(3) developing understanding of volume"
(excerpt from the Common Core State Standards Initiative website)
Multiplying decimals
Let me count the ways...
3 x 0.45
Traditional Method Lattice Method
Place Value Chart Graphic Organizer
These are just 4 ways that children are being taught how to multiply numbers with decimals.
Traditional Method- This is the way multiplying used to be taught. It is a method of procedure, and does not necessarily represent true understanding of what multiplying with decimals means.
Lattice Multiplication- This method uses a series of boxes and diagonal lines. This method allows students to multiply out of order. All they need to do make sure the answer in each box corresponds to the two numbers each box represents. They would then write the first digit of the answer above the diagonal line and the second number underneath the diagonal line. Students then need to add numbers along the diagonal lines. When it comes to multiplying with decimals, students need to find the decimals in the original numbers and follow them along the lines until they meet (see the lime green line in this example). This is another method of procedure. It does make it easier to find mistakes in a students work as each step is broken down into smaller steps.
Place Value Chart- Students use "disks" or dots. In this example, students need to show 3 groups of 45 hundredths (3 groups of 4 tenths and 3 groups of 5 hundredths). Then students begin with the smallest place value and bundle groups of 10. Once they make a bundle, they move it one place value to the left (representing it with one "disk" or dot). When all the bundling has been completed, students simply look at how many "disks" or dots are in each place value and copy the numbers in the correct place value columns. This method helps students visualize what is happening when they multiply decimals.
Graphic Organizer- Students begin by drawing an area model with the appropriate number of boxes (in this case, 2). Along the left side of the model, students write how many groups (in this case, 3). Along the top, students write how many of each place value they are multiplying (4 tenths and 5 hundredths). Students then multiply individual numbers and write the answer with the correct place value label. To finish, students add the numbers inside the aread model (in this case, 12 tenths and 15 hundredths). This method helps students to gain a deeper understanding of what it means to multiply decimals.
More questions on different ways to multiply decimals and begin to really understand what that means? Ask away!
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