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Big Ideas for DecimalsBig Idea #1: Decimal numbers are another way of writing
fractions. Relationship is key.
Big Idea #2: Base-ten place-value system extends infinitely in two directions. Between any two place
values, the ten-to-one ratio remains the same.
Big Idea #3: Decimal point is a convention to indicate the units position. The unit is to the left.
Big Idea #4: Percents are simply hundredths and so they are a third way of writing decimals and fractions. (MS)
Big Idea #5: Adding and subtracting with decimals is a simple extension from whole numbers.
From Van de Walle book
I’m hoping you won’t feel this way during the presentation but if you do PLEASE ask
questions.
3.75 3
Are these different?
Why or why not? Explain your thinking
Telling students that 0.75 is the same as ¾ can be very
confusing. We need to make sure we are clear that
numerations for decimals and fractions are systems that represent the same idea.
Base-Ten FractionsIt is important to provide models for these fractions using the same conceptual approaches that were used for fractions such as thirds and fourths.
What about money as a
decimal model?
Hmmm. Not so much. It is almost exclusively
a two-place system. Students’ initial
contact should be more flexible. Money is
a good application of decimal numeration.
Decimals as QuantitiesJust as students experienced numbers as quantities in the early grades, they need to experience decimals as quantities. These quantities are just in terms of tenths and hundredths.
When we explore decimals as quantities we need to make connections to place value. Decimals are an
extension of the place value system.Ex: 0.65 is read “sixty-five hundredths” but we also
need to be explicit in the use of place value. This must also be seen as 6 tenths and 5 hundredths.
Place Value of Whole NumbersReview with a partner. What is the relationship between the value of any two adjacent positions with our number system?
Tools for DecimalsShowing quantities with decimal numbers can be tricky.
One tool - Base Ten blocks.
Another tool – Decimal Squares
Decimal SquaresPull out just the red decimal squares. Make sure you and your neighbor can explain what is the “whole” and what are the “parts.”
110
This fraction can be easily represented using base ten notation.
Now the naming makes sense – the place is called tenths because the one was divided into ten smaller equal pieces. We call these tenths.
Base Ten Notation
hundreds tens ones tenths
symmetry in Base Ten naming
Decimal SquaresThis decimal square can be written as:
110 0.1 one-tenth
Pull out these decimal squares.
Write the fraction, decimal, and word form for both decimal squares.
Decimal SquaresTake out three-tenths and seven-tenths.
Which decimal is closer to one? How do you know?
Shuffle your decimal squares. Pull out two of them and tell your neighbor the inequality statement.
Decimal SquaresPull out just the green decimal squares. Review with your neighbor what is the “whole” and what are the “parts.”
30100
What is the decimal notation for this fraction?
What is the fraction for this picture?
Look at the three-tenths and the thirty-hundredths.
How are the same and howare they different?
Base Ten Notation
hundreds tens ones tenths hundredths
Explore resources
Close to One Materials: Decimal cards; pencil & paperPlayers: 2-4Directions:1. One student (dealer) shuffles the deck and gives one
card face down to each player.2. After each student looks at their cards, players ask the
dealer for as many extra cards as they want—giving one at a time.
3. After every player has the cards they want, all players show their set of cards.
4. The player whose sum of decimals is closest to 1, but does not go over, wins one point. The first player to win five points wins the game.
Reflection
hundreds tens ones tenths hundredths
Talk with your neighbor. What was new learning for you about decimals?
