Download Open Number Line Banner - Decimals

Open Number Line Banner - Decimals
Congratulations on your purchase of this Really
Good Stuff® Open Number Line Banner Decimals—an introduction to the open number line
strategy for solving addition and subtraction
problems with decimals.
This Really Good Stuff® product includes:
• Open Number Line Banner - Decimals,
laminated
• This Really Good Stuff® Activity Guide
Displaying the Open Number Line Banner Decimals
Before displaying the Open Number Line Banner Decimals, make copies of this Really Good Stuff®
Activity Guide, cut apart the reproducibles, and file
the pages for future use. Or, download another copy
of it from our Web site at www.reallygoodstuff.com.
Hang the Banner where students will be able to see
it easily.
Introducing the Open Number Line Banner Decimals
As you draw a horizontal line on the board and label
it with the numbers 1, 2, 3, and 4, remind students
that the number line shows the numbers that we
count. Then draw arrows on each end and review
that the arrows indicate that the number line goes
on forever in both directions. Explain that in between
each whole number there are an infinite number of
places that we can label with fractions or decimals
because they are part of a whole number. For
example, as you mark 1.5 on your number line, remind
students that 1.5 is halfway between 1 and 2. Then
ask students where the number 2.8 should be
marked along the number line. Show additional
decimals along the number line, if necessary.
Emphasize that the open number line is a powerful
problem-solving tool because it will let them use
whatever part of the number line they need.
Pointing to the Open Number Line Banner Decimals, indicate that you are going to use the
Banner to show them how to use an open number
line to solve problems that require addition and
subtraction of decimals. Read the first problem on
the Banner. Say, “From this, I know that Tory starts
with 4.8 meters and needs 0.64 meters more. I
need to find how much fabric she needs altogether.
First, I need to find 4.8 on the number line and then
add or move up the number line by 0.64. The whole
number of 4 tells me that 4.8 is greater than 4 and
less than 5 and the .8 tells me that it is between 4
and 5.” Point to 4.8 on the Banner. “Next, I need to
think about getting to a ‘friendly’ number. When I
work with decimals, I try to get to whole numbers for
‘friendly’ numbers. I know 4.8 is eight tenths away
from 4, so it is two tenths away from 5. My first
jump will be to 5, and I know two tenths can be
written as 0.2.” Point to the +0.2 arrow and say, “I
have moved two tenths of the 0.64 that I need to
move up the number line, so I need to figure out the
difference between two tenths (0.2) and sixty-four
hundredths (0.64).” Think aloud and say, “Two
tenths is equal to twenty hundredths and the
difference between 20 and 64 is 44, so I need to
move forty-four hundredths (0.44) farther up the
number line. Because I am starting from a friendly
whole number, it is easy to make this jump.” Move
your finger from 5 to 5.44 and say, “Tory needed a
total of 5.44 meters of fabric.”
Read the next problem on the Banner. Think aloud
and say, “I know Samantha had a race time of 55.28
seconds and that she wants to shave 3.1 seconds
off her time. That means she wants to be 3.1
seconds faster than she is right now. To solve this, I
need to start at 55.28 and subtract 3.1 or jump 3.1
down the number line. Since I’m subtracting and
moving down the number line, the larger number in
the problem (55.28) is labeled at the right-hand end
of the line. As I think about jumping 3.1 down the
number line, I need to get to a friendly number. In
this problem, the closest friendly number is 55, so I
am going to subtract 3. I know 55 – 3 = 52,
therefore, 55.28 – 3 = 52.28. I need to move one
All activity guides can be found online:
Helping Teachers Make A Difference®
© 2011 Really Good Stuff
®
1-800-366-1920 www.reallygoodstuff.com Made in USA #159714
Open Number Line Banner - Decimals
tenth (0.1) farther down the number line, so I need
to think that twenty-eight hundredths (.28) minus
ten hundredths (.10) equals eighteen hundredths, so
I end at 52.18. We know Samantha’s goal is 52.18
seconds.”
Introducing the Adding and Subtracting Decimals
Along an Open Number Line Reproducible
Copy and distribute the Adding and Subtracting
Decimals Along an Open Number Line Reproducible.
Write the first problem 6.8 + 2.35 = on the board.
Draw a number line and say, “The addition sign tells
us that we will be making jumps up the number line.”
Make an exaggerated arrow at the right-hand end of
the line. Say, “Let’s start with the bigger number of
6.8,” and write it on the left-hand side of the
number line.” Say, “The closest whole number, or
friendly number, is 7, so let’s jump there. That’s a
jump of +0.2.” Label the jump. Then say, “Because we
jumped an extra two tenths to reach the whole
number of 7, we need to subtract it from 2.35, that
is 2.35 – .2 = 2.15. That means, we have 2.15 left to
jump, and 7 plus 2.15 is 9.15.” Label 9.15 and the
jump of +2.15.
identify 58 as the closest “friendly” number and say,
“Let’s get to 58 because that is the closest whole
number and from there we can jump whole numbers:
from 58 to 59 to 60 to 61. This means we have
already jumped 3.2 up the number line. How much do
we still need to jump? (Guide them, if necessary, to
do: 3.6 – 3.2 = .4.) That’s right, from 61, we need to
jump .4 more. So we know that Felix weighed 61.4 at
the end of fifth grade.”
Answers: 1) 61.4 pounds, 21.8 points, 38.88
seconds, 9.95 feet
Thinking Flexibly
At times, it may make sense to “over jump.” For
example, write the problem 3.4 + 2.98 = on the
board. Say, “This problem asks us to jump up 2.98,
which is very close to the whole number 3, so we can
jump up 3 to 6.4 and then back .02 to 6.38.”
Challenge students to come up with multiple ways
to solve the same problem. Have students compare
their work with a partner and point out the
similarities and differences in their strategies.
Answers: 1) 9.15, 2) 4.12, 3) 44.58, 4) 14.13, 5)
30.2, 6) 14.82
Introducing the Decimals Problem Solving Along an
Open Number Line Reproducible
Copy and distribute the Decimals Problem Solving
Along an Open Number Line Reproducible. Read the
first problem together. Then say, “This problem is
asking us to find how much Felix weighs now, so we
need to add 57.8 and 3.6.” Label 57.8 along the
number line, and explain that the class will need to
jump 3.6 up the number line. Lead students to
Making Connections to Other Strategies
Have students solve one of the problems using other
addition or subtraction strategies. Help students to
recognize that there are multiple ways to solve the
same problem. Encourage them to make connections
between the two methods. Urge them to notice
things about the order they solve the problem and
the place value. Remind students that the open
number line can help them keep track of their jumps
a little easier.
All activity guides can be found online:
Helping Teachers Make A Difference®
© 2011 Really Good Stuff
®
1-800-366-1920 www.reallygoodstuff.com Made in USA #159714
Adding and Subtracting Decimals Along an Open Number Line Reproducible
Helping Teachers Make A Difference®
© 2011 Really Good Stuff® 1-800-366-1920 www.reallygoodstuff.com Made in USA #159714
Decimals Problem Solving Along an Open Number Line Reproducible
Helping Teachers Make A Difference®
© 2011 Really Good Stuff® 1-800-366-1920 www.reallygoodstuff.com Made in USA #159714