We included HMH Into Math Grade 5 Answer Key PDF Module 14 Lesson 1 Represent Decimal Addition to make students experts in learning maths.
HMH Into Math Grade 5 Module 14 Lesson 1 Answer Key Represent Decimal Addition
I Can use concrete models or drawings to represent decimal addition.
Spark Your Learning
A baker puts some flour onto a food scale as shown. What will the scale read if the baker adds another 0.29 pound of flour to the bowl?
Use a visual model to help you find the weight after the baker adds 0.29 pound of flour to the bowl. Draw to show your thinking.
Weight is 0.60 pound,
Given a baker puts some flour onto a food scale as shown.
The scale read if the baker adds another 0.29 pound of flour to the bowl,
Used a visual model to help me find the weight after
the baker adds 0.29 pound of flour to the bowl.
Drawn to show 0.4 + 0.29 = 0.69 pound above.
Turn and Talk How can you represent 0.4 in tenths and in hundredths? How did you represent tenths and hundredths in your visual model?
We take full as 1 whole in that 0.4 is a decimal number with a
place value of tenth, so the number word for 0.4 is four tenths,
Represented tenths and hundredths in my visual model above.
What will the scale read if the baker adds another 0.8 pound of flour to the bowl?
Use base-ten blocks to help you find the weight after the baker adds the flour. Let one flat represent one whole and one long represent one tenth.
A. Do you think the weight on the scale will be less than or greater than 1.0 pound? How do you know?
The weight on the scale will be greater than 1.0 pound,
We have 0.3 lb and if we add 0.8 pound more we will get
1.1 pounds which is greater than 1.0 pound.
B. What base-ten blocks do you use to show 0.3 and 0.8?
3 one tenths and 8 one tenths,
3 one tenths and 8 one tenths to show 0.3 and 0.8.
C. What do you get when you add the tenths?
1 whole and 1 tenths,
When we add the tenths we got 1 whole and 1 tenths.
D. Do you need to regroup? Explain.
Yes, When adding,
When adding 0.3 lb and 0.8 pound we get 1 whole and
0.1 so we need to regroup tenths to whole.
E. What is the weight after the baker adds the flour to the bowl?
Given 0.3 lb, if the baker adds another 0.8 pound of
flour to the bowl the weight after the baker adds the flour
to the bowl is 0.3 lb + 0.8 pound = 1.1 pounds.
Turn and Talk How is adding decimals using base-ten blocks like adding whole numbers using base-ten blocks?
The hundreds block as one whole,
Tens block as tenths,
To use base ten blocks to add decimal numbers,
we need to think of the base ten blocks a little differently.
We think of the hundreds block as one whole.
The tens block as tenths because we would need
ten of these to make one whole. Finally, the ones block as
hundredths because you would need a hundred of these
to make one whole.
The baker puts dried fruit onto the food scale. The scale reads 1.86 pounds. What will the scale read if the baker adds another 1.28 pounds of dried fruit to the scale? Use quick pictures to help you find the answer.
A. Draw a quick picture to represent each weight.
Drawn a quick picture to represent each weight as shown above.
B. How can you regroup the place values shown in your picture?
Adding 1.86 and 1.28 using tenths and whole,
1 whole 8 tenths and 6 hundreths plus
1 whole 2 tenths and 8 hundreths equals and
regrouped as 3 wholes 1 tenth and 4 hundreths.
C. Draw a quick picture to represent the total weight.
Drawn a quick picture to represent the total weight as
D. What is the weight of the dried fruit on the scale?
The total weight of the dried fruit is 3.14 pounds,
The weight of the dried fruit on the scale is 3.14 pounds.
Turn and Talk When performing decimal addition, when and how do you regroup?
Adding decimals means finding the sum of two or
more decimal numbers. Although adding decimals is
similar to the regular addition of whole numbers,
there are certain rules that need to be followed while adding them.
Adding decimals is similar to the usual addition of whole numbers.
We know that a decimal number is a number with a
whole number part and a fractional part which is
separated by a decimal point. However, this does not
change the rules for the addition of decimal numbers.
For this, we need to align the decimal numbers according
to their place values one below the other, keeping the
decimal point intact, and then add the numbers.
We should remember that the decimal place value chart
has some extra place values, like, the place value just after
the decimal point is called tenths, followed by hundredths,
thousandths and so on.
Rules for Adding Decimals:
While adding decimals, we need to remember some
rules that would be helpful and make the addition easier.
- Align the decimal numbers in such a way that they are placed in the correct place according to their place values.
- Always convert the decimal numbers to like decimals, wherever needed.
- Add zeros in the places wherever the length of the decimal numbers is not the same.
- Now, add the numbers and place the decimal point aligned with the given decimal points.
At the store, Jo buys 0.8 pound of white mushrooms and 0.2 pound of brown mushrooms. How many pounds of mushrooms does she buy? Draw a visual model to find your answer.
Jo buys 1.0 pound of mushrooms,
Given at a store Jo buys 0.8 pound of white mushrooms and
0.2 pound of brown mushrooms, So number of pounds of mushrooms
does she buys are 0.8 pound + 0.2 pound = 1.0 pounds,
Drawn a visual model of 0.8 pound + 0.2 pound = 1.0 pounds above.
On Your Own
The digital caliper shows the width of a foreign coin as 25.75 millimeters. What is the combined width of two of these coins?
Given the digital caliper shows the width of a foreign coin as
25.75 millimeters. The combined width of two of these coins
is 25.75 millimeters + 25.75 millimeters = 51.50 millimeters.
Attend to Precision A runner’s first sprint time for a 100-meter race is 10.76 seconds. The runner’s second sprint time is 10.85 seconds. What is the combined time for the two sprints? Which place value(s) require regrouping?
Hundreths, tenths and whole units and tens needs regrouping,
Given a runner’s first sprint time for a
100-meter race is 10.76 seconds,
the runner’s second sprint time is 10.85 seconds,
the combined time for the two sprints is
10.76 seconds + 10.85 seconds = 21.61 seconds.
We need to regroup hundreths place as 1,
tenths place as 6 and whole units place as 1 and
tens place as 2.
Add. Draw a visual model.
1.05 + 0.25 = ___________
Added 1.05 to 0.25 we get 1.30, drawn a visual model
_________ = 0.74 + 0.4
Added 0.74 to 0.4 we get 1.14, drawn a visual model
Use Tools Use the decimal model to show the addition of 0.16 and 0.25. Explain how you used the decimal model.
Used decimal model to show addition of
0.16 and 0.25 = 0.41 as shown above.
I’m in a Learning Mindset!
How can I make sure that my visual model represents the situation?
We do normal addition match and check with the visual
model representation if both are same I make sure that
my visual model represents the situation correctly.