Getting to the Point
with Decimal Fractions
Allan Turton
PROFESSIONAL LEARNING
www.origoeducation.com
Montana Common Core Standards – Decimal Fractions
4.NF
Understand decimal notation for fractions, and compare decimal fractions.
5. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this
technique to add two fractions with respective denominators 10 and 100. For example, express 3/10 as
30/100, and add 3/10 + 4/100 = 34/100.
6. Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100;
describe a length as 0.62 meters; locate 0.62 on a number line diagram.
7. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are
valid only when the two decimals refer to the same whole. Record the results of comparisons with the
symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.
4.MD
Solve problems involving measurement and conversion of measurements from a larger unit to a
smaller unit.
2. Use the four operations to solve word problems within cultural contexts, including those of Montana
American Indians, involving distances, intervals of time, liquid volumes, masses of objects, and money,
including problems involving simple fractions or decimals, and problems that require expressing
measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using
diagrams such as number line diagrams that feature a measurement scale.
5.NBT
Understand the place value system
1. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it
represents in the place to its right and 1/10 of what it represents in the place to its left.
2. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10,
and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a
power of 10. Use whole-number exponents to denote powers of 10.
3. Read, write, and compare decimals to thousandths.
a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded
form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).
b. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <
symbols to record the results of comparisons.
4. Use place value understanding to round decimals to any place.
5.NBT
Perform operations with multi-digit whole numbers and with decimals to hundredths.
7. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings within
cultural contexts, including those of Montana American Indians, and strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction; relate the strategy
to a written method and explain the reasoning used.
© ORIGO Education
1
Ones
Tenths
Total
Ones
Tenths
Total
Ones
Tenths
Total
Ones
Tenths
Total
Ones
Tenths
Total
Ones
Tenths
Total
Tenths
Hundredths
Tenths
Hundredths
Total
Tenths
Hundredths
Total
Total
Burnett, J. & Tickle, B. (2014). Fundamentals: Red Level, pages 58-59. ORIGO Education.
58
Fundamentals
© ORIGO Education
Tenths
Hundredths
Total
Tenths
Hundredths
Total
Tenths
Hundredths
Total
© ORIGO Publications Permission is given to instructors to reproduce this page for classroom use.
Addition and subtraction
2
Multiplication
1. Multiply the parts to figure out the total weight for each purchase.
b.
a.
(
×
)+(
×
+
(
)
=
4.2 kg
buy 9 bags
7.3 kg
buy 5 bags
×
)+(
+
kg
×
=
)
kg
2. Write the products. Shade parts of the squares to match.
a.
b.
0.5 × 0.3 =
c.
0.4 × 0.5 =
0.6 × 0.8 =
3. W
rite the common fractions that you could multiply to figure out each product.
Then complete the equations.
a.
b.
0.7 × 0.05 =
×
0.4 × 0.09 =
=
c.
×
=
d.
0.8 × 0.03 =
×
0.6 × 0.07 =
=
×
=
ORIGO Stepping Stones: Grade 5, Module 10
© ORIGO Education
3
Division
1.
Complete the parts and then write the answer.
a. $8.60 ÷ 4 is the same as
$
÷ 4 plus
¢ ÷ 4 =
$
b. $15.50 ÷ 5 is the same as
$
÷ 5 plus
¢ ÷ 5 =
$
c. $12.90 ÷ 6 is the same as
$
÷ 6 plus
¢ ÷ 6 =
$
2. Each large square represents one whole. Shade or outline parts to help you figure
out the quotients. Then complete the equations.
b.
a.
2 ÷ 0.2 =
2 ÷ 0.4 =
3. Read the equation. Then complete the picture to help you write the answer.
a.
b.
8 ÷ 0.2 =
× 0.2 =
1
×8
× 0.05 =
×8
× 0.2 =
4 ÷ 0.05 =
1
×4
8
×4
× 0.05 =
4
4. Write the missing numbers so the statements are true.
a.
0.9 ÷ 0.3
tenths ÷
tenths
÷
=
0.6 ÷ 0.2
tenths ÷
tenths
÷
=
b.
ORIGO Stepping Stones: Grade 5, Module 12
© ORIGO Education
4
Deci-strips
© ORIGO Education
5