CCSS Math: 5.NBT.B.7
Start with simple problems like 0.2 + 0.4 and build to more complex problems like 10.3 + 36.75.
The problems go from easier to more difficult, and along the way, there are examples and explanations for the times you get stuck. You'll learn the most if you look at the times you're confused as chances to learn!
Let's start by adding two tenths together.

# Section 1: Adding tenths less than one

Example: $0.1 + 0.3$
One strategy is to think in terms of tenths:
$\phantom{=}0.1 + 0.3$
$=1$ tenth $+ ~3$ tenths
$=4$ tenths
$=0.4$
Another strategy is to use tenths grids:
$\blueD{0.1} + \greenD{0.3} = 0.4$
Problem 1a
$0.5 + 0.4 =$

Beautiful, let's move on to problems with whole numbers and tenths.

# Section 2: Adding whole numbers and tenths

Example: $4 + 5.7$
Let's break $5.7$ down by place value:
\begin{aligned}&\blueD{4}+\greenD{5.7}\\ \\ =&\blueD{4}+\greenD{5}+\greenD{0.7}~~~~~~~~\small{\gray{\text{Break 5.7 into 5 and 0.7.}}}\\\end{aligned}
\begin{aligned} =&(\blueD{4}+\greenD{5})+\greenD{0.7}~~~~~~~~\small{\gray{\text{Group the whole numbers together.}}}\\ \\ =&9 + 0.7\\\end{aligned}
$= 9.7$
Problem 2a
$6.4 + 2 =$

Excellent, next up are problems where both numbers have a whole number and a tenth.

# Section 3: Adding tenths greater than one

Example: $14.3 + 5.2$
Let's break both numbers down by place value.
\begin{aligned}&\blueD{14.3}+\greenD{5.2}\\ \\ =&\blueD{14}+\blueD{0.3}+\greenD{5}+\greenD{0.2}\\\end{aligned}
\begin{aligned} =&(\blueD{14}+\greenD{5})+(\blueD{0.3}+\greenD{0.2})~~~~~~~~{\gray{\text{Group the whole numbers and the tenths.}}}\\ \\ =&19 + 0.5\\\end{aligned}
$= 19.5$
So, $14.3 + 5.2 = 19.5$.
Problem 3a
$3.7 + 22.1 =$

Rockin'! Let's move on to adding hundredths.

Example: $0.24 + 0.52$
One strategy is to think in terms of hundredths:
$\phantom{=}0.24 + 0.52$
$=24$ hundredths $+ ~52$ hundredths
$=76$ hundredths
$=0.76$
Another strategy is to use hundredths grids:
$\blueE{0.24} + \goldB{0.52} = 0.76$
Problem 4a
$0.31 + 0.64 =$

Sweet, now we're ready to solve problems with hundredths, tenths, and whole numbers.

# Section 5: Adding whole numbers, tenths, and hundredths

Example: $5.21 + 8.68$
Let's break both numbers down:
$\phantom{=}\blueD{5.21}+\greenD{8.68}$
$=\blueD{5} + \blueD{0.2}+\blueD{0.01}+\greenD{8}+\greenD{0.6}+\greenD{0.08}$
$=(\blueD{5} +\greenD{8})+(\blueD{0.2} +\greenD{0.6}) + (\blueD{0.01} +\greenD{0.08})~~~~~~~~\small{\gray{\text{Group by place value.}}}$
$=13 + 0.8 + 0.09$
$=13.89$
Problem 5a
$42 + 4.27=$

Great, let's finish with a few more challenging problems.

# Section 6: Challenge problems

Example: $10.16 + 36.75$
Let's break both numbers down by place value:
$\phantom{=}\blueD{10.16}+\greenD{36.75}$
$=\blueD{10} + \blueD{0.1}+\blueD{0.06}+\greenD{36}+\greenD{0.7}+\greenD{0.05}$
$=(\blueD{10}+\greenD{36})+(\blueD{0.1} +\greenD{0.7}) + (\blueD{0.06}+\greenD{0.05})~~~~~~~~\small{\gray{\text{Group by place value.}}}$
$=46 + 0.8 + 0.11$
$=46.91$
Problem 6a
$2.59 + 5.16=$