First, students will learn how to add two-digit numbers by adding the tens and ones separately. For example, \(52 + 43 = 50 + 40 + 2 + 3 = 90 + 5 = 95.\)

Breaking apart 2-digit addition problems by Khan Academy

Break apart 2-digit addition problems by Khan Academy

Next, students will learn how to add two-digit numbers by making tens. For example, \(53 + 17 = 50 + 20 = 70.\)

Watch these Khan Academy videos:

Add 2-digit numbers by making tens by Khan Academy

After that, lead this investigation. Watch this to learn how. After students have found a couple blotches, get them to notice the numbers must add to the total number of squares in the grid. Conclude by leading this investigation. Watch this and this to learn how.

Next, give your students this challenge:

Make the equation below true by replacing each letter with a unique digit (0-9).

$$BA = A \times A \times A$$Here's the solution:

\(A \times A \times A = A^3.\) Thus, \(BA = A^3.\) Hence, \(BA\) is a two-digit cubed number, ending in \(A.\) By listing the first few cubes, we find \(3^3 = 27\) and \(4^3 = 64\) are the only two-digit cubed numbers, and only \(64 = 4^3\) fits \(BA = A^3.\) In conclusion, our equation is \(64 = 4 \times 4 \times 4.\)

Conclude by leading this investigation:

Puppet Puzzle (counting, logic, proof)

by MathPickle

2.NBT.B.5: Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.