**High School Number Sense Lesson 22: Adding Squares with One Number being a Triple of the Other**

This is yet another example of why I believe in giving number sense concepts nicknames. And once again, the solution is probably quicker than reading the title. This concept showed up

**15 times**this year on high school tests--almost always between

**questions 21 & 25**, inclusive. I mentioned a couple of days ago that this skill is my personal favorite--it tends to come with the

**brightest "light bul**

**b"**

**moments**when I teach it.

__Note__: You may want to review Square11-20 and Square21-30 in conjunction with this lesson.**Number Dojo**

**Level: 169**

This is the easiest of several different questions about

**adding squares**. Look for problems where one of the numbers is

**three times** the other, such as:

**7**

OR

^{2}+ 21^{2}

33

33

^{2}+ 11^{2}**Why it Works:**

I usually hesitate to show the proofs behind these skills, because when you take a number sense test, I don't want you wasting time thinking about the math behind the math. I want you to solve the problems

**as quickly as you can**(which is why I created this blog). But this one is so cool, I want you to know the background. Here goes:

**a**

= a

= a

= a

= 1(a

= (1 + 9)(a

= 10(a

^{2}+ (3a)^{2}= a

^{2}+ (3a)(3a)= a

^{2}+ (3)(3)(a)(a)= a

^{2}+ (3 x 3)(a x a)= 1(a

^{2}) + 9(a^{2})= (1 + 9)(a

^{2})= 10(a

^{2})**How to Solve it:**

- Realize this is an
**AddSquareTrip**problem (because the bigger number is 3 times the smaller). - Square the smaller number.
- Add a zero at the end.
- You are done. (
*Why are you still reading this?*)

**Example 1:**

**3**

^{2}+ 9^{2}1.

**3**is the smaller number. 3

^{2}=

**9**.

2. Add a zero at the end. The answer is

**90**.

*You could have figured out that 3*

But you won't be able to do that quickly with the other examples.

^{2}= 9 and 9^{2}= 81, and 9 + 81 =**90**.But you won't be able to do that quickly with the other examples.

**Example 2:**

**13**

^{2}+ 39^{2}1.

**13**is the smaller number. 13

^{2}=

**169**.

2. Add a zero at the end. The answer is

**1690**.

**Example 3:**

**27**

^{2}+ 9^{2}1.

**9**is the smaller number. 9

^{2}=

**81**.

2. Add a zero at the end. The answer is

**810**.

**Example 4:**

**18**

^{2}+ 54^{2}1.

**18**is the smaller number. 18

^{2}=

**324**.

2. Add a zero at the end. The answer is

**3240**.

**Example 5:**

**75**

^{2}+ 25^{2}1.

**25**is the smaller number. 25

^{2}=

**625**.

2. Add a zero at the end. The answer is

**6250**.

**Example 6:**

**12 x 12 + 36 x 36**

*(Don't let the appearance fool you. This is the same as*

**12**.)^{2}+ 36^{2}1.

**12**is the smaller number. 12

^{2}=

**144**.

2. Add a zero at the end. The answer is

**1440**.

**Here's a free worksheet to help you practice AddSquareTrip:**

addsquaretrip.pdf |

**Up Next for High School: AbsoluteValue**