**Elementary School Number Sense Lesson 24: Squaring a 2-Digit Number**

This concept is closely related to

**Square31-40**,

**Square3Digit**, and

**FOIL2by2Digit**. It appeared

**3 times**this year, with a median placement at

**question # 74**.

**Like our Facebook Page (**

**https://www.facebook.com/numberdojo/**

**) if you want to see new number sense posts on your wall. I will reward you with a free concept index or flashcard file of your choice. Thank you!**

**Number Dojo Level: 201**

Use a (modified) FOIL method to solve these problems. As a reminder:

**F**: product of the first digits (the two tens digits)**O**: product of the outside digits (1st number’s tens digit times 2nd number’s ones digit)**I**: product of the inside digits (1st number’s ones digit times 2nd number’s tens digit)**L**: product of the last digits (the two ones digits)

For these problems, we will go in reverse order and combine the

**OI**steps into one (since they are the same).

**Example 1: 71 x 71 = ___**

**L**: 1 x 1 =**1**; write this down.**OI**: (7 x 1) x 2 = 7 x 2 =**14**; write the**4**in front and regroup the**1**.**F**: 7 x 7 =**49**, + the regrouped 1 =**50**. Write this in front.- The answer is
**5041**.

**Example 2: 86 x 86 = ___**

**L**: 6 x 6 =**36**; write down the**6**and regroup the**3**.**OI**: (8 x 6) x 2 = 48 x 2 =**96**, + the regrouped 3 =**99**. Write the**9**in front and regroup the**9**.**F**: 8 x 8 =**64**, + the regrouped 9 =**73**. Write this in front.- The answer is
**7396**.

**Example 3: 77 x 77 = ___**

**L**: 7 x 7 =**49**; write down the**9**and regroup the**4**.**OI**: (7 x 7) x 2 = 49 x 2 =**98**, + the regrouped 4 =**102**. Write the**2**in front and regroup the**10**.**F**: 7 x 7 =**49**, + the regrouped 10 =**59**. Write this in front.- The answer is
**5929**.

**Example 4: 63 x 63 = ___**

**L**: 3 x 3 =**9**; write this down.**OI**: (6 x 3) x 2 = 18 x 2 =**36**; write the**6**in front and regroup the**3**.**F**: 6 x 6 =**36**, + the regrouped 3 =**39**. Write this in front.- The answer is
**3969**.

**Example 5: 72 x 72 = ___**

**L**: 2 x 2 =**4**; write this down.**OI**: (7 x 2) x 2 = 14 x 2 =**28**; write the**8**in front and regroup the**2**.**F**: 7 x 7 =**49**, + the regrouped 2 =**51**. Write this in front.- The answer is
**5184**.

**Up Next for Elementary School: AddSeqConsec**