In Challenge A, one week, we **defined** both the “Identity property of Addition” and the “property of zero for multiplication” (see Lesson Two of 8/7 and 7/6 Saxon Math). Then we** compared** them by asking the question, “How are these operations different? How are they similar?” We talked about **relationship **between the operations and (brought a new operation into the relationship) by asking the question, “What will happen if we multiply 2 by 1 instead of 2 by 0?” We talked about **circumstance** by asking, “If we call zero the “additive identity” in 2+0=2, then what would we call the number 1 in 2 x 1? How do these “identities” affect the circumstances of the “math problem”? We wrapped up every conversation with **testimony**, “How do we know this is true?” The answer we consistently came up with was that we work it out and check our answers. Our Saxon Math book is also a great witness. We also compared our relationship with Christ to the “Identity property of addition” and the “identity property for multiplication” by observing that no matter what the given number was in the equation, the number 0 or 1 could not change its value. That’s us, in Christ, no matter what we try to multiply or add to our relationship with Him, we cannot change our value in Him as His favor and His love is based upon His own love for us and not upon anything we bring to the equation (add or multiply) or don’t bring to the equation (subtract and divide). Our identity can truly only be found in Him. We talked about Ephesians 2:8-9, “*For you are saved by grace through faith, and this is not from yourselves; it is God’s gift—not from works, so that no one can boast”* (HCSB).

**Identity property of addition:** “The sum of any number and 0 is equal to the initial number. In symbolic form,

a + 0 = a. The number 0 is referred to as the additive identity. The identity property of addition is shown by this

statement 13 + 0 = 13.” (Saxon Math 8/7).

**Identity property of multiplication: “**The product of any number and 1 is equal to the initial number. In

symbolic form, a x 1 = a. The number 1 is referred to as the multiplicative identity. The identity property of

multiplication is shown by this statement: 94 x 1 = 94.