Order of Operations

For Logic Pre-Algebra:  This morning, we did something a little different.  I gave the students three terms from our math vocabulary: order of operations, equation, and repetend. We read the definitions and then each student was to give a summary of how the term they chose of the three reflected the word “perseverance,” our 30 Character Quality word for the day.  Here were their answers.

Emma:  “The order in which we solve a problem reminds me of PEMDAS and the Order of Operations.  You need perseverance to follow it through even when some of the steps are hard.”

Sebastian:  “Through perseverance, I am persuaded that an equation is true.”

Alejandro:  “Sometimes you need perseverance in the order of operations because it get repetitive.”

This brought us to talk about G.K. Chesterton’s quote “Because children have abounding vitality, because they are in spirit fierce and free, therefore they want things repeated and unchanged. They always say, “Do it again”; and the grown-up person does it again until he is nearly dead. For grown-up people are not strong enough to exult in monotony. But perhaps God is strong enough to exult in monotony. It is possible that God says every morning, “Do it again” to the sun; and every evening, “Do it again” to the moon. It may not be automatic necessity that makes all daisies alike; it may be that God makes every daisy separately, but has never got tired of making them. It may be that He has the eternal appetite of infancy; for we have sinned and grown old, and our Father is younger than we.”

 Ellie:  “If a repetend somehow had an active conscience/free will, then it would (most likely) continue to repeat in order to equalize what it applies to.”

Christopher:  “God is a God of order and peace.  God is immutable; God never changes His mind.”

Jacob:  “I must persevere and make a perseverance speech about math such as order of operations or PMDAS.”

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Math clips

For Logic Pre-Algebra:  In review for the Bluebook, students shared some terms they will be defining, modeling, and illustrating next week.  Some highlights from today’s Logic Pre-Algebra were…

Aliyah while defining and comparing root and radicand noted: “We can be radical about our faith if we are rooted in His Word—Colossians 2:7, Rooted and built up in Him strengthened in the faith as you were taught and overflowing with thankfulness.” 

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Emma while defining a conditional equation noted:  a conditional equation reminds me of Easter.  If any of the prophecies didn’t come true during the crucifixion Easter would be invalid. 

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Ellie while defining opposites noted:  our sin is like a negative number and Jesus’ love and forgiveness counteracts all of our sin, so we are washed clean.

 

Circles

For Logic Pre-Algebra:  We started off Math, Week 3, Semester 2, with a discussion about “circles” (Lesson 60, Algebra ½ Saxon).  We defined words like “radius, chord, diameter, circumference, and then solved problems that had to do with finding the circumference and the area of a circle.  We related this to forgiveness and the circular benefits and consequences of forgiving and not forgiving.  Consider for yourself the words of Matthew 6:14-15, “For if you forgive people their wrongdoing, your heavenly Father will forgive you as well.  But if you don’t forgive people, your Father will not forgive your wrongdoing” (HCSB).  It causes me to think, as I write this, about the saying, “What comes around goes around.”  See the circle?  I never looked at this verse like that before. Revelation!  We  integrated some Logic here. We see in Matthew 6:14-15 some “if, then” propositional statements (similar to the ones we broke down in Logic today—see Exercise 7a pages 47-49 in Intermediate Logic) which we broke down into symbolic form (F means you forgive people their wrongdoing, G means your heavenly father will forgive you): F⸧G ⸳ ~F~G.  How awesome is God to integrate the verse of the day with exactly what we are learning in Logic and Math …and as you will see in other strands too.

Our students brought problems to the board and when I asked them how they saw God revealed in their problem these were their responses:

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PEMDAS reminded Christopher that God is a God of order.

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Trichotomy Axiom’s three Possibilities reminded Alejandro of the Trinity.

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Emma was reminded of God when she  was struggling with equivalence and then got it!

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Aliyah modeled how to graph coordinate planes.  She was also reminded of the

Trinity as she graphed three points to a triangle.

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Ellie simplified a very in depth problem and explained that God also breaks down and

simplifies difficult concepts—this led  us to talk about the parables and their  purpose (Matt. 13:11-15)

 

 

Digging for Truth in Math

For Logic Pre-Algebra:  We started off Math today talking about “Solving Equations in Two Steps” (Lesson 61 Saxon Algebra ½).  We had a Five Common Topic discussion wrapped around the terms variable and number.  This is what our board looked like when we were done.

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We concluded at the end of our math hour when we contemplated the question, “How have we seen truthfulness revealed in our Math time?” that the Math Problem must be faithful to be true.  If it is not right then it is wrong.  We compared seeking the right answer in math to digging for the truth in God’s Word.  Sebastian led us in this process in week 7 (Second Semester) through modeling this for us in his own math problem.  In light of this truth, we talked about Matthew 7:8, “For everyone who asks receives; the one who seeks finds; and to the one who knocks, the door will be opened” (NIV). After this, students worked out their own math problems.

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Emma: “Math must be faithful to the truth.”

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Sebastian: “Seek and you will find.”

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Aliyah: “PEMDAS…Where there’s order there’s peace.”

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Ellie’s problem reminded her of simplification and the way God makes complex ideas simple to us through His Word.  Specifically noted: parables.  The class also helped Christopher build his problem up by giving him corrective feedback.  His problem was built up in love (remembering when Aliyah talked about this in our devotion this morning, “…let each one of you speak the truth with his neighbor, for we are members one of another” (Ephesians 4:25).