Division
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Welcome to Division. As the name suggests, this unit is all about divison and is created for students from Kindergarten all the way to Grade 9. Starting with breaking things into equal groups, this unit builds a solid foundation in the concepts of what division is, how it works, the rules that apply to it, and has one whole unit focused on long division. Let's build a foundation together!
These are the main books in print and you will need one per student. Each step lasts about 5 weeks and contains a grade equivalent of content related to that topic. Spiral review is built in to all our levels as we explore multiple operations.
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Division
Foundations
Module 1
- What is equal?
- Equal means the same
- Learn the equal and not equal symbols
- Practice equal and not equal with a balance scale
- Trace and draw the equal and not equal symbols
- Identify numbers that are equal and not equal
- Count objects and draw the equal or not equal symbol
- Bible: Romans 2:11
- God loves everyone the same
- Demonstrate understanding of the equal and not equal symbols by drawing them correctly
- Draw lines to the equal groups
- Identify groups that are not equal
- Apply understanding of equal and not equal by drawing the symbols between two numbers
- Solve a word problem
Module 2
- Two sides
- Definition of symmetry
- Folded heart shows symmetry
- Symmetry is like a mirror image
- Draw right side of shapes to show symmetry
- Symmetry means that both sides match
- Bible: Genesis 2:18
- God made Eve so Adam would not be alone
- Draw lines to match left side and right side of objects
- Identify symmetrical images
- Find symmetrical objects in nature
Module 3
- Is it fair?
- Learn about sharing and being fair
- Think about how you want to be treated
- Identify images that show fairness or equality
- Draw circles to divide objects equally
- Discuss real-life situations with family or class about fairness
- Identify equal groups
- Bible: Luke 6:31
- The Golden Rule
- Demonstrate understanding of equal groups
- Evaluate responses in situations with family or class
Module 4
- Equal weight
- Introduction to a balance scale
- Learn the terms base, bar, and fulcrum
- Use seesaw as another image for balanced weight
- Learn that the same weight does not mean the same number of objects
- Identify heavier and lighter on a scale
- Draw shapes to make the scale balanced
- Understand what it means if a balance is straight
- Make a balance scale
- Bible: Proverbs 11:1
- God hates dishonesty
- Identify the heavier object
- Discuss a scenario of equal weight with family or class
- Understand that the largest does not necessarily mean the heaviest
- Demonstrate understanding of equal weight
Module 5
- Equal volume
- Volume is how much of something is in a container
- Containers must be the same size to compare volume
- Demonstrate understanding of equal volume with glasses and measuring cups
- Identify equal and not equal volume through images
- Demonstrate understanding of equal volume through multiple choice
- Color glasses to show equal and not equal amounts
- Practice volume with items such as rice, beans, or water using different sized cups
- Bible: Luke 3:11
- Share what we have with the needy
- Identify smallest volume
- Compare volumes with large and small cups
- Identify which containers would be used for different purposes
- Apply equal volume to a word problem
- Explain the difference between smaller volume and larger volume
Module 6
- Counting equal groups
- Make equal groups with cookies
- Divide bears into equal groups
- Draw circles to make equal groups
- Identify equal groups
- Identify which group is not equal
- Count the number of groups and the number of items in each group
- Make equal groups with small objects at home
- Bible: Proverbs 27:17
- Our groups (family, friends, church members) help encourage us
- Identify equal groups from images
- Identify equal and unequal groups in word problems
- Sort fish into tanks to make equal groups
Module 7
- Leftovers
- Compare food leftovers to math leftovers
- Draw circles to create equal groups and identify leftovers
- Leftovers are also called remainders
- Apply leftovers to sharing
- Divide small objects into equal groups to find leftovers
- Ask the questions "How many are left over?", "How many are remaining?", and "Can the leftovers be shared equally?"
- Sort with check marks and Xs to find leftovers
- Sort with lines drawn to groups to find leftovers
- Sort by coloring to find leftovers
- Bible: 1 Kings 17:15
- God takes small things and turns them into something big
- Demonstrate understanding by reading a word problem and circling equal groups to find leftovers
- Identify equal groups
Module 8
- Equal sides
- What are parallel lines?
- A square has 4 equal sides
- Squares have 2 sets of parallel lines
- Identify parallel lines in images
- Ask the questions "Are the lines the same length?", "Do the lines go in the same direction?", and "Will the lines ever touch if they keep going?"
- Trace lines and identify if parallel
- Trace and draw squares
- Color the 2 sets of parallel lines in a square
- Find parallel lines in real life
- Bible: Proverbs 3:5–6
- Trust in God and He will lead you
- Understand the definition of parallel lines
- Identify and color squares
- Identify parallel lines in a picture
Module 9
- Equal height
- Identify taller, shorter, and equal height
- Compare the heights of animals and choose the 2 that are equal
- Identify and circle the shorter and taller stacks of blocks
- Draw lines that are of equal height
- Demonstrate understanding of equal height in word problems
- Bible: 1 Samuel 16:6–13
- God does not look at the outward appearance
- Draw lines to identify taller and shorter
- Identify the towers of equal height in a group
- Find objects at home that are taller, shorter, and equal in height
Module 10
- Equal distance
- Understand distance and length as the same
- Objects of the same length are equal
- Identify taller and shorter in images
- Identify objects of equal length
- Draw lines of equal length
- Demonstrate understanding of length in a word problem
- Find two rooms of equal distance in home
- Bible: Ephesians 3:17–19
- Nothing can measure God's love
- Match objects of equal length
- Demonstrate understanding of longer distance in a word problem
- Measure distance with steps in home
Step 1
Module 1
- What is equal?
- Equal is the same
- Learn the equal and not equal signs
- Unequal means they are different
- Draw a line to identify equal and not equal
- Match equal tally marks
- Write equal or not equal in the blanks
- Bible: Isaiah 46:9
- There is no one equal to God
- Circle the correct sign in between two numbers
- Identify equal and not equal with pictures
- Read a word problem and identify equal or not equal
- Draw shapes to make both sides equal
Module 2
- Equal value
- Value is what something is worth
- Choose equal or not equal when comparing objects
- Read a word problem and choose equal or not equal
- Read a list of chores and decide if equal or not equal
- Discuss value of store-bought vs. handmade
- Match items of same value
- Bible: Luke 12:6–7
- God knows even the hairs on our head
- Circle equal or not equal when comparing pictures
- Demonstrate understanding of value through drawing and matching
Module 3
- Two equal parts
- Two equal parts of one whole are two halves
- Identify pictures with equal parts and unequal parts
- Draw circles around two equal groups
- Draw a line to divide an object into two equal parts
- Find common items to divide into equal groups
- Bible: Mark 12:31
- Sharing equally is loving others
- Circle pictures cut in half
- Trace lines to divide shapes into two equal parts
- Draw the missing half of shapes
- Split a snack equally with someone
Module 4
- Sharing with 2 people
- Half means 2 equal parts
- Introduction to fractions
- Use pictures to answer questions like "Is it split equally?" and "How many pieces are there in all?"
- Trace the fraction 1/2
- Draw a line to divide a circle in half
- Identify shapes split evenly in half
- Color in one-half of each shape
- Identify the correct way to write 1/2
- Bible: Luke 6:38
- When we give, sometimes we receive even more
- Draw lines to identify the parts of a fraction
- Color in one-half of a cup of water
- Circle pictures correctly showing 1/2 shaded in
- Demonstrate understanding of the terms whole, half, and unequal
Module 5
- Sharing with 3 people
- 3 equal parts are called thirds
- Use pictures to group objects into thirds
- Trace fraction lines on objects to represent thirds
- Made distintions between 1/2 and 1/3
- Reviewed parts of a fraction
- Determine how many pieces are in a third
- Create 3 equal groups
- Bible: Matthew 28:19
- The Trinity consists of three parts of God. Each part is equal yet has different purposes
Module 6
- Sharing with 4 people
- Identify fourths in real-world applications
- Apply knowledge of quarters to discover that 1 quarter is 1/4 of a dollar
- Solve and complete division word problems
- Distinguish objects that were split evenly into 4 and objects that were not
- Complete the missing parts of the fraction definition
- Shade in 1/4 of a given shape
- Divide a set into 4 equal groups
- Discuss the difference between fourths and four pieces
- Bible: Psalm 104:19
- God made the seasons that break up our year into fourths
Module 7
- Sharing with 5 people
- Dividing sets of numbers into 5 equal groups
- Identify parts of a division model (number of groups, number in each group, and total)
- Determined the number of groups in a division problem
- Identify if objects are shared fairly between 5 people
- Use and manipulate models to solve division problems
- Bible: Hebrews 13:16
- Jesus feeds the 5000
- Sharing makes God happy
Module 8
- Leftovers
- Define and explain leftovers
- Discuss what to do with leftovers
- Review division vocabulary
- When given models show equal groups and identify the leftovers
- Use division models to answer questions
- Use color and circles to create equal groups
- Bible: Luke 15:9
- The parable of the lost coin
- With Jesus, no one is unimportant or forgotten and everyone has a special place and purpose
Module 9
- Equal measurements (part 1)
- Define weight and capacity
- Relate capacity to measuring cups
- Discuss 1c = 2 half-cups
- Relate weights to words like heavy and light
- Discuss 1 pound = 16 ounces
- Note that when comparing numbers in measurements, the values need to be considered
- Match units to its measurement
- Analyze the value of measurements related to the whole
- Bible: Psalm 23:5
- God fills our hearts with blessing and His blessings never run out
Module 10
- Equal measurements (part 2)
- Define height and length
- Relate height and length to real-world objects
- Show tools used to measure height and length
- List equivalent measurements: 12 inches = 1 foot and 3 feet = 1 yard
- Note that when comparing numbers in measurements, the values need to be considered
- Match units to its measurement
- Match equal measurements
- Bible: Matthew 5:41
- Going the extra mile
Step 2
Module 1
- What is division?
- Sharing things equally or splitting into equal groups is division
- Use repeated subtraction to solve for division
- List steps for repeated subtraction
- Solve computation problems about division using repeated subtraction
- Analyze the meaning of division and repeated subtraction
- Bible John 13:34
- Love one another
- Being fair when we share is a way to show God's love
Module 2
- Division on a number line
- Connect number lines to real-world scenarios like hopscotch or jumping on stones
- List steps to go along with the visual
- Determined equal groups, or jumps
- Use visual number lines to answer questions about the total number of groups, and the number in each group
- Create a number line from a given scenario
- Bible: 1 Corinthians 14:33a
- God is fair and orderly and His ways bring us peace
Module 3
- Division with arrays
- Vocabulary: rows and columns
- Identify rows and columns and how they relate to equal groups
- Using a visual, answer questions about how many groups, how many in each group, and how many total
- Identify rows and numbers in each row from a given visual
- Analyze errors in the given array
- Use real items from home to create an array
- Bible: Matthew 7:24
- Arrays create order and stability; in life, Christ is that steady foundation
Module 4
- Equal groups of 1
- Any number (besides 0) divided by 1 is the same number
- Connect dividing by 1 to creating equal groups and to repeated subtraction on a number line
- Fill in the blank given the total number = how many groups of 1
- Match images to groups
- Determine true and false statements about dividing by 1
- Use a number line to show understanding of repeated subtraction and equal groups of 1
Module 5
- Making 2 equal groups
- Half means something is split into two equal parts
- Relate fractions to equal or not
- Identify parts of a fraction
- Top number tells us the number of parts
- Bottom number tells us how many total parts in the whole
- Identify groups that are split equally into two and those that are not
- Created group from given visual
- Answer the following with various problems: How many items total? How many groups? How many items are in each group?
- Color in one part of a half
- Bible: 1 Kings 17:16
- After the widow shared her last meal with Elijah, God cared for her—and He will care for you too, so we can trust Him with our resources
Module 6
- Making 3 equal groups
- Visually demonstrate 12 being divided by 3
- Visualize what 1/3 of a group is and how to write it as a fraction
- Circle groups to show 3 equal groups
- Shade in one part of 1/3
- Answer the following with various problems: What is the total? How many groups? How many in each group?
- Analyze a completed problem to determine if it was shared fairly or not
- Draw objects in each group
- Bible: Acts 10:40
- Jesus was raised on the third day, reminding us that three is significant and that God always has a plan—even when we need to be patient
Module 7
- Making 4 equal groups
- Sharing one dozen cupcakes with 4 people
- Relating 3 cupcakes to being 1/4 of the total cupcakes
- When given a scenario, identify the total, the groups, and the amount in each group
- Created 4 equal groups when given the total
- Identify 1/4, shade in the part of a shape
- Review the concept that a number divided by itself is 1
- Bible: 1 Timothy
- The four Gospels give us a full picture of what Jesus did for us while he was on Earth
- All scripture is God-breathed
Module 8
- Making 5 equal groups
- Review different ways to solve division problems
- Solve division problems with an array and a number line
- Determine ways we could and could not divide by 5
- Draw images of flowers being divided into pots
- When one object is cut into 5 equal pieces, the pieces are called fifths
- Identify fifths and shapes that were not cut into 5 equal parts
- Discuss how to divide 25 seashells
- Bible: Ecclesiastes 9:10
- Whatever your hand finds to do, do it with all your heart—God gave us five fingers that can remind us of ways to serve Him
Module 9
- Making 6 equal groups
- Review dividing using arrays and equal groups
- Practice drawing arrays
- Fill in the blank in repeated subtraction problems
- Determine if a model does or does not represent a given division problem
- Determined the total, number of groups, and number in each group of a given word problem
- Draw a model showing equal groups
- Determine which statement does not show a divide-by-6 problem
- Bible: Exodus 20:9
- God created the earth in six days, demonstrating that His work is intentional, ordered, and perfectly timed
Module 10
- Leftovers and remainders
- Determine what to do with leftovers in math.
- Define remainder
- Divisibility by 2: odds will have a remainder, evens will not
- Complete model to show remainder is not a part of a group
- Find errors in given model
- Given a scenario, answer questions like: How many equal groups can be made? What are the remainders?
- Bible: 1 Samuel 16:11
- David was a "leftover" son that was forgotten by many, but never by God
Step 3
Module 1
- Meet division
- Division means fair sharing
- Vocabulary: dividend, divisor, and quotient
- Label each part of a division problem
- Write division problems from given dividend, divisor, and quotient
- Write correlating division problems from the given multiplication problem
- Practice to reading/saying division number sentences
- Bible: Luke 22:19
- At the Last Supper, Jesus shared a meal with His disciples—even Judas—knowing he would soon betray Him
Module 2
- Dividing with 0
- Distinguish difference between dividing by 0 and something divided by 0
- Use real-life example
- Answers can be 0 or not possible
- Read poem to remember the rules
- Practice how to read division problems out loud
- Determine if given statements are true or false
- Show understanding through word problems, sorting activity, and multiple choice problems
- Explain why 7 cannot be divided by 0
- Bible: Genesis 1:1
- God can do the impossible, and since we cannot divide things into zero groups, it reminds us that God took nothing and created the whole world
Module 3
- Dividing by 1
- Make a connection between the dividend and the quotient being equal
- Demonstrate the example by showing an equal group
- Highlight the number in a divide-by-1 problem that will not change
- Solve using computation problems, word problems, and fill-in-the-blank
- Create own division problems using 1 as the divisor
- Bible: Hebrews 13:8
- Just as dividing by 1 leaves a number unchanged, Christ is the same yesterday, today, and forever
Module 4
- Dividing by 2
- Splitting objects right down the middle into two equal groups is called half
- Splitting objects into two equal groups is also called half, both mean dividing by 2
- Even numbers can always be divided by 2 evenly with no remainders
- Partition objects to show dividing by 2 and splitting in half
- Use knowledge of the opposite relationship between multiplication and division, write multiplication equations from a given division equation
- Divide simple computation problems
- Discuss what splitting something in half means
- Bible: Gensis 1:4
- The days on Earth are split into day and night, each created by God with a specific purpose
Module 5
- Dividing by 3
- Show dividing by 3 different ways: arrays, equal groups, fact families, repeated subtraction, skip counting, number lines
- Create divide-by-3 flash cards to memorize facts
- Practice concepts by filling in blanks, drawing tally marks to create equal groups, draw arrays, and complete a number line
- Bible: Matthew 13:34
- God is the greatest teacher, using different methods like parables to help everyone understand His truth
Module 6
- Dividing by 5
- Relate concept to nickels
- Shown equal groups and arrays to help deepen understanding
- Divisibility by 5: numbers end in 0 or 5
- Demonstrate understanding of the divisibility rule by circling numbers that are divisible by 5, and eliminating ones that are not
- Use arrays and equal groups to solve problems
- Match the equation to the model
- Fill in blanks to demonstrate understanding of repeated subtraction
- Discuss what method of division would be used to solve a given problem
- Bible: Mark 4:38
- Jesus calmed the storm, reminding us that even when we feel overwhelmed, He has perfect timing and brings peace
Module 7
- Dividing by 10
- Review skip counting and how it can be used to help solve division problems
- Demonstrate the "drop a zero" strategy to divide by 10
- Rhyme to remember the rule
- Solve 40÷10 4 different ways: equal groups, repeated subtraction, skip counting and drop a zero
- Skip count to divide by 10
- Drop a zero to divide by 10
- Determine if a given phrase was true or false
- Match problems to answers
- Bible: Ephesians 6:11
- Put on the full armor of God, just as in division nothing can be left out, because every piece matters and each part of His armor is essential for strength and protection
Module 8
- Dividing by 4
- Review ways to solve division problems: repeated subtraction and equal groups
- Discuss the importance of memorization, as it makes solving problems easier and faster
- Create divide-by-4 flash cards and sort out ones that need to be practiced
- Demonstrate knowledge of division by completing computation problems in various ways: repeated subtraction and making equal groups
- Match division problems to correct answers
- Given a scenario, determine how many objects there were to start, how many groups, and how many are in each group
- Bible: Matthew 13:23
- In Jesus’ parable of the four types of soil, people who hear God’s truth are divided into four groups, showing how differently people respond to His Word
Module 9
- Dividing by 6
- Review strategies to divide by 6: repeated subtraction and equal groups
- Show repeated subtraction in a visual graphic organizer
- Label dividend, divisor and quotient in a given equation
- Use repeated subtraction to solve a word problem
- Match a model to the equation it represents
- Complete an array based on a given scenario, then determine the answer
- Bible: Luke 10:40
- Jesus deserves our undivided attention, as seen when Mary chose to focus fully on Him while visiting, unlike Martha who was distracted by many tasks
Module 10
- Remainders
- Not all numbers fit evenly into groups, in math the leftovers are called remainders
- Write "R" in quotient: 28÷5 = 5 R3
- Practice using repeated subtraction to solve: instead of stopping at zero, we stop when we can't subtract the divisor anymore and the left over is the remainder
- Sorted expressions into categories: "has a remainder" or "no remainder"
- Analyze an example to identify the error
- Bible: Ruth 2:3
- Ruth gathered leftover grains in Boaz’s field, and God used those remainders to provide everything she needed
Step 4
Module 1
- Meet division
- Three parts of division: divisor, dividend, and quotient
- Division in a bracket
- Relate multiplication to division
- Repeat subtraction as an example
- Write division problem in brackets when given in a number sentence
- Used multiplication number sentence to generate two division problems
- Determine if a given statement is true or false
- Match division fact to the correlating multiplication fact
- Given a scenario, determine the number of groups, number in each group and the total
- Bible: Mark 1:35
- Sometimes there is a lot to do, but Jesus showed us how to divide our time wisely by stepping away from busyness to pray and spend time with God
Module 2
- Dividing by 7
- Use real-world scenario of a rollercoaster to visualize the problem
- Repeat subtraction and equal groups are used as examples
- Create flash cards of 7s division facts, then practice and sort out problems that need more review
- Determine repeated subtraction that correctly solves the given division problem
- Fill in blanks to solve for repeated subtraction
- Generate equal groups
- Bible: Proverbs 26:16
- The righteous fall seven times and rise again, God doesn't expect us to get things right the first time
Module 3
- Dividing by 8
- Review arrays as a way to help solve division problems
- Real-world problem: laying tile flooring
- Memorize 8s facts to solve problems quickly
- Listen to 8s fact song to help memorization
- Create flash cards on 8s facts
- Demonstrate understanding of the concept by using an array to generate an answer and by drawing arrays to solve
- Solve computation facts quickly, use song or flash cards to check
- Fill in the blanks to solve a repeated subtraction division problem
- Discuss what strategy works best
- Bible: Proverbs 7:3
- Memorizing scripture helps God’s Word come to mind when difficulties arise, just as memorizing math facts helps us recall answers quickly when solving problems
Module 4
- Dividing by 9
- Using a chart to see patterns in dividing by 9
- Large numbers are harder to solve with models, so memorizing facts can be really helpful
- Students will create division fact cards over 9
- Generate understanding of division problems by circling equal groups, using arrays, and repeated subtraction
- Determine if a given statement is true or false
- Complete computation facts as quickly as possible
- Bible: Galatians 5:22–23
- God gives us nine fruits of the Spirit, God-given traits that help us grow, reminding us that every character quality is important
Module 5
- Long division with 1 digit
- List long division steps
- Fill in blanks for long division problems
- Determine errors in long division
- Solve computation problems set up in brackets
- Change division problems from a sentence to a division bracket and then solve
- Solve a word problem
- Self-reflection rubric
- Bible: Psalm 119:105
- God gives us steps to follow in math and in life
Module 6
- Long division with a remainder
- Writing remainders with an "R"
- Review the steps to long division
- Given a scenario, find the total number of groups, the number in each group, and the amount of leftovers
- Use mental math to determine if a division problem will have remainders
- Solve long division problems that will have remainders
- Rewrite division number sentences to be in long division bracket, then solve
- Complete word problems
- Bible: 1 Samuel 16:7
- God looks at the inside, not outward appearance, so when you feel like an outsider, remember that He sees your worth
Module 7
- Multistep long division
- Real-world example of climbing a ladder to repeat the steps of long division
- Steps to solve multistep long division: divide, multiply, subtract, bring down, and repeat until all numbers are used
- Fill in the blank to solve the division computation problem
- Number the order of steps to take to solve
- Demonstrate understanding of the concept by finding errors in a solved problem and solving computation problems (with and without remainders)
- Solve word problem
- Bible: Proverbs 3:5–6
- Trust in the Lord with all your heart, knowing that God works through all situations—even small repeated steps of life—just as long division works through small repeated steps
Module 8
- Interpreting remainders
- Discuss 3 ways to address remainders, and provide situations for each: ignore it, round the answer up, or turn it into a fraction
- Given a scenario decided what to do with the remainder and solve, writing the answer accordingly
- Practice writing quotient with remainders 3 different ways when dividing computation problems
- Match scenarios to how remainders should be interpreted
- Solved several word problems that require interpretation of a remainder
- Bible: 2 Corinthians 12:9
- God’s power is perfected in our weakness, and even when mistakes happen—like in math—God works through them
Module 9
- Dividing by 2-digit numbers
- Following the same steps as the long division previously taught, use 2-digit divisors
- Estimation gives us an idea of what the answer could be
- List the factors of the dividend as a tool to help solve
- Practice computation problems by estimating using compatible numbers, then listing the multiples of the divisor, and finally solving
- When given the multiples of the divisors, students will complete the long division
- Determine if the given statement about division is true or false
- Fill in the blanks on a computation problem
- Demonstrate understanding of the concept by completing a word problem
- Bible: Colossians 3:23
- Whatever you do, work heartily as working for the Lord, taking time to do things well as a way to glorify God
Module 10
- Dividing money
- Decimal in the dividend, divided by a whole number
- Decimals in the wrong spot can change the value of the digits, it is important to make sure it is in the right spot
- Decimal goes straight into the quotient, and we divide like normal
- Given examples, place decimal in the quotient in the correct place
- Solve computation problems using knowledge of math facts
- Describe the importance of decimal placement
- Solve problems with decimals using long division
- Analyze errors in the worked example
- Bible: Luke 22:42
- Even Jesus aligned His will to God’s, as seen in His prayer in the Garden of Gethsemane
Step 5
Module 1
- Properties of division
- Review vocabulary: words, dividend, divisor, quotient
- Define: identity property, dividing a number by itself, dividing any number by 0, and dividing 0 by any number
- Match examples to properties
- Label parts of a division problem
- Given examples, explain which property helped solve them
- Bible: Psalm 100:5
- Math follows certain rules, this is an example of how God is purposeful, and creates order
Module 2
- Division with decimal divisors
- Change decimals in the divisor to a whole number by multiplying by factors of ten (multiply dividend and divisor)
- Multiply by 10, then divide
- Multiply by 100, then divide
- Used concepts taught to analyze erros in thinking
- Solve problems using visuals
- Match the equation to the equivalent equation and then to the quotient
- Bible: Proverbs 3:5
- Sometimes math and life can be confusing, but God tells us not to lean on our own understanding
Module 3
- Division and fractions
- Determine what to do with leftovers or remainders
- Turn remainders into a fraction
- Explain where the numerator and denominator comes from within the equation
- Discover how mental math can help solve these types of problems quickly
- Relate these types of problems to real-world scenarios
- Match the problems to answers
- Bible: Luke 16:10
- Every part of a math problem matters, even small parts like remainders, just as God cares about every detail of our lives
Module 4
- Dividing whole numbers by fractions
- Use a model to show the concept of how dividing a whole by a fraction will end up with a bigger number
- Keep, change, flip as a tool to solve (multiply by the reciprocal)
- Fill in the blank to solve
- Rewrite division problems as multiplication problems
- Order the steps to solve division problems that involve fractions
- Solve and divide fractions
- Explain why the quotient is larger than the start
- Bible: Proverbs 15:1
- Small things matter and can make a big difference
Module 5
- Dividing fractions by fractions
- Remember the trick to solve: keep, change, flip
- Whole numbers and mixed need to be changed to improper fractions before starting
- Recriprocol is a flipped version of a fraction, allows us to multipy instead of divide
- Visualize dividing fractions with models
- Identify mixed and improper fractions
- Rewrite mixed numbers into improper fractions
- Follow steps to solve for fraction by fraction division problems
- Bible: 1 Peter 3:9
- Do not repay evil for evil, instead flip it around and show kindness to those who are mean to you
Module 6
- Dividing by 10, 100, and 1,000
- Digits shift left on a base 10 chart when we divide by powers of 10
- The number of zeros there are in the power of ten is how many times we move the decimal to the left when dividing
- Practice moving decimals in whole numbers and in decimals
- Solve division problems, dividing by 10, 100, or 1,000
- Bible: Matthew 17:20
- Faith like a mustard seed: dividing a big number by 10, 100, or even 1,000 can make it more manageable or small like a mustard seed
Module 7
- Division on the building site
- When given the measurements of a tile and the area of a room, solve for how many tiles are needed
- Review dividing decimals: remember to multiply by a factor of 10 to the dividend and divisor to create a new problem that will give us the same answer
- Review dividing fractions: keep, change, flip
- When given the cost of building materials and the amount, solve for the unit price
- Calculate division of labor: 180 hours split between 4 people.
- Calculate the number of walls a gallon of paint can cover
- Bible: Luke 14:28
- Calculate the cost before building, just as we can apply wisdom in our walk with the Lord by considering small steps, planning outcomes, and understanding consequences
Module 8
- Isolating variables
- Define and identify variables as letters in a math problem that represent unknown values
- Solve one-step division problems involving variables
- Solve two-step problems that involve variables and division
- Highlight variables in the problem
- Fill in the missing parts in an equation to solve for the missing variable (one-step and two-step)
- Check answers by plugging in the variable
- Break down word problems into manageable parts, then put the parts together to solve
- Bible: Luke 14:28
- Before building a tower, who doesn't sit down and count the cost? Just like building takes planning and careful steps, so does living for God
Module 9
- Division on a road trip
- Relate division to a real-world scenario, traveling
- Solve for miles per gallon, miles per hour, and cost per gallon
- Determine which car would be a better option to take based on mpg
- Bible: Proverbs 21:5
- Planning diligently leads to abundance
Module 10
- Division at the store
- Calculate unit price
- Determine between two items, which would be a better buy based on the price per unit
- Number the steps to solving price per unit problems
- Bible: 1 Philippians 4:11
- Be content in every situation and use our resources well to serve the Lord
Step 6
Module 1
- Ratios and division
- Ratios are like horizontal fractions
- Follow steps to divide ratios
- Fill in the blanks to the steps
- Identify errors in problems
- Find the GCF to simplify ratios
- Apply steps to word problems
- Demonstrate understanding of dividing ratios by completing steps on own
- Bible: Matthew 20:1–16
- God is gracious and generous
- Psalm 145:26
- His ways may not always seem fair, but God is always good
- Write ratios
- Simplify ratios by finding the GCF
- Understand sharing as a ratio
Module 2
- Dividing exponents
- Exponents are used to show how many times a number is multiplied by itself
- Understand the terms base and exponent
- If bases are the same, subtract exponents when dividing
- If bases are different, solve each exponent and then divide
- Choose whether to subtract or solve exponents
- Division problems can also be written as fractions
- Complete division problems written horizontally and as fractions
- Bible: 1 Corinthians 12:12
- Each part of the body is important
- Write the rules for dividing exponents
- Identify the errors
- Demonstrate understanding of the rules for dividing exponents by correctly solving problems
- Rewrite horizontal division problems as fractions and solve
Module 3
- Dividing scientific notation
- Scientific notation makes numbers easier to deal with
- Understand how the base 10 system works
- Each digit to the left is 10 times higher than the one to the right
- Move the decimal place until one digit is to the left and count the number of times it was moved
- Learn the 3 steps to dividing scientific notation
- Identify "like" terms
- Follow the rules of dividing exponents
- Write large numbers in scientific notation
- Follow the steps to solve scientific notation division problems
- Bible: Matthew 28:19
- Go make disciples and grow the Kingdom of God
- John 3:16
- God loves everyone and sent His Son to die for everyone
- Identify the problems written incorrectly
- Explain the 3 steps to solve a division problem with scientific notation
- Write exponents as repeated addition
Module 4
- Dividing monomials
- Review of terms monomial, coefficient, variable, and exponent
- Follow steps to divide monomials by identifying "like" terms, dividing coefficients, and subtracting exponents if variables are the same
- Simplify monomial division problems on own
- Bible: Proverbs 27:17
- Iron sharpens iron like Christian friends help us grow in our faith
- Label each part of a monomial
- Explain the steps to solve monomials with like and unlike variables
- Identify when to subtract exponents
Module 5
- Dividing polynomials
- Introduction to polynomials
- "Poly" means many
- Polynomials must be separated by an addition or subtraction symbol
- Follow steps to divide polynomials by rewriting the problem as a fraction, separating into individual terms, simplifying coefficients, dividing exponents, and putting the remaining terms together
- Identify polynomials
- Simplify polynomial division problems on own
- Bible: Isaiah 41:10
- God gives us the courage to step outside our comfort zone
- Identify polynomials and monomials
- Number the steps to simplifying polynomial division problems
Module 6
- Dividing negative numbers
- Use parentheses to differentiate negative numbers from subtraction
- The rules of negatives: opposite signs give a negative quotient, same signs give a positive quotient
- Apply same rules of exponents, monomials, and polynomials when dividing by negative numbers
- Identify positive and negative quotients
- Divide positive and negative integers and apply the rules of negatives
- Simplify polynomial expressions with negative numbers
- Simplify monomial expressions with negative numbers
- Solve scientific notation problems with negative numbers
- Bible: Galatians 6:9
- Do not get tired of doing good
- Identify correct and incorrect answers by applying the rules of negatives
- Write own division problem that will result in a negative quotient
- Write own division problem that will result in a positive quotient
- Fill in the blanks to complete each division problem
Module 7
- Dividing percents
- Use division to find out the original prices
- Apply 3 steps: subtract to find the percent paid, change the percent to a decimal, divide the sales price by the percent paid
- Determine the percentage paid
- Practice changing percents to decimals
- Demonstrate understanding of dividing percents by solving word problems
- Determine which item has the lowest original price
- Write own real-life word problem
- Bible: 1 Corinthians 6:20
- Use your body to praise and serve God
- Explain the steps to solve a problem dividing percents
Module 8
- Dividing radical expressions
- A radical expression is another name for square root
- Introduce the radical symbol
- Introduce perfect squares
- When the numerator and denominator are both radicals, combine them under one
- Combine radicals and solve
- Factor out perfect squares to simplify
- Bible: Colossians 2:6–7
- Allow Jesus and God's Word to be your roots
- Identify radicals with perfect squares
- Solve square roots
- Apply knowledge of radicals to solve a word problem
Module 9
- Dividing irrational expressions
- Irrational numbers cannot be written as a fraction
- Identify the difference between irrational and rational numbers
- Rationalize the denominator when dividing irrational numbers
- Follow 3 steps to simplify irrational expressions: write as a fraction, multiply the top and bottom by the denominator, simplify
- Bible: Proverbs 3:5
- Trust in the Lord and do not rely on your own understanding
- Sort rational and irrational numbers
- Explain the steps to simplify an irrational expression
- Simplify irrational expressions on own
- Determine whether a quotient is simplified or not
Module 10
- Division in function rules
- Introduction to functions
- A function is a key that tells you what to do with a given number
- Learn the terms input and output
- A denominator resulting in 0 is undefined
- Use tables of numbers for input and output to identify function rules
- Solve to find the outputs for functions
- Solve functions with all math operations
- Write 3 numbers that can be used in a function
- Write 1 number that cannot be used in a function
- Bible: Galatians 6:7, 9
- You reap what you sow
- Match the functions to the correct outputs
- Solve functions when given x
- Identify undefined outputs