Multiplication
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Welcome to Multiplication. As the name suggests, this unit is all about multiplication and is created for students from Kindergarten all the way to Grade 7/8. Students begin by learning multiplication as repeated addition and building equal groups before moving into arrays, number lines, and multiplication facts. Upper levels explore multiplication with decimals, integers, exponents, and expressions, applying these skills to geometry, order of operations, and real-world problem solving. Our spiral and mastery style program introduces basic multiplication concepts and continues to reinforce them throughout the entire program.
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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These are the digital Skill Builders that have three extra practice sheets. They can be used for additional practice, reinforcement of concepts, or even to fill in gaps while you wait for your books to come. They are an instant download.
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Multiplication
Foundations
Module 1
- Stacking zero
- Introducing the concept of stacking numbers together
- Read, understand, and define the term zero
- Organize equations horizontally and vertically
- Apply knowledge of stacking zero to answer word problems
- Strategies in solving word problems: highlighting clue words
- Identify identical numbers
- Bible: Genesis 1:1–2
- God needed zero materials to create the heavens and the Earth
- God's power has zero limit
- Review of number recognition
- Write an equation for addition word problems
Module 2
- Equal vs. not equal
- Explain what is the same and different about numbers
- Compare with greater than and less than symbols
- Read, understand, and write symbols for greater than and less than
- Real-life application of equality: baking
- Use a scale to visually represent equal items or numbers
- Label numbers as equal or not equal
- Identify the greater number and smaller number in a set
- Match equal amounts
- Equal and not equal symbols
- Choose the correct symbol to compare sets of objects
- Bible: Galatians 3:28
- We are all the same to God
- God created all of His children for a purpose
- Trace and draw symbols used in equality equations
- Identify incorrectly solved math statements
- Explore one-to-one correspondence
Module 3
- Stacking one
- Organize into equal groups
- Skip count by one
- Real-life examples of creating equal groups of one
- Add groups of one
- Apply knowledge of skip counting by one to solve word problems
- Create and solve addition number sentences
- Identify equal and unequal groups of one
- Bible: we are never alone
- God is always with us
- Matthew 28:20
- Deuteronomy 3:16
- Rewrite horizontal equations vertically
- Find groups of one
- Read and write the number one in word and digit form
Module 4
- Stacking two
- Real-life applications of groups of two
- Skip count by two
- Kinesthetic + visual approaches to counting by two
- Solve addition equations
- Apply knowledge of counting by two to solve word problems
- Identify equal groups of two
- Bible: we were created for community
- Encourage and build one another up
- Ecclesiastes 4:9–10
- Write horizontal equations vertically
- Use pictures to skip count by twos
Module 5
- Stacking three
- Adding groups of three
- Real-life examples of groups of three
- Skip count by three
- Fill in missing groups of three in a number sequence
- Solve addition equations
- Identify equal and not equal groups of three
- Use kinesthetic learning techniques to count by threes
- Bible: the number three has special meaning in the Bible
- The Trinity: God the Father, Son, and Holy Spirit
- Matthew 28:19
- 2 Corinthians 13:14
- Write horizontal addition equations vertically
- Use pictures to create groups of three
- Apply knowledge of adding groups of three to solve word problems
Module 6
- Stacking four
- Real-life examples of groups of four
- Skip count by four
- Apply knowledge of adding groups of four to solve word problems
- Add equal groups of four
- Identify equal and not equal groups for four
- Use pictures to skip count by four
- Kinesthetic learning techniques for skip counting by four
- Bible: Psalm 34:1
- Praising God for every season
- Write horizontal equations vertically
Module 7
- Stacking five
- Real-life examples of groups of five
- Observe patterns in numbers
- Visual strategies used in math: highlighting
- Skip counting by five
- Add groups of five
- Identify equal groups of five
- Draw pictures to show equal groups of five
- Apply knowledge of adding groups of five to solve word problems
- Bible: feeding the 5,000
- John 6:11
- God can multiply small things into something much bigger
- Complete existing patterns
- Solve addition equations
- Write horizontal equations vertically
Module 8
- Stacking ten
- Skip count by ten
- Observe patterns in numbers
- Visual strategies in math: highlighting
- How to read tens aloud
- Fill in the missing digits when counting by ten
- Make groups of ten
- Apply knowledge of counting by ten to solve word problems
- Match numbers to their word form
- Add groups of ten
- Bible: Moses and the Israelites
- The Ten Commandments
- Exodus 20:3
- How to put God first
- Solve addition equations
- Identify equal and not equal groups of ten
Module 9
- Word problems
- Why we solve word problems in math
- Steps to solve word problems
- Identify key words in word problems: total, all together, in all
- Draw pictures to write equations and solve word problems
- Apply knowledge of adding to solve word problems
- Visual strategies in math: highlighting
- Use concrete objects to make equal groups and add objects
- Create a word problem of your own
- Bible: Psalm 119:105
- Isaiah 41:10a
- Ephesians 4:23
- The Bible can give us clues to light our path
- Add groups of the same number
Module 10
- Making groups
- Strategies in math: creating equal groups and skip counting
- Apply knowledge of making groups to solve word problems
- Write equations based on word problems
- Real-life scenarios of making groups
- Sort a group into equal parts
- Use concrete items to make equal groups
- Create and use skip counting to solve equations
- Bible: Proverbs 27:17
- 1 Corinthians 15:33
- The importance of the groups you belong to
- Choose to lift others up or tear them down
- Make equal groups of coins
Step 1
Module 1
- Skip counting by 2
- Read and write numbers that can be skip counted by 2
- Put items into equal groups when skip counting
- Observe patterns in counting
- Use a number line to skip count by 2
- Hands-on activity: compare times of counting with and without skip counting
- Kinesthetic learning techniques with skip counting
- Fill in missing numbers to complete patterns
- Add groups of 2
- Bible: Jesus had 12 disciples that traveled with Him
- Mark 6:7
- Jesus gave his disciples partners so they could work together
- We are never alone
- Identify numbers that are skip counted incorrectly
- Draw to create equal sets
- Solve addition problems
Module 2
- Skip counting by 3
- Tools used in math: number lines
- Read and write numbers that can be skip counted by 3
- Moving three spaces on a number line
- Parts of a whole
- Organize groups into smaller parts
- Use concrete objects to make equal groups of three
- Skip count by 3 to find the total number
- Complete missing numbers in sequences
- Kinesthetic learning strategies to memorize numbers that can be skip counted by three
- Bible: tri- means three
- The Trinity is three-in-one
- Matthew 28:19
- Count objects in a group with repeated addition
- Solve horizontal addition problems
- Use pictures to make equal groups of three
- Identify incorrectly written equations with groups of three
Module 3
- Skip counting by 4
- Visual strategies in math: highlight, circle, and color-coding
- Use a number line to skip count by four
- Observe patterns in numbers when counting by four
- Read and write numbers that can be skip counted by four
- Memorize addition sequences with numbers that can be skip counted by four
- Use pictures to add multiples of four
- Solve addition equations with groups of four
- Kinesthetic learning techniques to use while skip counting by four
- Bible: there are four seasons each year
- Calculate how many seasons you have experienced in your life
- Genesis 8:22
- Seasons will be faithful to return
- Complete missing multiples of four on a number line
- Geometric principle: squares have four sides
- Identify whether addition equations with groups of four are correct or incorrect
- Determine groups that are equally divided into fours
- Use concrete items to make groups of four
Module 4
- Skip counting by 5
- Read and write numbers that can be skip counted by five
- Real-life examples of multiples of five: number of fingers
- Observe patterns in numbers when counting by five
- Tools in math: number charts
- Solve horizontal addition problems with groups of five
- Use skip counting to calculate the total amount of nickels
- Complete number sequences using multiples of five
- Bible: 1 Thessalonians 5:16–18
- Ways to pray for others using your hands
- Apply knowledge of skip counting by five to solve word problems
- Use concrete objects to make equal groups of five
Module 5
- Skip counting by 6
- Read and write numbers that are skip counted by six (up to 18)
- Use pictures to add multiples of six
- Real-life example of skip counting by six: insect legs
- Create equal sets of six
- Read aloud number sequences with multiples of six
- Apply knowledge of skip counting by six to solve word problems
- Complete number lines by writing the missing multiple of six
- Draw pictures to represent equal groups of six
- Bible: Proverbs 6:6
- Work hard and prepare ahead of time
- Identify and correct numbers that are incorrectly skip counted by six
- Use geometric shapes to count in multiples of six
- Draw hexagons with six sides
- Use kinesthetic learning techniques to memorize multiples of six
Module 6
- Skip counting by 10
- Identify patterns in numbers skip counted by ten
- Read and write numbers that can be skip counted by ten
- Complete the missing multiples of ten in each set
- Apply knowledge of skip counting by ten to solve word problems
- Use pictures to skip count by ten
- Solve addition equations with multiples of ten
- Skip count by ten to add dollar values
- Bible: count blessings you are thankful for
- All good things come from God
- Give freely with a generous heart
- Luke 6:38
- James 1:17
- Ephesians 3:20
- Identify equal groups of ten
Module 7
- Identifying equal groups
- Read, understand, and write symbols used to compare: greater than, less than, and equal
- Use pictures to show equal groups
- How to read comparison problems aloud
- Identify equal sets
- Apply knowledge of identifying equal groups to answer word problems
- Match pictures with number sentences
- Compare numbers with symbols
- Bible: Matthew 7:12
- The Golden Rule
- We are all equal in God's eyes
- Mark 12:28–30
- Love and treat others well
- Order numbers from least to greatest
Module 8
- Creating equal groups
- Draw, build, and separate to create equal groups
- Skip count to make equal groups
- Organize a larger group into smaller equal groups
- Fix incorrect number sentences to make them equal
- Label sets of numbers as equal or not equal
- Complete skip counting sequences
- Sort concrete objects into equal groups
- Bible: 2 Corinthians 6:14
- Surround yourself with friends who have have similar beliefs
- Use pictures to write equal number sentences
- Fill in missing numbers to create equal number sentences
- Kinesthetic learning techniques in equal numbers of movements
- Number recognition with color coding
Module 9
- Word problems
- Skip counting in word problems
- Highlight clues in word problems: in all, all together, and in total
- Draw pictures and write number sentences to solve word problems
- Apply knowledge of adding equal groups to solve word problems
- Determine whether skip counting can be used to answer word problems
- Write addition problems based on a word problem
- Bible: the words we speak give clues about what is in our heart
- Luke 6:45
- Speak kind words
Module 10
- Building arrays
- Row and columns help to organize information
- Arrange objects on a chart
- Compare row vs. column
- Real-life examples of arrays: chocolates in a box, eggs in a carton, and muffin trays
- Use arrays to add vertically and horizontally
- Identify the number of rows and columns in an array
- Write addition equations based on arrays
- Apply knowledge of building arrays to solve word problems
- Build an array with concrete objects
- Count the total number of objects in an array
- Bible: God desires for us to have peace
- Corinthians 14:33
- How clearing clutter can be helpful
- Skip count objects in arrays
- Draw objects in arrays to represent information from word problems
Step 2
Module 1
- Meet multiplication
- Operations in math: multiplication, addition, and subtraction
- Read aloud and understand the meaning of the multiplication symbol (x)
- Visual representation of multiplication equations
- Observe the relationship between multiplication and addition
- Match number words and digits
- Complete multiplication expressions with missing numbers
- Match number sentences and images
- Identify repeated addition equations and multiplication equations that are equal
- Draw pictures to make equal groups
- Create multiplication expressions based on pictures
- Bible: feeding the 5,000
- John 6:1–14
- God can multiply what little we have to offer
- Ephesians 3:20
- Use concrete objects to make equal groups and write a number sentence
- Apply knowledge of multiplication to answer word problems
Module 2
- Multiplication on a number line
- Multiplication sentences as addition sentences
- Use number lines to solve multiplication problems
- Referring to multiplication as jumps on a number line
- Factors can be written in any order
- Bible: 1 Samuel 16:7
- God looks at the heart, while man looks at the outward appearance
- Recognize multiplication sentences in word form and number form
- Matching multiplication sentences to a number line
- Write addition and multiplication sentences
- Skip count by 3 and 5
- Write multiplication sentences for groups of images
Module 3
- Multiplying by zero
- Intro to commutative property of multiplication
- Intro to zero property of multiplication
- Match multiplication sentences written two different ways
- Match addition sentences to multiplicaiton sentences
- Recognize written form of multiplication sentences
- Bible: John 15:5
- Jesus is the vine, and we are the branches
- God can multiply our talents to grow His Kingdom
- Write multiplication sentences in word form
- Solve multiplication sentences with zero
- Recognize factors can be written in any order
Module 4
- Multiplying by 1
- Introduction to identity property of multiplication
- Multiplication as repeated addition
- Review of commutative property of multiplication
- Identify which factor remains the same when multiplying by 1
- Match word phrases with multiplication sentences
- Draw shapes to demonstrate understanding of multiplying by 1
- Use shapes to represent multiplication equations
- Bible: Hebrews 13:8
- Jesus remains the same yesterday, today, and forever
- Identify multiplication sentences according to groups of images
- Write the word form of multiplication sentences
Module 5
- Multiplying by 2
- Multiplication as repeated addition
- Skip counting by 2
- Look for patterns on a number chart
- Doubling to find the answer
- Use and recognize the commutative property of multiplication with visuals
- Bible: John 14:15
- If we love God, we will keep His commandments
- Ephesians 6:1
- Obey your parents
- Write multiplication sentences as repeated addition
- Identify multiplication sentences according to groups of images
- Create equal groups with small objects
Module 6
- Multiplying by 5
- Identify patterns when counting by 5s
- Learn 5s multiplication facts by memory
- Demonstrate understanding of word phrases by writing number sentences
- Use the commutative property of multiplication with 5s
- Write multiplication sentences based on groups of images
- Illustrate multiplication sentences with shapes
- Solve multiplication problems with mental math
- Bible: Psalm 119:11
- Keep God's word in your heart
- Skip count by 5s
- Tools in math: number lines
- Practice multiplication facts with flash cards
- Increase multiplication fluency
- Write multiplication sentences for word problems
- Real-life applications of multiplying by 5s
- Use multiplication facts when telling time
Module 7
- Multiplying by 10
- Identify patterns when counting by 10s
- Add zero to answers when multiplying by 10
- Match word phrases to multiplication problems
- Write a multiplication problem based on groups of images
- Write a multiplication problem to solve a word problem
- Real-life application of multiplying by 10
- Bible: Luke 6:38
- God can multiply our offerings
- 2 Corinthians 9:7
- God cares about how we give and not just what we give
- Skip count by 10s
- Answer multiplication facts by memory
- Increase fluency of multiplying by 10
Module 8
- Multiplication and division
- Division is the opposite of multiplication
- Rewrite multiplication as division
- Match related multiplication and division problems
- Biggest number goes first in division
- Identify and solve problems in different fact families
- Observe relationships between numbers in multiplication and division
- Bible: Proverbs 18:24
- Jesus is a friend who sticks closer than a brother
- Write a multiplication problem and a division problem based on images
- Use knowledge of multiplication to solve math puzzles
Module 9
- Using arrays
- Introduction to arrays
- Arrays as a way to organize lots of objects
- Arrays can help skip count
- Arrays can help multiply
- Identify the number of rows and columns in an array
- Demonstrate understanding of arrays by matching them to multiplication problems
- Using arrays to write multiplication problems
- Complete an array based on information from a word problem
- Create an array with small objects
- Bible: Ephesians 2:10
- We are created by God with a special purpose
- 1 Corinthians 14:3
- God creates order
Module 10
- Word problems
- Identify clue words to help know which operation to use to solve word problems
- Identify equal groups in word problems
- Demonstrate understanding by highlighting clue words
- Ask "What is being repeated?" and "How many times?"
- Use an array to solve a word problem
- Apply knowledge to write own multiplication word problem
- Bible: Psalm 141:3
- Guard our lips and choose kind words
- Draw pictures to help solve word problems
Step 3
Module 1
- Meet multiplication
- Multiplication as repeated addition
- Identify factors and products
- The x sign means multiplication, times, and groups of
- Multiplication is faster than skip counting
- Write multiplication problems for repeated addition problems
- Write repeated addition problems as multiplication problems
- Bible: Matthew 5:14, 16
- We are the light of the world
- Sharing God's light goes farther than we imagine
- Identify the x symbol
- Recognize factors and products
- Match phrases to multiplication problems
- Write a multiplication problem based on images
Module 2
- Multiplication rules
- Introduction to zero property, identity property, commutative property
- Multiplying by 10
- Demonstrate understanding of properties by matching
- Solve multiplication facts with 0, 1, and 10 as factors
- Demonstrate understanding of commutative property by rewriting factors
- Write own examples of each property
- Bible: Proverbs 4:26
- Follow God's rules
- Circle true or false for multiplication property statements
- Identify property used in multiplication sentences
Module 3
- Multiplication charts
- Numbers are full of patterns
- Multiplication charts are like arrays
- Identify rows and columns in a multiplication chart
- Identify horizontal and vertical directions
- Demonstrate the ability to read a multiplication chart by finding products
- Commutative property of multiplication
- Find patterns in the 2 times tables
- Find a product and write a multiplication problem
- Identify a pattern in the 5 times tables
- Bible: John 14:6
- Jesus is the way, the truth, and the life
- Fill in a row on a multiplication chart
- Apply the commutative property by flipping factors
Module 4
- Multiplying by 3
- Multiplying means adding equal groups
- Use jumps on a number line to learn the concept of multiplication
- Write a multiplication problem as __ equal groups of __
- Use jumps on a number line to fill in multiplication problems
- Make flash cards with the 3 times tables
- Apply different strategies to memorize the 3 times tables (visual, auditory, kinesthetic)
- Use objects to create equal groups and write products
- Solve a word problem using the 3 times tables
- Bible: Matthew 28:19
- God the Father, Jesus the Son, and the Holy Spirit
- The importance of having the Trinity in our lives
- Use music, dance, or voice to practice the 3 times tables
- Draw a picture to help solve a word problem
- Write a multiplication problem from a word problem
- Fill in the blanks of a sequence by 3s
Module 5
- Multiplying by 4
- Use the strategy of double doubling
- Product is always even when multiplying by 4
- Color charts to solve multiplication facts
- Fill in the missing numbers while skip counting by 4
- Copy the 4 times tables and read out loud
- Bible: Luke 19:8
- Zacchaeus gives back 4 times as much
- Seek forgiveness from the people we have hurt
- Identify incorrect answers
- Use a multiplication chart to find answers
- Solve the 4 times tables using memorization
- Demonstrate understanding by reading a word problem, writing a multiplication problem, and solving
Module 6
- Multiplication by place value
- Identify standard form vs. expanded form
- Expanded form helps with mental math
- Place value strategy for multiplication
- Write numbers in expanded form
- Multiply each number in expanded form by the same factor
- Add products together to find final answers
- Apply the place value strategy by following steps to solve multiplication problems with larger numbers
- Multiplying by multiples of 10 and 100
- Bible: Romans 6:23
- The Gospel in a nutshell
- Demonstrate understanding of the place value strategy by putting the steps in order
- Write numbers in standard form
- Apply the place value strategy to a word problem
Module 7
- Vertical multiplication with one digit
- Definitions of vertical and horizontal
- Write math problems vertically and horizontally
- Line up digits according to place value
- Number with fewest digits goes on bottom
- Multiply the bottom number with each top number
- Carry tens digit if needed
- Identify incorrect answers
- Correct errors in vertical multiplication problems
- Identify first digits to be multiplied
- Write vertical problems horizontally
- Identify whether or not to regroup
- Identify second digits to be multiplied
- Bible: Genesis 11:1-9
- Tower of Babel was result of selfishness
- Colossians 3:23
- Work as for God and not for people
- Write horizontal problems vertically
- Show steps for vertical multiplication
- Solve vertical problems and regroup
- Write a vertical multiplication problem from a word problem
Module 8
- Estimating
- Estimation makes math easier
- Use rounding for estimation
- Look to the digit to the right of the place value when rounding
- If digit is 5 or greater, round up
- If digit is 4 or lower, round down
- Identify the wavy equal sign (≈) for approximately or about
- Round to the nearest dollar for money
- Identify if someone has enough money by estimating
- Ignore the zeros of an even ten or hundred and add in after estimating
- Identify whether to round up or down
- Follow steps to solve estimation problems
- Use estimation to solve word problems
- Round to the nearest ten and hundred
- Bible: Proverbs 21:5
- Think ahead and plan carefully
- Highlight the digit to the right of the place value being rounded
- Identify correct and incorrect rounding
- Demonstrate understanding of estimating by explaining why it is useful in math
Module 9
- Multiplication to find area
- Learn abbreviations of L (length), W (width), W (area)
- Write small raised 2 when calculating area
- Read area as squared
- Learn L x W = W
- Ignore zeroes to even tens and add after multiplying
- Real-life scenarios using area: square footage of a house, painting a room
- Use given measurements to find area of squares and rectangles
- Add the small raised 2 to every answer
- Write multiplication problems to find area
- Use knowledge of area to answer a word problem
- Bible: Genesis 6:22
- God guided Noah when building the ark
- God leads us still today
- Answer true or false for statements regarding area
- Identify errors in area calculations
- Label squares and rectangles with given measurements and solve for area
- Build a rectangle, measure it, and solve for area
Module 10
- Multiplication on a calculator
- Calculators are tools that help us do math faster
- Learn how to input numbers of a multiplication problem on a calculator
- Icons for x or * both mean multiply
- Practice using a calculator to solve large equations
- Match the calculator buttons to the order in which they are pressed
- Use a calculator to solve a word problem
- Is memorization or using a calculator faster?
- Bible: Psalm 119:11
- Memorize scripture
- Explain how calculators are helpful tools
- Identify correct and incorrect answers using a calculator
- Write vertical multiplication problems to solve word problems and check answers with a calculator
Step 4
Module 1
- Multiplication and its properties
- Define operation
- Multiplication as repeated addition
- Identify multiplicand, multiplier, factor, and product
- Identify x sign as times
- Introduction to the commutative and associative properties
- Demonstrate understanding of a multiplication problem by labeling the numbers
- Recognize examples of the commutative and associative properties
- Write equations according to the commutative property
- Circle equations according to the associative property
- Identify properties in word problems
- Bible: Romans 8:28
- God is working out a plan for our lives
- Explain the commutative and associative properties
- Write own examples of the commutative and associative properties
- Show the commutative property through images
Module 2
- Multiplying by 6
- Strategies for memorizing multiplication facts
- Visual, auditory, and kinesthetic learning styles
- Apply strategies for each learning style
- Say multiplication facts aloud
- Create an array to solve multiplication problems
- Copy facts
- Build math problems
- Bible: Psalm 119:11
- Hide God's word in our hearts
- Isaiah 41:10
- Psalm 118:24
- James 1:19
- Jeremiah 17:14
- Memorize scripture to recall when in difficult situations
- Do exercises with multiplication facts
- Choose the correct equations for arrays
- Create arrays with small objects
Module 3
- Multiplying by 7
- Memorization of 7 times tables
- Use visual, auditory, and kinesthetic strategies to practice the 7 times tables
- Apply all three strategies to create an array, copy multiplication facts, and say them out loud
- Bible: Matthew 18:21–22
- Forgiving others 77 times
- Hebrews 10:17
- God does not keep track of our sins
- Recite the 7 times tables out loud
- Listen to a song to help learn the 7 times tables
- Fill in the blanks for the 7 times tables
- Draw groups of shapes/objects to show a multiplication problem
- Write a multiplication problem from a word problem
- Fill in a chart converting weeks to days
Module 4
- Multiplying by 8
- Identify the pattern in the 8 times tables
- Apply visual, auditory, and kinesthetic strategies to multiplication facts
- Write factors when given products
- Read the 8 times tables out loud
- Copy multiplication facts
- Bible: Genesis 8:22
- We see beautiful patterns all over creation
- Seasons change, but God remains the same
- Draw pictures or use objects to represent multiplication problems
- Move around while practicing the 8 times tables
- Fill in the blanks to solve multiplication facts
- Demonstrate understanding of multiplying by 8 by solving a word problem
Module 5
- Multiplying by 9
- Use strategy with fingers to help learn 9 times tables
- Use strategy of multiplying by 10 and subtracting 1
- Check answers by adding digits, which should equal 9
- Say equations out loud
- Copy the 9 times tables
- Demonstrate understanding of a word problem by filling in blanks
- Apply the commutative property
- Demonstrate understanding of a word problem by writing a multiplication problem and solving
- Bible: Matthew 7:13–14
- God's way can be harder, longer, and tougher
- Solve multiplication problems by using a multiplication table
- Solve word problems using strategies
- Compare (<, >, =) 9 times tables
- Use arrays to solve multiplication problems
- Apply strategies to solve the 9 times tables
Module 6
- Vertical multiplication with two digits
- Line up digits according to place value
- Number with fewest digits goes on bottom
- Always start with smallest place value on bottom
- Multiply the bottom number by each top digit
- Carry tens as necessary
- Write horizontal equations vertically
- Demonstrate understanding of steps by circling first digit to multiply
- Demonstrate understanding of steps by filling in blanks
- Bible: Proverbs 4:25–27
- Keep focus on Jesus
- Identify errors in two-digit multiplication problems
- Apply steps by solving two-digit multiplication problems on own
- Solve word problem with two-digit multiplication
Module 7
- Multiplication for conversion
- Real-life examples using conversion: recipes, time, measurement
- Identify whether or not multiplication is needed in word problems
- Use multiplication to convert a recipe for more people
- Solve word problem converting yards to feet
- Solve word problem converting days to hours
- Bible: 2 Corinthians 5:17
- Isaiah 43:25
- We are new creations in Christ
- Fill in the blanks using multiplication to convert units
- Convert feet to inches
- Complete chart for increases in recipe batches
Module 8
- Division and multiplication
- Division is the opposite of multiplication
- Ask what factors multiply together to help solve division problems
- Long division helps check multiplication work
- Match division problems to opposite multiplication problems
- Demonstrate understanding of division and multiplication as opposites
- Solve division equations by finding the missing factors
- Apply knowledge of division as the opposite of multiplication by writing division problems in the same fact family as multiplication problems
- Bible: Isaiah 59:2
- Sin separates us from God
- Use division and multiplication signs correctly
- Apply the commutative property to write two multiplication problems for each division problem
- Identify the correct division problem to solve a word problem
Module 9
- Multiplication to find volume
- Review of area for 2D shapes as length x width
- Volume is the amount of space a 3D shape occupies
- Volume is length x width x height
- Volume is always cubed
- Area is always squared
- Identify 2D and 3D shapes
- Label the length, width, and height of a 3D shape
- Demonstrate understanding of the difference between area and volume
- Write multiplication problems to find volume
- Use 3D shapes and dimensions to solve for volume
- Find volume in a word problem
- Bible: John 3:30
- We want to make more room for God in our lives
- Fill in the blanks to create multiplication problems for volume
- Convert feet to inches and find the volume
- Identify smaller and larger volume
Module 10
- Multiplying by 11
- Apply the double the digit strategy for single-digit numbers multiplied by 11
- For two-digit numbers, add the two digits together and put the answer in the middle of the digits
- Review of the identity property of multiplication
- Solve multiplication by 11 vertically and horizontally
- Fill in an 11s multiplication chart
- Demonstrate understanding of both strategies by choosing the correct one for different problems
- Use the double the digit strategy
- Complete a table using the second strategy for double-digit numbers
- Apply a strategy to solve a word problem
- Explain the two strategies in own words
- Bible: Matthew 28:19
- The Great Commission and sharing our faith
- Highlight the errors and solve for the correct answers
- Match the multiplication problems to the correct answers
- Apply knowledge of 11 times tables to solve a word problem
- Fill in the blanks to make division problems true
Step 5
Module 1
- Multiplication properties
- Simple groups of whole numbers
- Repeated addition
- Read, understand, and identify the parts of a multiplication problem: multiplier, multiplicand, factors, multiplication symbol (times), and product
- Relationship between multiplication and addition
- Different properties in math: commutative, associative, distributive, identity, and zero
- Match problems with the correct properties
- Explain how multiplication properties work
- Create examples of different multiplication properties
- Bible: having a strong foundation
- Building your life on the Word of God
- Matthew 7:24
- Matthew 7:25–27
- Identify the parts of a multiplication equation
- Complete the missing digits in multiplication equations to demonstrate the zero property
- Apply knowledge of multiplication properties to solve word problems
- Use different properties to solve multiplication problems
- Create multiplication equations using the commutative property
Module 2
- Multiplying by 12
- Strategies to multiply by 12: double the number and add to its neighbor
- Look for patterns on a number chart
- Practice 12 times tables
- Increase fluency when multiplying by 12
- Reflect on understanding of 12 times table
- Skip count by 12
- Bible: Matthew 10:1
- Jesus calls the 12 disciples
- Matthew 28:19
- Jesus is still calling us to be disciples today
- Increase math fluency with 12 times tables
- Use strategies to solve multiplication problems with 12
- Apply knowledge of multiplying by 12 to solve word problems
- Real-life application of counting by 12
- Use a number line to skip count by 12
Module 3
- 3+ digit multiplication
- Step by step introduction to 3+ digit multiplication
- Write zeros for correct place value
- Multiply every digit in the bottom number with every digit in the top number
- Place value in 3+ digit multiplication
- Start in the ones place
- Visual strategies in 3 + digit multiplication: highlighting and color-coding
- Bible: Matthew 6:33
- Put Jesus first
- Acronym JOY to help set priorities
- Identify errors in 3+ digit multiplication problems
- Practice 3+ digit multiplication
Module 4
- Multiplying fractions and whole numbers
- Convert whole numbers to fractions
- Multiply numerators and denominators
- Simplify fractions
- Rewrite multiplication problems to allow solving
- Explain how to multiply a fraction and a whole number
- Bible: Genesis 11:1–9
- God knew the pride of the people who built the Tower of Babel
- Colossians 3:23
- Do Christ's work with humility
- Convert improper fractions to mixed numbers
Module 5
- Multiplying mixed fractions
- Use tool of a check mark visual to convert mixed fractions to improper fractions
- Multiply numerators and denominators
- Simplify answer to be written in lowest common terms
- Identify mixed numbers from improper fractions
- Practice using a calculator to solve multiplication equations with fractions
- Bible: Matthew 18:12
- Parable of the lost sheep
- We are important to and loved by God
- Demonstrate understanding of multiplying mixed numbers by explaining in words
Module 6
- Multiplying decimals
- Real-life applications of multiplying decimals: taxes and tips
- Count decimal places in factors to put decimal in product
- Identify how many decimals are needed in products
- Use the strategy of putting the number with the fewest digits on bottom
- Rewrite multiplication problems vertically
- Apply knowledge of multiplying decimals to word problems
- Bible: Matthew 13:31–32
- Parable of the mustard seed
- God can use the smallest faith and multiply it
- Identify errors when multiplying decimals
Module 7
- Calculating surface area
- Real-life application of calculating surface area: water striders
- Use multiplication to calculate surface area of rectangular prisms and cubes
- Surface area in square units with exponents
- Define surface area
- Bible: 1 Corinthians 3:10
- God as the foundation of our lives
- Using God's tools to build our lives
- Demonstrate understanding of surface area through word problems
- Explain how to find the surface area of a rectangular prism and cube
Module 8
- Understanding exponents
- Understand exponents as multiplication
- Learn new terms: exponential expression, base, exponent
- Exponents as repeated addition
- Solve problems with exponents of 0, 1, 2
- Learn ways to say exponential equations: squared, raised, power of
- Rewrite exponential expressions as multiplication problems
- Identify incorrectly solved exponential expressions
- Use knowledge of exponents to solve word problems
- Bible: Ephesians 3:20
- God's power multiplies
- He pours out blessings in abundance
Module 9
- Order of operations
- Memorize and explain acronym PEDMAS
- Apply PEDMAS to solve equations
- Demonstrate understanding with multilevel equations
- Bible: Psalm 119:105
- God's word is a lamp
- Have faith and follow God one step at a time
- Write order of operations
- Demonstrate understanding by writing own multistep equation
Module 10
- Multiplying integers
- Identify integers as positive or negative whole numbers
- Memorize rules for multiplying integers
- Identify problems with a positive or negative product
- Answer multiplication problems according to rules for multiplying integers
- Apply rules to horizontal and vertical equations
- Explain when to use different properties with integers
- Bible: Galatians 6:7
- What we plant is what we get
- Apply rules to fraction multiplication problems
Step 6
Module 1
- Ratios and multiplication
- Applying multiplication
- Ratios are a way of comparing quantities
- How to simplify and scale ratios
- Different ways to write ratios: as fractions, with a colon, or in words
- Real-life examples of ratios: recipes, demographics, and profit to cost
- Scale given ratios
- Apply knowledge of ratios to solve word problems
- Fill in the missing parts of ratios
- Bible: God's clear instructions on resting on Sabbath (Shabbat)
- Exodus 20:9–10
- Exodus 20:8
- The ratio of rest days to work days in a week
- Use deductive reasoning to solve math riddles
- Reflect on understanding of exponents and multiplication
Module 2
- Multiplying exponents
- Diagram of an exponent
- Exponents are repeated multiplication
- How to multiply exponents in varying scenarios: same exponents, same bases, or all different
- Use a calculator to solve exponents
- Solve exponents by multiplying and showing your work
- Solve multiplication problems when exponents are the same
- Solve multiplication problems when bases are the same
- Solve multiplcation equations with different bases and exponents
- Bible: The Great Commission
- Matthew 28:19
- The early church grew exponentially
- How to share the Gospel with others
- Write exponents in expanded form
- Explain how to solve for different types of exponent problems
- Identify the exponent equation that is solved incorrectly
- Use deductive reasoning to solve exponent math puzzles
- Reflect on understanding of multiplying exponents
Module 3
- Multiplying scientific notation
- Define scientific notation
- Reducing numbers in relation to the base 10 system
- Location and movement of the decimal in scientific notation
- Steps to multiply numbers written in scientific notation
- The use of parenthesis in multiplication of scientific notation
- How to reduce numbers written in scientific notation
- Add missing parenthesis to multiplication problems with scientific notation
- Solve and reduce multiplication problems written in scientific notation
- Use a calculator to solve multiplication problems with scientific notation
- Identify scientific notation expressions and equations that are written incorrectly
- Bible: God knows, sees, and loves each of His children
- Jeremiah 1:5a
- Isaiah 43:1b
- Psalm 139:1
- Psalm 33:13–15
- Explain how scientific notation works
- Correctly write expressions in scientific notation
- Use knowledge of scientific notation to solve math puzzles
- Reflect on understanding of multiplying scientific notation
Module 4
- Multiplying monomials
- Algebraic concepts in multiplication
- Diagram of a monomial: coefficient, variable, and exponent
- How to multiply monomials with similar variables, different variables, and multiple powers
- Identify terms that are monomials
- Multiply to solve and simplify equations with monomials
- Solve monomial expressions with multiple powers
- Bible: God has uniquely designed each person for a special purpose in His kingdom
- Ephesians 2:10
- Explain how to solve different types of monomial multiplication expressions
- Complete the missing parts of monomial multiplication expressions
- Find the value of variables in monomial multiplication expressions
- Reflect on understanding of multiplying monomials
Module 5
- Multiplying binomials and trinomials
- Define and identify a monomial, binomial, and trinomial
- Write and solve algebraic equations with binomials and trinomials
- Follow steps to multiply binomials and trinomials
- Parts of an algebraic equation: parentheses, variables, exponents
- Combine like terms
- Organize terms from largest exponent to smallest
- Bible: tri- means three
- The recognition of the Trinity: God the Father, God the Son, and God the Holy Spirit
- The Great Commission
- Matthew 28:19
- Simplify expressions with binomials and trinomials
- Reflect on understanding of multiplying binomials and trinomials
Module 6
- Multiplying polynomials
- Define the term polynomial
- Rules for identifying a polynomial
- Use the distributive property to combine equations
- Use parentheses to combine equations
- Follow steps to multiply polynomials
- How to combine like terms with polynomials
- Identify polynomial expressions
- Bible: Exodus 20:3
- Defining polytheistic religion
- The importance of putting God first
- Explain the process of multiplying monomials by polynomials and polynomials by polynomials
- Simplify expressions with polynomials
- Apply knowledge of scientific notation expressions to solve math riddles
- Reflect on understanding of multiplying polynomials
Module 7
- Multiplying percentages
- Real-life examples of multiplying percents: discounts, tips, tax, and data
- Convert percents to decimals
- Use a calculator to multiply percents
- How to multiply percents
- Count decimal places in factors
- Multiply by percents to solve for tax owed
- Calculate the total cost of items after tax
- Apply knowledge of multiplying percents to solve word problems
- Bible: James 1:17
- Tithing is a way to give back to God for our blessings
- Leviticus 27:30
- Calculate the tip owed
- Use knowledge of multiplying percents and deductive reasoning to solve math riddles
- Reflect on understanding of multiplying percents
Module 8
- Multiplying radical expressions
- Real-life examples of radical expressions: architecture, construction, physics, engineering, and computer graphics
- Read, understand, and label the parts of a radical expression: root symbol, radicand, root index, and cube root
- Rules to follow when multiplying radical expressions
- Working with positive and negative radicands
- Multiply radicands and coefficients
- Practice using a calculator while multiplying radical expressions
- Multiply and solve binomial radical expressions
- Simplify and organize radical expressions
- Bible: your roots, beliefs, faith, and morals serve as the foundation of your life
- God can combine our roots with other believers to make them stronger
- Ecclesiastes 4:9–10
- Stay rooted in God
- Colossians 2:7
- Solve problems to demonstrate understanding of multiplying radical expressions
- Apply knowledge of multiplication to solve math puzzles
- Reflect on understanding of multiplying radical expressions
Module 9
- Multiplying rational expressions
- Real-life examples of rational expressions: computer programming, finance, chemistry, and engineering
- Rules for multiplying rational expressions
- Simplify expressions
- Options for factoring
- Greatest common factor (GCF)
- How to combine, cancel, and rewrite an expression
- Simplify by finding the GCF
- Factor by breaking apart perfect squares
- Factor with trinomials
- Cancel and simplify fractions in rational expressions
- Bible: Beauty in simplifying
- Clutter can hinder relationships with God
- Hebrews 12:1–2a
- Identify perfect squares
- Determine which equations can be simplified
- Explain how to factor when simplifying equations
- Apply knowledge of multiplication to solve math logic puzzles
- Reflect on understanding of multiplying rational expressions
Module 10
- Scaling matrices
- Arrays and matrices are used to organize things into rows and columns
- Matrices help to represent and interpret data
- Real-life examples of matrices: video games, engineering, robotics, computer science and coding, GPS, image processing, music production, economics, and business
- Read and understand the term element
- How to scale a matrix
- Observe the relationship between numbers in a matrix
- Use lambda to multiply elements of a matrix
- Identify the number of rows and columns in a matrix
- Write the dimensions of a matrix
- Scale matrices
- Explain what a matrix is, how to use one, and why they are utilized
- Bible: examples of God giving directions
- Noah
- Moses
- Solomon
- Exodus 26:15–30
- 1 Kings 6:2–6
- 1 Corinthians 14:33
- Clear clutter to increase peace
- Label the parts of a matrix problem
- Reflect on understanding of scaling matrices