Modular Math: Number Sense

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Foundations: Kindergarten equivalent
Step 1: Grade 1 equivalent
Step 2: Grade 2 equivalent
Step 3: Grade 3 equivalent
Step 4: Grade 4 equivalent
Step 5: Grade 5/6 equivalent
Step 6: Grade 7/8 equivalent

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Number Sense

Welcome to Number Sense, the first unit in our innovative Modular Math curriculum for Kindergarten-Grade 8. We start at the very beginning to build a solid foundation and understanding of numbers. Younger levels will work on their counting skills using a number line, skip counting, tally marks, and number words. As we work our way up, we’ll explore place value, Roman numerals, ordinal numbers, expanded form, prime vs. composite numbers, rounding, square and cube roots, exponents, factoring, and so much more! Learning these basic concepts is crucial and will set students up for success in future units.

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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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Number Sense Scope and Sequence

Foundations

Module 1

Numbers 0–9
Every number has a name
Count by 1's
Count objects to learn number meaning
Represents numbers 0–9 with concrete objects, pictures, and kinesthetic movement
Read, trace and write numbers 0–9
Matches sets and numbers
Demonstrate number comprehension: 0–9
Bible: Hebrew words for numbers 0–9

Module 2

Count forward + back 0–10
Take one away from 10 down to 0
Real-life applications of counting down
Count forward to 10 + backward from 10
Express number meaning by drawing or circling objects
Demonstrate number comprehension using kinesthetic approach
Count and identify 1 more than or 1 less than a number 0–10
Bible: 2 Peter 3:9

Module 3

Tally marks 1–10
Group tally marks in sets of 5
Trace + draw tally marks
Understand relationship between tally marks + number meaning
Bible: 1 Corinthians 13:4–5

Module 4

Numbers: 11–20
2 digits together: make new number
Count from 11–20
Number recognition: 11–20
Understand numbers 11–12 as a group of 10 and 1s
Number meaning: 11–20
Represents numbers 11–20 using pictures + kinesthetic movement
Bible: Hebrew words for numbers 11–20

Module 5

Compare numbers within 20
Real life application of bigger + smaller
Understand terms used in comparing: bigger, larger, more + lesser, smaller, less
Identify smaller + larger numbers
Identify the larger + shorter path
Demonstrate understanding of comparing quantities
Demonstrate understanding of comparing numbers
Bible: 2 Corinthians 10:12b
Comparing ourselves to others

Module 6

Numbers before and after
Identify + represent numbers before and after
Identify a set of numbers in the correct order
Complete the set of 3 descending numbers with the correct number
Identify numbers that come before + after
Bible: Jeremiah 1:5
God knows us + loves us
He decided our beginning + has a plan for us

Module 7

Count by 2s
Use pictorial cues to skip count by 2s
Practice skip counting out loud following written numbers
Demonstrate understanding of counting by 2
Circle objects into groups of 2
Use concrete objects to count by 2s
Fill in the missing numbers when counting by 2s
Bible: two of every single bird, animal, + insect on the ark
Genesis 7:8–10

Module 8

Count 1–20 using the number line
Number line: useful for skip counting, comparing numbers, + before and after
Parts of a number line
Identify and fill in missing parts + numbers on a number line
Understand number relationships using a number line
Use a ruler to measure objects + compare numbers
Create a number line on paper or using concrete objects
Bible: God has no beginning and no end
Psalm 90:2
God is faithful

Module 9

Ordinal numbers to 5
Identify + represent ordinal position
Understand + use ordinal numbers: 0–5
Match the ending of ordinal number names with the written numbers
Number events in a list in the correct order
Bible: Matthew 6:33
Make God our priority

Module 10

Dozen/half dozen
Use concrete objects to understand + show dozen and half dozen
Group pictures into half dozen and dozen
2 half-dozens = 1 dozen
Kinesthetic activity to represent a dozen
Demonstrate understanding of terms: dozen + half dozen
Bible: Jesus and His twelve disciples
The Holy Spirit lives in you when you choose to follow Jesus

Step 1

Module 1

Number words zero to five
Express numbers in 3 ways: quantity of objects, symbol/digits, + word
Real-life applications of number words
Read, spell, + write number words: zero to five
Understand meaning of number words zero to five
Use concrete objects to show number comprehension
Bible: Hebrew words for numbers
Review: tally marks to represent a number
Review: skip count by 2s to 10

Module 2

Count by 2s: 0–20
Benefits of learning to count by 2
Use visual cues to count by 2
Pair: a group of two
Identify 2 more and 2 less using a number line
Bible: groups of 2 throughout
Ecclesiastes 4:9
Review: writes + reads number symbols 0–20

Module 3

Tally marks 1–20
Counting by 5: every number will end in 0 or 5
Count by 5s
Count the tally marks + identify the number they represent
Use tally marks to represent quantity + number
Bible: Jesus had 12 apostles
Mark 3:14
When we confess, God forgives us
Jesus's blood washes us clean

Module 4

Compare numbers within 20
Read, write, + understand greater than/less than equations
Correctly use the > and < symbols
Understand terms for comparing
Bible: God's value system is different than ours
1 Samuel 16:7b
God looks at our motivation

Module 5

Ordinal numbers to 10
Read + write ordinal numbers and ordinal number words
Match the ordinal number to its small ending: first through tenth
Ordinal numbers can be shown in 3 ways: objects, symbols with small letters, written words
Understand and use ordinal numbers to 10
Bible: Matthew 19:30
Test our hearts, thoughts + motivations
Review: counting forward + back using visual cues

Module 6

Number words six to ten
Read, write, + spell number words: six to ten
Represent quantities of number words zero to ten
Understand and use number words zero to ten
God created everything in six days
Bible: Genesis 2:3
Seventh day: God rested from all his work

Module 7

Place value to 10
Introduction to place value: one's and ten's
Each place can only fit 9
Count by 10s
Identify digits in one's and ten's places
Use place value knowledge to compose 2-digit numbers
Bible: Ten commandments given to Moses from God

Module 8

Count by 5s and 10s
Use visual cues to count by 5
Use visual cues to count by 10
Demonstrate understanding of counting by 5
Demonstrate understanding of counting by 10
Bible: Jesus took five loaves and two fish, multiplied them, and fed 5,000 people

Module 9

Place value to 100
Understand that numbers have rules they always follow
Identify digits and place value in 3-digit numbers
Understand value of each place to hundred's
Bible: Luke 15:4–7
God cares about each and every one of us

Module 10

Odd and even numbers
Identify, use, + understand even and odd numbers
Write + spell even and odd
Bible: God teaches us to forgive, love, + rejoice for others
Deuteronomy 31:8
God is always with you: you are never left out by Him

Step 2

Module 1

Place value to 1,000
Numbers: mean different things based on place
Read + write whole numbers to the thousands (4-digit numbers)
Understand places each only fit 0–9
Skip count by tens to 100
Identify the place value of digits to 1,000
Demonstrate understanding of place value in 4-digit numbers
Bible: God made us to walk with Him, but sin entered
Sin: broken world
Jesus: making a new home for us
John 14:2–3
Review: even numbers, comparing, tally marks, count by 5s, ordinal numbers

Module 2

Number words and word problems
The process for solving word problems
Real life applications for spelling number words
Demonstrate understanding of word problems
Read, spell + write number words: eleven to twenty
Understand meaning of number words
Clue words in word problems: most
Read + solve word problems: ordinal numbers, subtraction, comparing numbers, skip count by 2s
Comparing numbers: > or < signs
Write a number equation for comparison
Bible: Hebrew words for numbers

Module 3

Count by 100s to 1000
Use place value understanding to count by hundreds
Understand + use ordinal numbers
Apply counting by hundreds to word problems
Identify how many hundreds are in each number
Bible: God is bigger than time
2 Peter 3:8
God is limitless
God has no beginning + no end
Identify hundreds number that comes before + after
Make number comparisons: 100s
Review: place value, number words

Module 4

Count by 3 to 60
Patterns when skip counting by 3
Use visual cues to skip count by 3
Solve word problems by skip counting by 3
Demonstrate understanding of skip counting by 3
Bible: the number 3 throughout the Bible
Matthew 12:40
Jonah: 3 days in the belly of big fish
Jesus died, He was buried, He rose 3 days later
Connections throughout the Bible
Apply skip counting by 3 to word problems
Jacob: renamed Israel by God + 12 sons became known as tribes of Israel

Module 5

Ordinal numbers to 20
Endings of ordinal numbers
Read, write, + understand ordinal numbers: 1st–20th
Use ordinal numbers through 20 to describe position
Bible: 1 Corinthians 12:27
God has a special plan for your life
He gave you talents, strengths, + spiritual gifts
1 Corinthians 12:14–15
Your part is important
Review: Identify a pattern

Module 6

Count by 25
1 quarter = 25 cents
100 cents = 1 dollar
Use visual cues to skip count by 25
Identify patterns when counting by 25
Demonstrate understanding of counting by 25
Apply counting by 25s to comparison and word problems
Bible: Matthew 6:25
God will take care of our needs

Module 7

Roman numerals to 10
Roman numerals show value of a number
Understand the rules of Roman numerals
Real-life application of Roman numerals
Use Roman numerals to represent numbers to 10
Read + write Roman numerals to 10
Bible: Roman Empire
Jesus: the Messiah
Isaiah 43:19
God can do things we never thought of

Module 8

Expanded + standard form to the thousand's place
Read + write 4-digit numbers in expanded form + standard form
Demonstrate understanding of place value by using expanded form
Bible: Isaiah 54:2–3
Seasons of "expansion" or growth
Make room for God so that we can grow

Module 9

Show understanding of numbers by comparing them
Compare 3- and 4-digit numbers
Correctly use the < and > signs
Order 4-digit numbers from least to greatest or greatest to least
Demonstrate understanding of terms used when comparing
Bible: Matthew 20:1–16
Parable of the laborers in the vineyard: God gives the same gift of salvation to any who will receive it
We can get caught in comparison with others
New perspective of His kingdom math: what is truly great and truly lesser
John 16:33b

Module 10

Counting by 50s to 500
Half of 100 is 50
Understands before + after when counting by 50
Identify how many sets of 50 make a number 50–500
Apply skip counting by 50s to word problems
Bible: the number 50 throughout the Bible
Year of Jubilee
Days between Jesus's resurrection and Pentecost
Feast of Weeks
Nun in Hebrew means pure, free, full/abundant
Count the blessings in your life

Step 3

Module 1

Place value to 10,000
Place tells us what a number is worth
Understand places each only fit 0–9
Periods: each group of 3 digits + separated by commas
Read + write large numbers to ten thousand's place
Identify place value of digit in 5 digit numbers
Compose numbers when given place value of digits
Bible: value of how we spend our time
1 Corinthians 10:23 NIV
Demonstrate understanding of place value to 10,000
Review: ordinal numbers to 20
Review: count by 25s to 200
Review: Roman numerals to 10
Review: expanded form
Review: word problems

Module 2

Count by 4
Use visual cues to count by 4
Group items into sets of 4
Solve word problems by counting by 4
Demonstrate understanding of counting by 4
Bible: the number 4 throughout
Revelation 4:8b
See God's creation + order + structure when we study numbers
Review: skip count by 2s, 5s, 10s, 25s, 100s
Review: determine the number pattern + continue

Module 3

Compare numbers with up to 4-digits
Use + understand symbols used when comparing numbers: > , <, =
Read + write equations of comparison
Review: understand tally marks
Order numbers from largest/greatest to smallest/least
Order numbers from smallest/least to largest/greatest
Bible: comparing ourselves to others
Galatians 6:4–5
Look at our own jobs God has given us to do
Review: demonstrate understanding of number words, Roman numerals, tally marks, + skip counting when comparing amounts

Module 4

Expanded form to 10,000
Read + write 5-digit numbers in expanded form + standard form
Demonstrate understanding of place value by using expanded form to the 10,000s
Understand terms: expanded form + standard form
Bible: parables of Jesus about values + treasures
Matthew 13:44–46
Value of God's kingdom

Module 5

Count by 6
Understand what it means to skip count
Use visual cues to count by 6
Demonstrate understanding of counting by 6
Use skip counting by 6 to determine total
Solve word problems by counting by 6
Bible: 6th day of creation
Genesis 1:24–26
God is a God of order: patterns + structure in the way he created living things

Module 6

Negative and positive numbers
Real life application of negative numbers
Understand the meaning of positive and negative numbers
Negative numbers always need negative symbol
Use a number line to understand negative and positive numbers
Bible: Lives are balanced when living surrendered to Him
Take steps to bring us back into alignment with God's word
John 15:5
Use > and < signs to compare negative and positive numbers

Module 7

Round to the nearest 10
Real life application of rounding to ten's place
Rules for rounding to nearest 10
Use visual cues to round to the nearest 10
Demonstrate understanding of rounding 2-digit numbers to the nearest 10
Bible: Philippians 4:8

Module 8

Roman numerals to 100
Real life application of Roman numerals
Rules for how to write Roman numerals to 100s
Read + write Roman numerals to 100s
Apply knowledge of expanded form to Roman numerals to 100s
Demonstrate understanding of Roman numerals to 100s
Bible: Codes in the Bible
John 6:35
Write numbers in words, tallies, + roman numerals

Module 9

Word problems
Clue words for solving word problems
Word problems use both sides of your brain
Apply knowledge of rounding + skip counting to word problems
How to break word problems into steps
Determine strategy used when solving word problems
Use addition, subtraction, multiplication, division, rounding, + skip counting to solve word problems
Solve 2-step word problems
Bible: Parables
Mark 4:9b
The Holy Spirit: opens our eyes so we can see and our ears so we can hear

Module 10

Count by 7
Use visual cues to count by 7
Demonstrate understanding of counting by 7
Bible: Number seven throughout the Bible
Other groups of seven God made
Use skip counting by 7 to determine total
Divide a total into groups of 7
Use skip counting by 7 to solve word problems + complete comparison equations

Step 4

Module 1

Place value to 100,000
Periods in large numbers
Read + write numbers to the hundred thousands place
Identify the period of digits
Understand place value of a digit in 6-digit numbers
Bible: God has built in pauses
Psalm 62:8
Selah
Pause + reflect on what God has done
Review: use > and < signs to compare 4- and 6-digit numbers
Review: round to the nearest 10
Review: write negative and positive numbers in order from least to greatest
Review: determine the number pattern + continue the pattern
Review: compare Roman numerals
Review: follow clues to compose a number

Module 2

Expanded form to 100,000
Real life application of spelling + writing number words
Identify standard form vs. expanded form
Word problems: expanded form + standard form
Read + write 6-digit numbers in words, standard form, + expanded form
Psalm 77:11
Remember what the Lord has done: list our blessings
Compose + decompose 5- and 6-digit numbers
Order numbers from greatest to least + combine them into standard form
Understand the relationship between numbers in standard form, expanded form, + word form

Module 3

Count by 8
Memorize the number sequence when skip counting
Identify every 8th number from 1–100
Use picture cues to count by 8
Bible: do not step skips in life
Colossians 3:23
Work hard as an offering to Him
Review: skip count by 2, 3, 4, 5, 6, 7, 10, 20

Module 4

Roman Numerals to 1,000
Rules for Roman numerals to 1,000
Real world application of Roman numerals
Read + write Roman numerals to 1,000
Apply knowledge of expanded form to Roman numerals
Bible: the Roman Empire during Jesus's time
Matthew 16:3b
Skip count using Roman numerals
Demonstrate understanding of Roman numerals to 1,000

Module 5

Comparing numbers: = vs. ≠
Demonstrate number comprehension by comparing them
Use = or ≠ to compare two numbers or expressions
Apply knowledge of addition, subtraction, skip counting, Roman numerals, negative numbers when determining = or ≠
Bible: 2 Corinthians 6:14
Importance of being equally yoked

Module 6

Count by 9
Trick for multiples of 9 to 90
Use visual cues to skip count by 9
Use skip counting by 7 to determine total
Bible: 9 gifts from the Holy Spirit
1 Corinthians 12:8–10
Thank God for the gifts He gives
Demonstrate understanding of skip counting by 9
Use skip counting by 9 to solve word problems + complete comparison equations
Apply knowledge of skip counting by 9 to Roman numerals

Module 7

Prime + composite numbers
Attributes of numbers: odd or even, negative or positive, + prime or composite
Understand terms: prime + composite
Demonstrate understanding of prime + composite numbers
Describe what makes a number prime or composite
Identify prime + composite numbers
Bible: Hebrews 4:12
God's word is not dead!
Read God's word + allow Him to work in you
Apply knowledge of prime + composite numbers to Roman numerals, expanded form + number words

Module 8

Count by 11
Tricks for multiples of 11
Multiplication means skip count a certain number of times
Multiply 2-digit numbers by 11
Demonstrate understanding of skip counting by 11
Bible: Matthew 20
The eleventh hour: last minute
The parable of the laborers in the vineyard
It is never too late to accept Jesus
Sins are never too great to be forgiven
2 Peter 3:9
It is never too late for God to move
We can trust His plans
Use skip counting by 11 to determine totals

Module 9

Round to the nearest 100
Rules for rounding to the nearest 100
Demonstrate understanding of rounding to the nearest 100
Apply knowledge of rounding to solving word problems
Bible: Matthew 18:12b–13
God is unwilling to skip even one of His children
El Roi: the God who sees you

Module 10

Count by 12
Strategy for counting by 12
Connect skip counting by 12 to multiplication
Apply counting by 12 to word problems
Demonstrate understanding of counting by 12
Identify patterns in number sequences
Write x12 multiplication equations
Bible: God built in numbers, patterns, + structure in creation
Twelve throughout the Bible
Hebrew: 12 means perfect government
Think about things that come in sets of 12

Step 5

Module 1

Place value to 100 million
Understand the pattern of periods to the millions period
Identify the place value of digits in a 9-digit number
Write 9-digit numbers in expanded form
Bible: the effects of money in life
Matthew 22:22–23
Be a good steward of money
Read + write large numbers to hundred millions place in number + word form
Compose 9-digit numbers when given place value of digits
Identify patterns in number sequences + complete the pattern
Review: rounding, comparing numbers, roman numerals, skip counting, prime + composite numbers

Module 2

Math symbol: π
Meaning of pi
World record holder for reciting the most digits of pi: Suresh Kumar Sharma
Estimate pi to be 3.14 when solving problems
Divide the circumference by the diameter: answer is always pi
Demonstrate understanding of π: symbol, numerical value, meaning
March 14: international pi day + Albert Einstein's birthday
Bible: circular/cycle pattern in creation
Revelation 22:13
God and His love for you are constant + unchanging

Module 3

Round numbers to 10,000
Steps + rules for rounding to the nearest 10,000
Demonstrate understanding of rounding numbers to the 10,000 place
Bible: we have an effect on other believers
1 Corinthians 12:26
Bride of Christ: metaphor for the Church as all the believers around the world

Module 4

Integers + inverse operations
Understand the meanings of integer + inverse operations
Read + write equations using inverse operations
Apply the commutative property to equations
Bible: Jesus cancels our sin
Positive power of the blood of the Lamb
Colossians 2:13–14
Demonstrate understanding of integers + inverse operations

Module 5

Factor trees
Identify prime + composite numbers
Strategies for breaking numbers into factor trees
Create factor trees
Understand prime factorization using factor trees
Bible: motivations of our hearts
Hebrews 4:12
Spend time in His word + seeking His voice
Multiply factors to find product

Module 6

Greatest common factor (GCF)
Meaning of common factors
Identify common factors + greatest common factor of 2 numbers
Bible: Acts 4:32
The early church
Followers of Jesus have a lot in common
Use prime factorization to find common factors, + greatest common factor

Module 7

Least common multiple (LCM)
Use skip counting to find the least common multiple of 2 numbers
Write least common multiple questions
Bible: Holy Spirit is alive + active in every believer
1 Corinthians 3:16
Describe meaning of LCM
Demonstrate understanding of LCM

Module 8

Base-10 system
Understand clear patterns + structures to help numbers make sense
Meaning of base-10 system
Read, write + use base-10 system to determine place value
Read + write numbers using expanded notation
Strategy for multiplying multiples of 10
Bible: God does not distribute love according to place or position
Galatians 3:28
Use base-10 system to compare + order numbers

Module 9

Squared numbers
Real-life example of square numbers
Read, write, + use squared numbers
Use multiplication expression to represent squared numbers
Find values of squared numbers
Define squared
Bible: Ecclesiastes 4:9–10
God designed us to be in relationship with others
Demonstrate understanding of squared numbers

Module 10

Inverse operations: multiplication and division
Meaning of inverse operations
Applications of inverse operations
Identify inverse operations
Use fact families to write multiplication and division equations
Read + write inverse equations + fact family triangles
Bible: triangle can represent Biblical principles
John 16:12–15
The Holy Spirit helps us when we pray to God

Step 6

Module 1

Exponential place value
Meaning of exponent and base
Symbol for exponent: superscript number
Use base-10 system to understand exponential place value
Read + write different ways to represent place value: exponential, number word, number symbols, multiplication
Write equations to show meaning of exponents
Demonstrate understanding of base, exponent, exponential place value, + base-10 system
Bible: Jesus was raised from the dead by the power of God
Romans 6:4
2 Corinthians 5:17
Solve equations with exponents
Review: expanded notation, least common multiple, greatest common factor, pi

Module 2

Cubes
Real-life application of cubing numbers
Identify base + superscript in cubed numbers
Read + write equations to show meaning of cubed numbers
Solve equations to find cubed numbers
Demonstrate understanding of cubed + cubed numbers
Bible: King Solomon
Measurements of temple were precise: a perfect cube
1 Kings 6:20
Specific measurements throughout the Bible
God built math + order into creation
Review: inverse operations

Module 3

Negative exponents
Understand meaning of positive + negative exponents
Read + write reciprocal form of negative exponents
Read + write equations to solve negative exponents
Explain the relationship between terms: reciprocal + negative exponent
Bible: Adam + Eve in the Garden of Eden
Jesus' death + resurrection changed everything: the curse was reversed
John 3:16

Module 4

Square roots of perfect squares
Symbol for square root
Meaning of terms: radical, radicand, + perfect squares
Write radical equations
Write radical form of perfect squares
Write multiplication equations to show inverse operation of radical expressions
Use a calculator to find square roots
Bible: Hebrews 12:15
Weed of bitterness
Ephesians 4:26

Module 5

Rational and irrational numbers
Application of rational and irrational numbers in math
Understand meaning of terms: rational and irrational
Identify rational + irrational numbers
Bible: teaches us right + wrong
Old Testament: Ten Commandments
Isaiah 5:20

Module 6

Cube roots
Understand meaning of cube root as the inverse operation of a number cubed
Symbols used for cube roots: radical and index
Real life applications of cubed roots
Write radical equivalent for cubed numbers
Rules for writing radical form of negative cubed numbers
Read, write + use multiplication problems to express cube root
Bible: 3 things the Bible mentions being rooted in
Colossians 2:6–7
Ephesians 3:17
Jeremiah 17:7–8

Module 7

Comparing integers
Understand meaning of terms: integers, opposite integers, absolute value
Symbols for negative numbers + absolute value
Read, write, + use signs of numbers
Identify opposite signs + opposite integers
Determine absolute values of integers
Write equations to compare numbers with and without absolute value
Define absolute value
Bible: Matthew 20:16
God is concerned with motivation of our hearts
Matthew 7:21
Follow His will for us

Module 8

Square + cube roots with factoring
Importance of learning to solve perfect roots
Use factoring to solve perfect square + cube roots
Symbol for approximation
Estimate square roots when a number is not a perfect square
Estimate cube roots when a number is not a perfect cube
Describe the relationship between prime factors + perfect roots
Bible: personal intimacy with the Father
The importance of prayer, time with God, and obedience
Matthew 25:1–13

Module 9

Laws of exponents
Use of systems, rules, + steps in math
Match laws of exponents to the equation that illustrates it
Simplify exponents by using the laws of exponents
Use the laws of exponents to solve problems
Bible: Romans 3:20
Rules help us define right from wrong
Jesus is the only way, the truth, and the life

Module 10

Scientific notation
Simplify very long numbers using scientific notation
Understand steps for making a number smaller using scientific notation
Read + write numbers in scientific notation
Compare numbers written in scientific notation
Convert numbers from scientific notation to standard form
Demonstrate understanding of scientific notation
Describe usefulness of scientific notation
Bible: many stories + truths shared multiple times throughout Bible
James repeated teachings from the Sermon on the Mount
Matthew, Mark, Luke, + John: recounted many of the same stories
Joshua 1

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