Decimals
Release Date: August 10
Welcome to Decimals! Designed for students in Grades 4–9, this Modular Math unit builds a strong understanding of decimals through real-world applications like money and measurement while developing skills in place value, comparing, ordering, and operations. As students progress, they apply decimals to fractions, percents, equations, geometry, scientific notation, probability, statistics, and other advanced math concepts through a mastery-based approach.
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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Decimals
Foundations
Module 1
- Introducing tenths
- Decimals show amounts between whole numbers
- Ones and tenths place value
- Ten tenths = one whole
- Use a visual to show one tenth
- Read a decimal aloud
- Identify a digit in the tenths place
- Write a decimal with given numbers
- Identify incorrectly written decimals
- Write the word form of a decimal
- Write a decimal for a shaded visual
- Fill in a place value chart
- Match decimals to their word form
- Shade blocks to show a decimal
- Bible: Nehemiah 3–4 (specifically 4:6)
- God uses each of our small "parts" for His big "whole"
Module 2
- Tenths in real life: temperature, length, weight
- 5/10 = 1/2
- Match the decimal to what it decribes
- One dime = 1/10 of a dollar
- Write the corect decimal for a group of dimes
- Write the words as a decimal
- Solve word problems with decimals
- Bible: 2 Corinthians 9:7
- "Tithe" means tenth; give back to God cheerfully
Module 3
- Fractions to tenths
- Decimals and fractions both show parts of a whole
- 4/10 = 0.4
- Turn a fraction with a denominator of ten into a decimal
- Change decimals into fractions
- Write mixed numbers as decimals
- Match decimals with their correct fractions
- Bible: Colossians 2:9–10
- Only Jesus can fill in the gaps and make us whole
Module 4
- Introducing hundreths
- Hundreths on a place value chart
- Visualize hundreths
- Read hundreths aloud
- Write decimals to the hundreths place from given numbers
- Identify incorrectly written hundreth decimals
- Write given hundreths decimals in word form
- Write decimals for shaded blocks
- Shade blocks to represent a given decimal
- Add a zero after the tenth places to compare tenths and hundreths
- Bible: Galatians 6:9
- Small things add up to bigger things over time
Module 5
- Hundreths in real life
- One dollar = 100 cents means one penny is one hundreth of a dollar
- Read price tags with dollars (wholes) and cents (parts)
- Write down prices on a place value chart
- Write price amounts in word form
- Match written money amounts to their decimal form
- Solve money word problems
- Self assessment for Module 5
- Identify increasing decimals in order
- Bible: Matthew 10:29–31
- Nothing is too small for God to notice and nothing is too big for Him to handle
Module 6
- Fractions to hundreths
- Turn fractions with denominator of 100 into decimals
- Place the numerator in the hundreths place, after the decimal
- For fractions with whole numbers, place that in front of the decimal point
- Write the decimals as fractions
- Write the word form as a fraction and a decimal
- Write a decimal and fraction for a given visual
- Practice solving word problems, writing the answer as a decimal and a fraction
- Bible: Luke 16:10
- Being trustworthy with smaller tasks helps us gain larger responsibilities
Module 7
- Comparing and ordering decimals
- Stack numbers and align the decimal points
- Begin with the largest place value to compare
- Compare and order money
- Identify if decimals are in the correct order from least to greatest
- Use greater than/less than symbol to compare two decimals
- Place a given set of decimals in order from least to greatest
- Identify which place value you need to look at to compare a set of decimals
- Order prices from least to greatest
- Bible: Matthew 6:33
- Rank things in your life in the correct order, with God being of the highest place value
Module 8
- Rounding to the nearest tenth
- Look at the place value to the right of the number being rounded
- Four or lower rounds down and five or higher rounds up
- Identify if a given decimal will round up or down
- Reveal a hidden picture by choosing the numbers that round to 0.5
- Round using a number line
- Except with money, we leave off a zero at the end of a rounded decimal
- Identify if a decimal has been correctly rounded
- Label decimals on a number line and identify the place values by highlighting or underlining as instructed
- Solve a word problem that requires rounding decimals to the nearest tenth
- Bible: Proverbs 3:5–6
- Trust God to guide you to the right path
Module 9
- Adding decimals
- Always stack the numbers with the decimal points aligned before adding
- Practice lining up the decimals correctly to add them
- Practice adding correctly lined up decimals
- Practice adding money
- Solve a word problem that requires adding decimals
- Identify incorrectly aligned decimal addition problems
- Rewrite decimal addition problems vertically
- Bible: 1 Thessalonians 5:11
- Choose wise words to build others up, not tear them down
Module 10
- Subtracting decimals
- Align the numbers just like in addition with decimal points over each other
- Add zeros to empty spaces
- Remember to borrow correctly just like in regular subtraction
- Always bring down the decimal point in the same place
- Practice subtracting the given set of decimals
- Rewrite the given equations vertically
- Find and correct mistakes in an equation, then solve
- More than two numbers in an equation? Subtract together OR subtract them seperately
- Solve word problems that require subtracting decimals
- Solve a word problem to fill in the chart
- Bible: Psalm 141:3
- Words are powerful; ask God to be a watchman over your mouth
Step 1
Module 1
- Base 10 below zero
- Review how our number system works: base 10, place value, whole, tenth, hundreth
- Visualize decimals with base 10 blocks
- "And" tells where the decimal point is
- Write the standard form for a set of base 10 blocks
- Fill in the place value table for each given decimal
- Write the standard form for a given decimal word form
- Follow directions to identify each part of a given decimal
- Use clues to write out a decimal
- Bible: Jeremiah 29:11
- God built order into creation; God has a plan for your life
Module 2
- Introducing thousandths
- Dividing a hundreth by 10 makes a thousandth
- Base 10 blocks: flat = 1/10, rod = 1/100, cube = 1/1000
- Practice writing the thousandths decimals shown in base 10 blocks
- Label each place value in a given decimal
- Practice writing the thousandths decimals as fractions
- Practice comparing decimals to the thousandths place
- Identify the digit in the thousandths place
- Bible: 1 Corinthians 12:12
- Every single person is important to the body of Christ
Module 3
- Rounding decimals to hundreths
- Review steps to rounding
- Round whole numbers, rounding decimals
- Visualize rounding on a number line
- Identify place value to thousandths and rounding
- Find which numbers round to 0.11
- Use a number line to round
- Identify which numbers are correctly rounded to hundreths
- Solve the word problem by rounding to hundreths
- Correctly list heights shortest to tallest by rounding to hundreths
- Bible: Matthew 7:13–14
- Pay close attention to making wise decisions for God
Module 4
- Adding decimals to thousandths
- Use a place value chart to organize your work when adding decimals
- Practice rewriting incorrectly written decimal equations
- Practice adding decimals to thousandths
- Practice adding three numbers with thousandths
- Practice finding approximate values by combining rounding and adding
- Practice adding multiple decimals to solve the word problem
- Bible: Psalm 86:11, Psalm 51:10, Lamentations 5:21, Luke 22:42b
- Align your life with Jesus for the best outcome
Module 5
- Subtracting decimals to thousandths
- Steps to subtracting decimals: align, add zeros as placeholders, borrow and regroup as needed
- Check answer by adding the two smaller numbers in the problem to get the bigger one
- Practice subtracting two decimals with thousandths
- Identify mistakes in a problem; correct, rewrite, and solve
- Identify even numbers in thousandths place
- Bible: Galatians 6:2
- We can lean on other believers when we are in need
Module 6
- Multiplying decimals by whole numbers
- Steps to multiplying decimals: multiply, count numbers to right of decimals, place decimal that many places to the left in the answer
- Practice putting a decimal where it goes in a solved equation
- Identify and correct mistakes in given multiplcation equations
- Solve word problems that require multiplying decimals
- Self-assessment of comprehension and performance
- Bible: Philippians 4:4
- Joy is something we practice over and over
Module 7
- Multiplying decimals by decimals
- Multiply as usual, count the total numbers of digits after both decimals, place the decimal that many places to the left in the answer
- Practice adding the decimal to an answer
- Solve a word problem by multiplying two decimals
- Identify incorrectly solved equations with two decimals
- Bible: Proverb 3:5
- Small details matter in our walk with God
Module 8
- Dividing decimals by whole numbers
- Two strategies: you can ignore the decimal and solve, or you can move up the decimal and then solve
- Practice correctly adding decimals to a quotient
- Practice adding zeros to make the place values even
- Identify errors in decimal division equations and rewrite correctly
- Practice using multiplication to check division answers
- Practice rewriting division equations using the division bar
- 2 Corinthians 13:5
- Take time to pause and check your heart against God's Word
Module 9
- Converting fractions to decimals
- 0.5 = 1/2
- Visualize what each part of a fraction represents
- Visualize what each part of a decimal represents
- Use division to turn a fraction into a decimal
- Practice setting up fractions as division problems
- Identify correctly written fraction to division equations
- Practice solving to convert fractions to decimals
- Identify which method you prefer
- Match fractions to their decimal forms
- Bible: 2 Corinthians 5:17
- Jesus completely transforms us from within
Module 10
- Decimals in long division
- Division rules stay the same as normal
- Decimal moves straight up into the quotient
- Practice dividing with one decimal
- Solve a word problem that requires dividing a decimal
- Identify if a problem is completely solved
- Bible: Philippians 4:19
- God fills the empty places in our life and renews us to carry on; God has no limit
Step 2
Module 1
- Converting mixed numbers to decimals
- Whole number stays the same and fraction is rewritten as a decimal
- Tenths, hundreths, and thousandths line up perfectly, with no division needed
- Dividing terminating decimals
- Writing repeating decimals with a line over the top or rounding
- Practice converting mixed numbers to decimals
- Compare mixed numbers and decimals to see which is bigger
- Solve a word problem by ordering mixed numbers and decimals least to greatest
- Bible: Lamentations 3:22
- God's love is free and unending
Module 2
- Dividing decimals by decimals
- Convert divisor to a whole number by multiplying by 10
- Do the same to the dividend to make them equal
- Divide as usual, bringing any remaining decimal straight up into the answer
- Practice converting the divisors in the given equations
- Practice solving problems with two decimals
- Solve the word problem using what you learned
- Bible: Romans 12:2
- We can see things through God's eyes when we allow Him to renew our mind
Module 3
- Multiplying decimals by powers of 10
- Digits remain the same while the decimal moves to change place value
- Multiplying by 10 moves the decimal to the right once
- Multiplying by 100 moves the decimal to the right twice
- Multiplying by 1,000 moves the decimal to the right three times
- Use a number line to visualize the changes
- Practice multiplying decimals by 10, 100, and, 1000
- Identify which power of 10 the numbers were multiplied by
- Solve the word problem by multiplying by 10
- Bible: Ephesians 3:20
- God is great in power
Module 4
- Dividing decimals by powers of 10
- It is similar to multiplying but instead move the decimal to the left to make the numbers smaller
- Number of zeros in the power tells how many places to move the decimal
- Practice dividing decimals by 10, 100, and 1,000
- Identify what power a decimal was divided by
- Solve a word problem by dividing by 10
- Practice writing your own equations using division by 10, 100, and 1,000
- Bible: 1 Kings 19:12
- Even small shifts can make a big difference; God chooses to work quietly sometimes
Module 5
- Decimal errors analysis
- Error analysis: looking carefully at a solved problem to find and fix mistakes
- Step 1: Check to make sure the setup is correct
- Step 2: Check that each step is correct and follows the rules
- Step 3: Find the first mistake
- Step 4: Finish the problem or solve it correctly from the beginning
- Practice finding errors in a problem
- Fix the errors found in a problem and then solve
- Practice explaining the error in a problem
- Bible: Psalm 139:23
- Ask God to examine your heart and reveal to you anything that needs fixed or changed
Module 6
- Order of operations with decimals
- Remember: P.E.M.D.A.S.
- P: Solve anything inside parentheses
- E: Solve any exponents
- M or D: Left to right, solve multiplication and division
- A or S: Left to right, add or subtract
- Before solving, convert all numbers to either decimals or fractions if the problem contains both
- Practice explaining the steps you would take to solve the given problem
- Practice identifying what to do first in a given problem
- Practice following the order of operations to solve the equations
- Practice writing the order of operations
- Bible: Matthew 22:37–39
- God gives us a clear order of how to live and love
Module 7
- Fraction, decimal, and percent conversions
- Percentage to decimal: remove the percent sign and move the decimal two places to the left
- Percentage to fraction: remove the percent sign and write the number over 100, simplifying if possible
- Decimal to percent: move the decimal two places to the right and add the percent sign
- Decimal to fraction: write the place value as the denominator and simplify
- Fraction to decimal: divide the numerator by the denominator
- Fraction to percent: convert fraction to decimal, then move the decimal two places to the right and add a percent sign
- Complete the conversion chart
- Practice the conversions learned today
- Bible: Proverbs 9:10
- God is our starting point
Module 8
- Unit rate with decimals
- Unit rate is understanding one part of total
- Find the unit cost by dividing the total by how many units there are
- Practice finding speed by dividing the distance traveled by the time spent traveling
- Solve the word problems by finding the unit rates
- Bible: Matthew 6:11
- Focus on what we need for each day
Module 9
- Decimals on a number line
- Decimals are found between whole numbers on a number line
- Benchmarks are the two numbers that show where the decimal fits
- Make 10 smaller spaces between the benchmarks
- Practice creating number lines for given numbers
- Practice labeling a given number line
- Bible: Psalm 119:105
- The Bible is our benchmark
Module 10
- Long division with decimals
- Everything already learned about division stays the same
- Dealing with larger numbers may require a couple extra steps of dividing until there is no remainder or a repeating decimal
- Listing multiples of the divsor may be helpful when working without a calculator
- Practice correctly setting up the long division problems
- Practice solving long division problems
- Identify errors in the long division problems given
- Practice checking answers with multiplication
- Bible: Galatians 3:9
- Persist in carefully following the steps on your journey set by God
Step 3
Module 1
- Repeating and terminating decimals
- When dividing, you usually end up with two types of decimals: repeating or terminating
- Terminating decimals come to an end on their own
- Repeating decimals continue with a clear pattern and end with one or more digits that repeat forever
- How to write a repeating decimal
- Write a given repeating decimal to eight digits
- Write the repeating decimals with a bar over the pattern
- Complete a table with examples
- Practice using a calculator to find the answers and identify if the answer is terminating or repeating
- Convert fractions into decimals and identify if the answer is terminating or repeating
- Bible: John 3:16
- God's love is infinite
Module 2
- Convert repeating decimals to fractions
- Use algebra to eliminate repeating decimals
- Four steps to create an equation
- Check answers with a calculator
- Practice following the four steps to convert the repeating decimals to fractions
- Determine the power of 10 needed to convert the decimal to a fraction
- Bible: Romans 8:28
- God is at work in every moment
Module 3
- Adding and subtracting mixed rational numbers
- Rewrite rational numbers to be the same form (all decimals, all fractions, etc.)
- Convert fractions to decimals
- Convert all of the numbers to decimals and solve
- Convert all of the numbers to decimals, solve, and rewrite as a fraction
- Solve word problems by converting mixed rationals and solve
- Try to memorize some common conversions
- Convert decimals to fractions and solve
- Bible: 1 John 1:9
- Restoration requires adjustment
Module 4
- Multiplying negative decimals
- Multiply as usual, then place the decimal back in the correct place
- Positive x positive = positive
- Negative x negative = positive
- Positive x negative = negative
- Identify if the answer to an equation will be positive or negative
- Practice multiplying given sets of decimals
- Convert all values in a problem to decimals, then solve
- Solve word problems using what was taught today
- Practice explaining the rules for multiplying positive and negative decimals
- Practice rounding to the nearest hundreth
- Bible: John 1:5
- God can use a negative for positive things in your life
Module 5
- Dividing with negative decimals
- Goal is to make the divisor a whole number by moving the decimal point to the right
- Do the same thing to divisor and dividend
- Same sign results in positive; different signs result in negative
- Practice rewriting as whole numbers and identify if the answer will be positive or negative
- Practice converting all numbers in a problem to decimals and divide
- Solve word problems using what was taught in the lesson
- Bible: 1 Corinthians 15:33
- Be intentional about who you spend time with because they can influence your attitude, choices, and character
Module 6
- Solving equations with decimals
- Put together what you have learned to solve equations with multiple steps
- Goal is to get the variable by itself
- Explain the steps used to solve a given equation
- Solve equations by isolating the variable
- Check work with a calculator
- Solve word problems using multi-step equations
- Bible: Hebrews 12:1
- Let go of what slows you down or holds you back from growing in God
Module 7
- Scientific notation with decimals
- Scientific notation is a way of writing larger numbers more simply
- Scientific notation is always written as a coefficient multiplied by 10 to a certain power (exponent)
- Rule 1: coefficient must be between 1–10
- Rule 2: positive exponents mean the number is greater than 1, negative exponents mean the number is less than 1
- Steps to change scientific notation into standard form
- Practice writing each number in standard form
- Practice rewriting each number with scentific notation
- Practice addition problems with scientific notation
- Practice subtraction problems with scentific notation
- Solve word problems using scentific notation
- Explain the steps needed to change numbers to standard form
- Identify correctly written scientific notations
- Bible: 1 Corinthians 14:33, Philippians 4:6
- God brings peace in the midst of chaos
Module 8
- Comparing rational numbers on a number line
- Begin by making all numbers consistent forms
- Compare sets of numbers
- Correctly place given numbers on a number line
- Find the distance between two numbers on a number line
- Correctly read a number line
- Arrange a set of numbers from least to greatest
- Bible: Galatians 6:4
- Focus on your growth and don't compare it to others
Module 9
- Solve proportions with decimals
- When two quantities change together at a steady rate it is called proportional relationship
- Two options to solve the problem: find the unit rate or set up a proportion
- Practice isolating the variable to solve
- Practice solving word problems by finding the proportions
- Practice finding the unit rate to complete a table
- Bible: Matthew 6:33
- Putting God first establishes the right order for our lives
Module 10
- Applying decimals in geometry
- Formulas for finding the perimeter and area of a rectangle
- Formulas for finding the circumference and area of a circle
- Practice finding the circumference and area of circles
- Practice finding the perimeter and area of rectangles
- Solve word problems by using the correct formula
- Find the radius of circles by the given diameter
- Bible: 1 Peter 4:10
- God gives each person unique gifts to use for His purpose
Step 4
Module 1
- Decimals and scientific notation
- Write very large or very small numbers as 1–10 multiplied by a power of 10
- The exponent tells how the size changes
- How to convert from scientific form to standard
- How to convert from standard form to scientific
- Always make sure the exponents match
- Steps to add or subtract scientific notation
- Practice rewriting problems to have matching exponents
- Practice converting numbers to scientific notation
- Identifying mistakes in scientific notation problems
- Practice adding scientific notation
- Practice subtracting scientific notation
- Bible: Psalm 147:5
- God holds every detail no matter how big or small
Module 2
- Using decimals in linear equations
- Isolate the variable to find its value
- Step 1: Move all variable terms to one side so they can be combined
- Step 2: Undo addition or subtraction to remove constants
- Step 3: Undo multiplication or division to isolate the variable
- Apply every step on both sides for balance
- Check your work
- Explain the steps you would take to solve a given equation
- Identify the mistakes in an equation
- Practice solving by isolating the variable
- Identify the next step in solving an equation
- Bible: John 14:6
- Truth is only found in Jesus
Module 3
- Systems of equations with decimals
- A system of equations is made up of two or more equations that use the same variables
- The solution must work on both equations at the same time to be right
- Check your solution by substituting the values and working it out
- Check the given solutions
- Practice using graphs to answer questions
- Practice solving equations to complete the pairs
- Bible: Jeremiah 33:3
- God will guide us and lead us
Module 4
- Pythagorean theorem with decimals
- Pythagorean theorem formula
- Steps for calculating
- Use the given lengths to write an equation
- Solve the equations and round to the nearest hundredth
- Find the missing side of the triangle
- Answer questions based on a diagram
- Solve a word problem using the pythagorean theorem
- Use a calculator to find the square root while solving the problems
- Use a map to answer questions
- Bible: Psalm 119:105
- God's Word is steady and unchanging
Module 5
- Distance formula using decimals
- Use ordered pairs to set up distance equation
- Practice solving equations to find the distance and round to hundredths
- Identify and explain mistakes in the calculations given
- Practice finding the sides of a triangle using distance formula
- Write and explain how to use the distance formula
- Bible: Psalm 121:8, Matthew 28:20
- God cares about every point in our lives
Module 6
- Volume and surface area with decimals
- Use with rectangular prisms
- Volume formula: V = l x w x h
- Surface area formula: SA = 2(l x w)+2(l x h)+2(w x h)
- Cube the answer for volume and square the answer for area
- Use the given measurements to set up the formulas to find surface area and volume
- Practice finding the volume
- Practice finding the surface area
- Identify the mistake and solve correctly
- Explain the difference between volume and surface area
- Bible: Proverbs 4:23, Philippians 4:7–8
- What we allow into our hearts determines who we become
Module 7
- Using decimals in ratios and rates
- Ratios compare two amounts of the same unit
- Rates compare quantities with different units
- Equivalent proportions show the same relationship between ratios or rates
- Set the problem up as proportions
- Option 1: find the factor
- Option 2: cross multiply
- Practice multiplying by a factor to solve
- Practice using division to find the scale factor
- Practice using cross multiplication to solve
- Find the error in an equation and fix it
- Use the scale factor to multiply a recipe
- Explain two ways to solve ratio and rate equations
- Bible: Galatians 6:7, James 3:18, Luke 6:38, Luke 16:10, Matthew 6:3–4
- We get out what we put in
- Practice memorizing Scripture
Module 8
- Mean, median, and mode with decimals
- How to find mean, median, mode, and range
- Explain what each measure does to organize a data set
- Determine which measure makes the most sense in each scenario
- Determine the mean and range of each data set
- Find the median of each set
- Find measures for the given charts of data
- Bible: Romans 12:2
- Character and transformation happen through consistent daily patterns
Module 9
- Rounding word problems
- How to determine what place to round to
- Practice rounding to different places
- Use a calculator to solve and then round to the appropriate place
- Solve without a calculator and round to the appropriate place
- Use the information given to answer questions
- Bible: James 1:5
- Ask God for wisdom and clarity when you're not sure what to do
Module 10
- Decimal coefficients in expressions
- How to set up equations using real world situations
- Practice writing equations for scenarios
- Evaluate given expressions
- Bible: Colossians 3:23
- Do everything as though you are doing it for God
Step 5
Module 1
- Simple and compound interest with decimals
- Interest is how your money grows over time
- Simple interest formula: I = Prt
- Compound interest formula
- Practice setting up the given information in an equation with the correct formula
- Practice solving simple interest problems
- Practice solving compound interest problems
- Explain what you think is better: simple or compound interest
- Explain the difference between simple and comound interest
- Explain what each variable means in the formulas
- Identify if an example is compound or simple interest
- Bible: Colossians 2:6–7
- Establish a firm foundation in Jesus and grow in your relationship with Him
Module 2
- Slope and rate of change with decimals
- A slope tells us how fast a change is happening and in which direction
- Rise (the y axis=how much the line goes up or down) over run (the x axis=how much the line goes left or right)
- An ordered pair is written (x,y)
- Slope formula
- Practice using a graph to estimate an ordered pair
- Practice finding slopes by completing formulas
- Explain what each slope means for a given formula
- Bible: Matthew 12:35
- What we allow in our hearts and minds determines the direction of our lives
Module 3
- Interpreting decimal coefficients
- The coefficient is the number attached to or multiplied by the variable
- Independent variables change on their own
- Dependent variables change because of the data we put into the equation
- Identify what numbers represent in an equation
- Identify dependent and independent variables in an equation
- Answer questions about the coefficient equations
- Write an equation for a word problem
- Explain the terms learned in the lesson
- Bible: Ephesians 2:10
- Our lives are not random or accidental
Module 4
- Probability and statistics using decimals
- How to find the probability: compare the number of desired outcomes to the number of possible outcomes
- Answers written as fraction, percent, or decimal
- Statistics help us identify what actually happened after the data is collected
- Reminder of what mean, median, mode, and range are
- Practice finding probability
- Identify mean, median, mode, and range from given information in a chart
- Explain what mean, median, mode, and range are
- Bible: Luke 12:7
- Our value comes from being known by God
Module 5
- Analyzing graphs with decimal scales
- Different types of graph used to display data
- Estimate when decimals are involved
- How to interpret information on a graph to answer questions
- Using a dot plot
- Practice using a graph to answer questions
- Find a range of data using a graph
- Label x and y axis on a graph
- Bible: Romans 8:28, 2 Corinthians 4:17
- God sees the whole picture and works accordingly
Module 6
- Decimal inequalities
- Inequalities represent a range of possible values
- Inequality symbols
- How to graph inequalities
- Steps to solve a two-step inequality
- Solve inequalities
- Translate statements into decimal inequalities
- Determine if a solution is viable
- Bible: John 17:17
- God gives us clear standards
Module 7
- Proportional reasoning with decimals
- How a proportional equation shows the same cost relationship between two numbers
- Start with just one to find the unit
- A constant rate means a predictable relationship
- Use proportional reasoning to find the cost
- Practice multiplying a recipe
- Explain how you found information to solve a problem
- Practice finding the unit price to find the better deal
- Explain the reasoning behind buying in bulk
- Solve the word problems
- Bible: Luke 16:10
- Small acts of faith can multiply
Module 8
- Percentage increase or decrease
- Use proportions to compare original value to new amount and solve for the missing value
- Find the information needed to answer questions about a problem
- Determine if there is an increase or decrease in the scenarios
- Use proportions to solve problems
- Bible: John 15:2
- Growth often comes through removal
Module 9
- Using decimals in geometry
- Scale factors show how something has been reduced or enlarged but kept the same proportions
- How to solve when a scale factor is given
- How to solve when a scale factor is not given
- Find the scale factor between two shapes
- Draw and label a shape following the scale factor given
- Identify the scale factor in a word problem
- Explain how you know if two objects are proportional from the given information
- Explain what scale factor means
- Bible: James 1:22
- Obedience is important to God
Module 10
- Solving systems with decimal coefficients
- System of equations: two or more linear equations that use the same variables
- Find the one solution that makes all of the equations true
- Check the answer to see if it is true and why
- Practice using substitutions to solve
- Practice solving for x in the system
- Bible: 1 Thessalonians 5:21
- Pause, reflect, and examine your actions
Step 6
Module 1
- Functional relationships with decimals
- Use variables and functions instead of listing every possibility
- Function equations begin like this: Æ’(x) where Æ’ means function and x stands for the input
- The variable can be any letter, not just x
- The output will also have a variable in its place until solved
- Monetary answers should always be rounded to the nearest cent
- Practice writing a function for a word problem
- Practice solving for x
- Fill in the charts using the given functions
- Bible: 1 Corinthians 12:4
- God gives each person different gifts and roles all to glorify Him
Module 2
- Tolerance in measurements
- Tolerance refers to an accepted variance in measurement
- Nominal value is the expected measurement
- Use the "plus or minus" symbol to show the acceptable variation amount
- Identify each part of a measurement
- Find the tolerance ranges of given information
- Practice measuring something in your home and find the values
- Explain each term from the lesson in your own words
- Bible: John 1:8, 2 Corinthians 12:9
- No one is perfect; confess and repent for forgiveness
Module 3
- Decimals in trapezoid and circle formulas
- Round answers to the nearest hundreth
- Finding the perimeter of a trapazoid: add all four sides
- Finding the area of a trapazoid: add two base lengths, divide by two, then multiply by height
- Finding the circumference of a circle: multiply two times the radius by pi
- Finding the area of a circle: square the radius and multiply by pi
- Practice finding the area and perimeter of a trapazoid
- Practice writing a formula and solving for area and circumference of a circle
- Draw and label a trapazoid with the given information
- Draw and label a circle with the given information
- Solve word problems by using what was learned in the lesson
- Practice dividing a diameter to find a radius
- Bible: 2 Peter 3:18a
- Make daily choices that will help you grow in faith and wisdom
Module 4
- Decimal approximations of irrational numbers
- Irrational numbers cannot be written as simple fractions, and their decimals never end or repeat
- Round to get approximate answers
- Always use the "about equal" sign when estimating
- Use a calculator to solve the given equations
- How to use perfect squares to estimate
- Practice finding nearest perfect squares for irrational numbers
- Use division to find a more perfect decimal
- Use the checklist to grade understanding and performance for last two mods
- Estimate decimal form to the nearest tenth
- Bible: Hebrews 11:1
- Faith means trusting what is true
Module 5
- Calculator skills and decimal precision
- Using significant figures (sig figs) to show a more precise answer
- Which digits in a number are significant?
- Rule to remember in multiplication/division: keep the same number of sig figs as the measurement with the fewest sig figs
- Rule to remember in addition/subtraction: keep the same number of decimal places as the measurement with the fewest decimal places
- Practice identifying the number of decimal places the answer should have
- Practice identifying the number of sig figs the answer should have
- Solve equations with a calculator and write the precise answer
- Practice writing equations with the given information
- List the sig figs in a number and explain how you know
- Bible: Matthew 6:19–20
- What we invest in spiritually lasts forever
Module 6
- Accuracy vs. precision
- Accuracy describes how close a measurement is to the true value
- Precision describes how close measurements are to one another
- Ask two key questions: Are the measurements close to the true value? Are they close to each other?
- Four possible outcomes: not accurate or precise, accurate but not precise, precise but not accurate, precise and accurate
- Identify data sets that represent the most precise results
- Practice explaining the difference between accuracy and precision
- Examine given data and choose which of the four target outcomes they represent
- Bible: 2 Timothy 2:15
- Be accurate and precise when handling Scripture
Module 7
- Margin of error
- Researchers collect sample data from a smaller group to estimate information about a whole
- Margin of error describes how much results differ from the true population
- Larger samples lead to smaller margins of error
- Smaller samples lead to more uncertainty
- How to calculate the margin of error when results are reported as a percentage
- Practice finding the correct numbers for given variables
- Practice writing equations to find the margin of error for given information
- Solve equations to find the margin of error
- Explain two factors that affect margin of error
- Explain how to find margin of error
- Bible: Proverbs 18:15
- Learning is ongoing, so stay humble and seek God's wisdom
Module 8
- Decimal coefficients
- The coefficient is the number that is attached to a variable
- Find the variable by dividing to isolate the variable and find its true value
- Practice isolating variables and solving the equations without a calculator
- Use a calculator to check answers
- Explain how to solve for x in an equation
- Bible: Psalm 24:4–5
- Walk with God patiently and trust His process
Module 9
- Modeling with decimals in real life
- Money, measurements, discounts, and rates are all examples
- Questions to ask before solving a word problem: What do we know? What do we want to know? What information is missing?
- Practice solving a word problem using the equation and information given
- Practice solving a word problem by writing an equation with the information given
- Compare two situations to solve the word problem
- Use what you learned to order three prices from lowest to highest unit rate
- Bible: Proverbs 21:5
- God calls us to be thoughtful, intentional, and wise
Module 10
- Slope from decimal coordinates
- Slope: how a line changes when graphed on an x and y axis
- Y value = rise
- X value = run
- Slope can represent things like speed, cost per item, how fast something is heating up
- How to plug pairs into the slope formula
- How to find a slope by using a graph
- Practice using given pairs to set up the slope formula and solve
- Practice using a graph to find the slope of two lines
- Identify incorrect slopes
- Bible: James 1:2–4
- Difficulties can lead to a "positive slope" in our character