Hello and welcome to my class page!!!!!!!

Darlene Williams

I am excited to be starting my 4th year at NTXCA North Campus as the Middle School Math Teacher.

I am the proud parent of 3 children and grandmother to 5 wonderful grandkids. I have been married to my great husband for 26 years.

I have a Bachelor of Science degree in Mathematics from Texas Woman's University. I also have a Masters degree in Curriculum and Instruction in Mathematic Teaching from the University of Texas at Arlington.

My Schedule

Intervention 7:30 - 8:00

Character 8:00 - 8:15

  5th Math 8:15 -9:20

  6th Math 9:22-10:22

  7th Math 10:24-11:24

  8th Math 11:26-12:26

Lunch 12:28-12:58

Workshop 1:00- 1:50

(Mon/Fri - 5th grade Tue - 6th grade Wed - 7th grade Thur - 8th grade)

Conference 1:52-2:37

Elective 2:39-3:25


Contact Me

darlene.williams@ntxca.org

I will get back to you during my conference time.

What are the 5th Graders learning the 5th six weeks?

Categorical vs. Numerical Data

When we analyze data, we divide it into two main types: categorical data and numerical data.

  1. Categorical Data (Also called Qualitative Data)

    • This data represents groups, labels, or categories rather than numbers.

    • Examples:

      • Favorite color (Red, Blue, Green)

      • Types of pets (Dog, Cat, Fish)

      • Yes/No answers (Do you like pizza?)

    • How We Teach It:

      • We collect data from the class and create bar graphs to show how often different categories appear.

  2. Numerical Data (Also called Quantitative Data)

    • This data represents numbers that can be measured or counted.

    • Examples:

      • Heights of students (in inches)

      • Number of siblings

      • Test scores

    • How We Teach It:

      • We collect data and organize it into dot plots, histograms, or line graphs to see patterns.

Discrete Paired Data

When we have two sets of related numerical data, we call them paired data. If the data points are countable (not continuous like temperature), we call them discrete paired data.

  • Example 1: Comparing students' ages and the number of books they’ve read.

  • Example 2: Recording the number of hours studied vs. the test scores received.

How Parents Can Help at Home

  1. Categorical Data:

    • Have your child survey family members (e.g., favorite fruit, type of car) and create a bar graph.

  2. Numerical Data:

    • Track daily temperatures and graph them to see changes over time.

  3. Paired Data:

    • Compare screen time vs. bedtime to see if there is a trend.

STAAR Review: Key 5th-Grade Math Concepts

As 5th graders prepare for the STAAR test, they will focus on whole numbers, fractions, and decimals, identifying the correct operations to solve problems and verifying their solutions. Below is a breakdown of essential concepts with real-world applications.

1. Whole Number Operations

Students must determine when to add, subtract, multiply, or divide whole numbers.

  • Key Clue Words:

    • Addition: total, sum, altogether, combined

    • Subtraction: difference, fewer, how many more

    • Multiplication: product, times, groups of

    • Division: per, each, shared equally

  • Example: A bakery makes 235 muffins each day. How many muffins are made in 12 days?

    • Operation Needed: Multiplication

    • Solution: 235×12=2,820 muffins

2. Fractions in Problem Solving

Students will solve problems involving adding, subtracting, multiplying, and dividing fractions.

  • Example:
    Amy ran 3/4 of a mile on Monday and 5/6 of a mile on Tuesday. How far did she run in total?

    • Find a Common Denominator: 3/4 = 9/12 and 5/6 = 10/12

    • Add the Fractions 9/12 + 10/12

    • Amy ran 1 9/12 miles or 1 and 7/12 miles

3. Decimal Operations

Students will work with adding, subtracting, multiplying, and dividing decimals in real-world scenarios.

  • Example:
    A shirt costs $15.75, and tax is $1.26. What is the total cost?

    • Operation Needed: Addition

    • Solution: 15.75+1.26=17.01

    • The total cost is $17.01.

4. Choosing the Correct Operation

Students must decide which operation to use based on the problem.

  • Example:
    A pizza place has 36 slices of pizza. If 9 friends share the pizza equally, how many slices does each get?

    • Clue Word: “share equally” → Division

    • Solution: 36÷9=4

    • Each friend gets 4 slices.

5. Justifying & Verifying Solutions

Students must check their work by:
Estimating first to see if their answer is reasonable.
Using the inverse operation to verify their solution.
Explaining their steps in words or pictures.

  • Example: A store sells 2.5 pounds of apples for $3.75 per pound. What is the total cost?

    • Operation Needed: Multiplication

    • Solution: 2.5×3.75=9.375

    • Estimate: 3 × 4 = 12 (Close to the actual answer!)

    • The total cost is $9.38 (rounded).

How Parents Can Help at Home

Use real-world math:

  • Calculate grocery totals before checkout.

  • Split a bill at a restaurant.

  • Double or halve a recipe.

Have students explain their answers:

  • Ask why they chose an operation.

  • Have them check their work with estimation.

Make math visual:

  • Use fraction strips, number lines, or area models.

  • Draw pictures to model problems.

What are the 6th Graders learning the 5th six weeks?

Types of Data

  1. Numerical Data (Quantitative Data)

    • Definition: Data that consists of numbers and represents measurable quantities.

    • Examples:

      • Heights of students (in inches)

      • Number of pets per household

      • Test scores

    • Common Representations:

      • Dot Plots (shows frequency of data points)

      • Histograms (groups data into ranges)

      • Box Plots (shows quartiles and median)

  2. Categorical Data (Qualitative Data)

    • Definition: Data that represents categories or groups rather than numbers.

    • Examples:

      • Favorite sports (Soccer, Basketball, Football)

      • Eye color (Blue, Green, Brown)

      • Types of pets (Dog, Cat, Fish)

    • Common Representations:

      • Bar Graphs (compares categories)

      • Pie Charts (shows proportions of each category)

How We Use Data to Solve Problems

Students learn how different representations help answer questions and make decisions:

  • Example 1: A class survey shows that most students prefer basketball over soccer. The school uses this data to decide what sport to add to P.E.

  • Example 2: A dot plot of test scores shows a cluster of low scores, helping a teacher decide to review certain topics.

Describing Center, Spread, and Distribution

Once data is collected, we analyze it using three key ideas:

  1. Center (Measures of Central Tendency)

    • Mean (Average) → Add all numbers and divide by how many there are.

    • Median (Middle Value) → The middle number when ordered from least to greatest.

    • Mode (Most Frequent) → The number that appears the most.

    • How It Helps: If we calculate the mean score of a math test, we can compare how well the class did as a whole.

  2. Spread (How Data Varies)

    • Range → Difference between the highest and lowest values.

    • Interquartile Range (IQR) → Measures how spread out the middle 50% of the data is.

    • How It Helps: If test scores range from 50 to 100, this shows a large variation in student performance.

  3. Distribution (How Data is Shaped)

    • Symmetric (data is balanced)

    • Skewed Left or Right (more data on one side)

    • Clusters & Outliers (data groups together or has extreme values)

    • How It Helps: If a histogram of students' heights shows most between 55-60 inches, we know the typical height range.

How Parents Can Help at Home

  1. Collect Data: Have your child survey family members (e.g., favorite hobbies) and create a bar graph or dot plot.

  2. Find the Center: Ask them to calculate the mean or median of their daily screen time for a week.

  3. Analyze Spread: Compare scores from different quizzes to see the range and distribution.

Understanding Financial Literacy in 6th Grade

Financial literacy is an important life skill that helps students learn how to manage money wisely. In 6th grade, students explore key financial concepts such as banking, credit, taxes, budgeting, and financial planning. Below is a breakdown of each topic and how it applies to real life.

Banking & Credit

  1. Checking Accounts

    • A checking account is used for everyday expenses.

    • Money can be deposited (added) and withdrawn (spent).

    • People use checks, debit cards, and online banking to access their money.

  2. Debit Cards vs. Credit Cards

    • Debit Card: Linked to a checking account; money is immediately deducted when used.

    • Credit Card: Borrowed money that must be repaid later, often with interest.

  3. Credit Reports & Credit History

    • A credit report is a record of how well a person pays back money they borrow.

    • Credit history shows past loans and payments.

    • A good credit score helps people get loans for houses and cars at lower interest rates.

Paying for College

There are several ways to pay for college, including:

  • Scholarships (free money based on achievement)

  • Grants (free money based on financial need)

  • Work-study programs (part-time jobs for students)

  • Student loans (borrowed money that must be repaid with interest)

Earning Money & Taxes

  1. Salaries for Various Occupations

    • Different jobs have different salaries based on skills, education, and experience.

    • Example: A doctor earns more than a cashier because of years of training.

  2. Sales Tax & Income Tax

    • Sales Tax: Extra money added to the price of goods and services.

    • Income Tax: Money taken from a paycheck to pay for government services (roads, schools, etc.).

Financial Planning & Budgeting

  1. Financial Assets & Liabilities

    • Assets: Things a person owns that have value (cash, car, house).

    • Liabilities: Money a person owes (loans, credit card debt).

    • Net Worth Statement: Assets minus liabilities = net worth.

  2. Personal & Family Budgets

    • A budget helps people track their income and expenses.

    • It ensures people can pay bills, save money, and plan for the future.

Monetary Incentives

  • Bonuses, discounts, and rewards encourage people to spend or save money.

  • Example: Some credit cards offer cash back for purchases.

How Parents Can Help at Home

  • Practice budgeting: Give your child a small allowance and help them plan how to spend/save it.

  • Compare payment methods: Discuss when to use cash, debit, or credit.

  • Explain sales tax: When shopping, point out how tax increases the total price.

What are the 7th Graders learning the 5th six weeks?

Understanding Data Representations in 7th Grade

In 7th grade, students learn how to represent, compare, and analyze both numerical and categorical data. They also use data to make comparisons and inferences to solve real-world problems.

Types of Data

  1. Numerical Data (Quantitative Data)

    • Definition: Data that consists of numbers and represents measurable amounts.

    • Examples:

      • Heights of students (in inches)

      • Test scores out of 100

      • Number of books read in a month

    • Common Representations:

      • Histograms (shows frequency of data in intervals)

      • Box Plots (shows median, quartiles, and range)

      • Dot Plots (displays individual data points)

  2. Categorical Data (Qualitative Data)

    • Definition: Data that represents groups or categories rather than numbers.

    • Examples:

      • Favorite sports (Basketball, Soccer, Baseball)

      • Eye color (Blue, Green, Brown)

      • Types of pets (Dog, Cat, Fish)

    • Common Representations:

      • Bar Graphs (compares different categories)

      • Pie Charts (shows proportions of each category)

Comparing Data

Students learn how to compare two or more sets of data using:

  • Mean, Median, Mode (to compare the center of different groups)

  • Range & Interquartile Range (IQR) (to compare variability)

  • Overlapping Box Plots (to compare distributions of data sets)

Example:
A teacher compares test scores from two different classes using box plots. If Class A has a higher median than Class B, the teacher can infer that Class A performed better overall.

Making Inferences from Data

Students use data to make predictions and draw conclusions.

  • Example 1: If a survey shows that 60% of students prefer pizza over burgers, we can infer that most students in the school might have the same preference.

  • Example 2: If a histogram of test scores is skewed right, we can infer that more students scored higher.

Solving Problems Using Data

  • Real-world Example: A store tracks sales of different products in a bar graph. If sales of one product are low, the manager might decide to stop selling it.

  • Math Example: A scientist collects temperature data over a month and uses a line graph to determine patterns.

How Parents Can Help at Home

  1. Collect & Compare Data: Have your child track daily screen time for a week and make a bar graph.

  2. Analyze Graphs: Look at graphs in newspapers or websites and discuss what information they show.

  3. Make Predictions: Ask questions like, “If this trend continues, what might happen next?”

STAAR Review: Key 7th-Grade Math Concepts

As students prepare for the STAAR test, they will review important topics related to rational numbers, proportionality, percents, linear relationships, and similar shapes. Below is a breakdown of each concept with real-world connections.

1. Operations with Rational Numbers & Sales Tax

  • Rational Numbers include fractions, decimals, and integers. Students will apply addition, subtraction, multiplication, and division rules when working with them.

  • Sales Tax:

    • To calculate sales tax, multiply the price by the tax rate.

    • Example: A $50 shirt with an 8.25% sales tax → 50×0.0825=4.1350 The total cost is $54.13.

2. Ratios & Rates

  • Ratios compare two quantities (e.g., 3 boys to 5 girls → 3:5 or 3/5).

  • Rates compare different units (e.g., 60 miles per 2 hours → 30 miles per hour).

  • Unit Rate: Divide to find the value per 1 unit.

    • Example: 240 miles in 4 hours → 240÷4=60 miles per hour

3. Constant Rate of Change & Constant of Proportionality

  • Constant Rate of Change refers to how much a quantity changes per unit.

    • Example: A car drives 50 miles every hour. The rate of change is 50 miles per hour.

4. Linear Relationships Using Various Representations

Students must recognize linear relationships in:

  • Equations: y=mx+b (where m is the slope and b is the y-intercept).

  • Tables: A constant rate of change between x and y.

  • Graphs: A straight line.

  • Verbal Descriptions: Situations that involve a constant rate of increase or decrease.

Example:

  • If a babysitter earns $10 per hour, the relationship can be represented as:

    • Equation: y = 10x

    • Table:

      Hours (x)Pay (y)

    • Graph: A straight line through (0,0) with a slope of 10.

5. Problems Involving Percents

Students will work with percent increase, percent decrease, and simple interest.

6. Similar Shapes & Scale Factor

  • Similar Figures: Have the same shape but different sizes. Their sides are proportional.

  • Scale Factor: The ratio of corresponding sides.

    • Example: A small triangle has a side of 4 cm, and a similar larger triangle has a corresponding side of 8 cm. The scale factor is 8 ÷ 4 = 2.

  • Using Proportions to Solve for Missing Sides

How Parents Can Help at Home

  1. Use Real-World Examples:

    • Calculate sales tax at the store.

    • Compare prices using unit rates.

  2. Practice Proportionality:

    • Resize a recipe to double or halve ingredients.

  3. Graph Data Together:

    • Track weekly expenses and create a graph.

What are the 8th Graders learning the 5th six weeks?

STAAR Review: Key 8th-Grade Math Concepts

As 8th graders prepare for the STAAR test, they will review essential topics including one-variable equations, loans, slope and y-intercept, direct variation, functions, scatterplots, transformations, and the Pythagorean Theorem. Below is a breakdown of each concept with real-world applications.

1. Solving One-Variable Equations

Students will practice solving one-step, two-step, and multi-step equations, including those with variables on both sides.

  • Example: Solve for x: 3x−5=10

    • Add 5 to both sides: 3x=15

    • Divide by 3: x=5

2. Total Cost of Repaying a Loan

Students will understand interest and loan repayment.

  • Formula for Simple Interest:

    I=P×r×t

    • P = Principal (amount borrowed)

    • r = Interest rate (as a decimal)

    • t = Time in years

  • Example:
    A $2,000 loan has a 5% annual interest rate for 3 years .

    I=2000×0.05×3

  • I =$300

    The total cost to repay the loan is $2,300.

3. Slope & Y-Intercept in Proportional and Non-Proportional Situations

  • Proportional relationships have equations in the form y=kx and pass through (0,0).

  • Non-proportional relationships have equations in the form y=mx+b where b≠0 (the y-intercept).

  • Example:

    • Proportional: y=3x (passes through origin)

    • Non-Proportional: y=3x+2 (intersects y-axis at 2)

4. Direct Variation

  • A direct variation is a proportional relationship written as:

    y=kx

    • k is the constant of proportionality.

  • Example: If y=10 when x=2, find k :

    k=yx

    • The equation is y=5x.

5. Function Representations

Functions can be represented in multiple ways:

  • Tables: Show input-output pairs.

  • Graphs: Plot points on a coordinate plane.

  • Equations: Algebraic rules (e.g., y=2x+3).

  • Verbal Descriptions: "A taxi charges a $3 fee plus $2 per mile."

    • Equation: y=2x+3

6. Scatterplots & Trend Lines

Students will analyze scatterplots to determine relationships between variables.

  • Positive Correlation: As x increases, y increases (e.g., height vs. shoe size).

  • Negative Correlation: As x increases, y decreases (e.g., time studying vs. number of mistakes).

  • No Correlation: No clear pattern (e.g., student height vs. test score).

7. Transformational Geometry

Students will work with translations, reflections, rotations, and dilations.

  • Translation: Moves a shape left, right, up, or down.

  • Reflection: Flips a shape across an axis.

  • Rotation: Spins a shape around a point.

  • Dilation: Enlarges or reduces a shape proportionally.

  • Example:

    • Reflection over the y-axis: (3,5) → (-3,5)

    • Dilation by a scale factor of 2: (3,5) → (6,10)

8. Pythagorean Theorem

  • Used to find missing sides in right triangles.

  • Formula:

    a^2 + b^2 = c^2

    • a, b = Legs (shorter sides)

    • c = Hypotenuse (longest side)

  • Example: Find the hypotenuse of a right triangle with legs of 6 cm and 8 cm.

    26^2 + 8^2 = c^2

    • The hypotenuse is 10 cm.

How Parents Can Help at Home

Set Up Real-World Problems:

  • Compare car loan repayment options.

  • Analyze grocery sales tax.

  • Use maps to apply the Pythagorean Theorem.

Practice with Graphing:

  • Track daily temperatures and plot a scatterplot.

  • Identify trends in spending or saving money.

Hands-On Geometry:

  • Cut out triangles and prove the Pythagorean Theorem.

  • Explore transformations using graph paper.