Algebra Fun – Multiplying Polynomials

My newest iBook, Algebra Fun, is inspired by my oldest grandson Rhys, age 12. He is taking Algebra 1 in middle school. I am delighted!

The main focus of the book series, Algebra Fun, is to instill an enjoyment of mathematics, and to develop a deep understanding and knowledge of beginning Algebra concepts. Throughout the first book of the series, the instructional lessons, student activities, and interactive slide shows are designed to provide students with opportunities to identify factors of polynomials, multiply factors using a variety of techniques, and apply multiplication of polynomials to real life situations. The independent practice and check for understanding offer an online assessment of students ability to achieve the goal of the book, to competently and confidently perform arithmetic operations on polynomials, and to determine the concepts that need further instruction.

This book is available for download on your Mac or iPad through the iTunes Book Store.

Algebra Fun

Algebra Tiles

Sunday morning, I was driving to Santa Barbara with my son Paul, his wife Holly, and his two sons Rhys, age 12, and Archie, age 7. I am sitting in the back seat with my two grandsons, somewhat bored. Like most boys their ages, Rhys and Archie are on their iPads playing video games. Spoken like a true son of a retired math teacher, Paul asks Rhys to show Grandma the app he is using to practice math concepts that he is learning in his seventh grade math class. Rhys opens the app, Algebra Tiles Playground created by his Great-Uncle Fred, my brother. You can find the Algebra Tiles Playground app at Ventura Educational Systems.

Together, Rhys and I slide the positive (black) tiles and negative (red) tiles on the screen to create the requested binomial expressions in Level 1 of the Algebra Tiles app. Then we progressed to Level 2, to create the trinomial expressions on the iPad screen. Finally, we worked through Level 3, by placing the positive and negative tiles on the screen to add binomials. Paul and Holly, sitting in the front seat of the car, are listening to our conversation as we are traveling to the Santa Barbara Natural History Museum. Archie, sitting in the back seat to the right of Rhys, is very quiet but listening and observing our algebra discussions.

We arrived at the museum and joined Fred, Marne, and their daughter, son-in-law, and two children and their son, daughter-in-law, and two children. Rhys and Archie are impressed that they are spending the day with Great-Uncle Fred, someone who develops apps for the iPad. We enjoyed the day visiting, to name only a few, the gem display, Chumash exhibit, dinosaur park, and butterfly tent.

On the drive home, Archie opened the iPad to the Algebra Tiles Playground app and created pictures by placing the positive tiles and negative tiles on the screen. Archie said, “At the top of the screen, it says Algebra Tiles Playground. I decided to create pictures.” He made a picture of a happy face. Then he explained that the face had an expression of 3x²+5x+9. While we were at the museum, Archie lost one of his baby teeth. So, I asked Archie, what is the expression if the happy face lost a tooth. Archie without a pause answered, “3x²+5x+8″. He proceeded to remove a black tile from the smile to prove that his answer was correct. Remember, Archie is 7 and just starting second grade.

One More Online Class

One more class I am offering through an online educational organization called Outschool to make mathematics fun and interesting. The interactive class is especially designed for online teaching to elementary grade children to encourage, support, and enhance mathematical learning. More classes are in the design process.

Fun Investigating Mathematics is designed for children ages 8 and 9. In this four-day class, children will have fun as they explore a variety of mathematical topics including palindromes, patterns, ratio and proportion, and equivalent fractions.

Fun Investigating Mathematics
by Donna Ventura.

Fun Investigating Mathematics

Ages 8-9

This course develops problem-solving and higher-level thinking skills, builds an understanding of mathematics with age-appropriate activities using “hands-on” materials, and instills appreciation and love for mathematics.

Class Experience

Fun Investigating Mathematics is an enrichment course that includes four 55-minute sessions. Each session provides children opportunities to develop problem-solving and higher level thinking skills, to build an understanding of mathematics with age-appropriate activities using “hands-on” materials, and to instill an appreciation and love for mathematics. This course is designed for children beginning grade four in the 2020-2021 school year. Topics included in the enrichment course are aligned to the school curriculum and the Common Core State Standards and focus learning into the general categories of Operations and Algebraic Thinking, Number and Operations in Base Ten, Number and Operations in Fractions, and Measurement and Data. The lessons offer an instructional approach that progresses from the use of concrete objects found around the home, to simple representational drawings on paper with pencils and crayons, and finally to abstract thinking using numbers and mathematical symbols. The student activities provide children with the opportunity to express their creativity, imagination, and artistic talents as they demonstrate their understanding and mathematical knowledge. They will explore palindromes with whole number addition, analyze patterns with the traditional handshake problem, statistical concepts of mean, median, and mode, ratio and proportion using dried beans, multiplication of two-digit numbers, and fractions, mixed numbers, and equivalent fractions.

Read more on Outschool.com

Online Classes

I hope everyone is staying safe. Here are a few fun classes I am offering through an online educational organization called Outschool. The interactive classes are especially designed for online teaching to elementary grade children to encourage, support, and enhance mathematical learning. More classes are in the design process.

1. Play Tic, Tac, Toe with Addition and Subtraction is designed for children ages 6 and 7. In this one-day class, children will play the traditional game of Tic, Tac, Toe a with slight twist. The will use addition facts and subtraction facts to determine where they place their X or their O.
2. Fun Use of Addition, Subtraction, Multiplication, and Division in Problem Solving is designed for children ages 8 and 9. In this 4-day course, third-grade students will solve interesting and challenging problems using addition, subtraction, multiplication, and division.

Play Tic, Tac, Toe with Addition and Subtraction
by Donna Ventura.

Play Tic, Tac, Toe with Addition and Subtraction

Ages 6-7

Class Experience

Play Tic, Tac, Toe with Addition and Subtraction is an enrichment session that includes one 55-minute session. The session provides children opportunities to develop problem-solving and higher level thinking skills as they build an understanding of addition and subtraction. As needed, children may use “hands-on” materials to visualize the addition and subtraction problems. This course is designed for children beginning grade one in the 2020-2021 school year. The session is aligned to the first grade curriculum and the Common Core State Standards for Mathematics. The focus of learning is on two categories of Number and Operations in Base Ten and Operations and Algebraic Thinking. The lesson offers an instructional approach that progresses from the use of concrete objects found around the home, to simple representational drawings on paper with pencils and crayons, and finally to abstract thinking using numbers and mathematical symbols. The activities provide children with the opportunity to express their creativity, imagination, and artistic talents as they demonstrate their understanding and mathematical knowledge of addition and subtraction. The children will use strategies such as counting on, making ten, decomposing a number leading to a ten, using the relationship between addition and subtraction, and creating equivalent but easier or known facts.

Read more and to register go to Outschool.com

Fun Use of Addition, Subtraction, Multiplication, Division in Problem Solving
by Donna Ventura.

Fun Use of Addition, Subtraction, Multiplication, and Division in Problem Solving

Ages 8-9

Class Experience

Fun Use of Addition, Subtraction, Multiplication, and Division in Problem Solving is an enrichment course that includes four 55-minute sessions. Each session provides children opportunities to develop problem-solving and higher level thinking skills, to build an understanding of mathematics with age-appropriate activities using “hands-on” materials, and to instill an appreciation and love for mathematics. This course is designed for children beginning grade three in the 2020-2021 school year. Topics included in the enrichment course are aligned to the school curriculum and the Common Core State Standards for Mathematics. The focus of learning is on the general categories of number sense, number operations, algebra, geometry, probability and statistics, measurement, and logic. The lessons offer an instructional approach that progresses from the use of concrete objects found around the home, to simple representational drawings on paper with pencils and crayons, and finally to abstract thinking using numbers and mathematical symbols. The student activities provide children with the opportunity to express their creativity, imagination, and artistic talents as they demonstrate their understanding and mathematical knowledge of addition, subtraction, multiplication, and division in problem solving situations.

Read more and register go to Outschool.com

Celebrating Pi Day

 

Celebrating Pi Day on March 14 with my granddaughter, Sophia, by making berry pies.

I hope through the use of the ideas found on these blogs, teachers, home school providers, and parents find the beauty of mathematics and instill in children a love for learning and doing math. The books in the Math Fun series that are described in previous blogs are available for download on your Mac or iPad through the iTunes iBook Store.

For more information about the Math Fun series, visit my website, Ventura Curriculum and Assessment Solutions.

Math Fun, Writing Projects : An Interactive Book

The Math Fun, Writing Projects is part of the Math Fun series of interactive books. This book is intended to provide classroom teachers, home school providers, and parents with a multitude of ideas that can be easily implemented as mathematical content is introduced and presented to their children. The lesson plans, student activities, and online assessments in this book are coordinated with stimulating and exciting writing projects to enhance mathematical learning and to share their feelings towards their learning. The books in the Math Fun series are available for download on your Mac or iPad through the iTunes iBook Store.

The focus of Math Fun, Writing Projects, Volume 1.0 is to provide children with opportunities to express creative thoughts and artistic talents as they demonstrate their understanding and knowledge of such mathematical concepts as number, geometry, and measurement. Many of the projects allow students to not only articulate their knowledge but also their feelings towards their learning of mathematical concepts. Throughout the book, the instructional approach and student activities are motivating and engaging for children of all ages. Children are provided with various opportunities to express their creativity and artistic talents as they engage in writing activities to demonstrate their understanding and knowledge of the content and to reveal their feelings towards the mathematical content. The online interactive assessment provide immediate feedback for both the teacher and for the children.

The four chapters are described below.

1. Writing in a Mathematics World : Relates the writing process to mathematical problem solving
2. All About Me : Enhances students self awareness through mathematical thinking
3. Story Starters : Provides opportunities to express creative thinking
4. Poetry and Mathematics : Encourages an expression of mathematical thought through a variety of types of poems, such as cinquains, concrete, haiku, limericks, and alliteration.

One example of the writing activities allows students to describe their feelings towards mathematics by creating a poem.

1. Write the word “MATH” vertically using uppercase letters.

M

A

T

H

1. Next to each letter write a word that describes your feelings towards mathematics. An example of this type of poem is shown below.

Mysterious

Applicable

Tough

Happy

1. Share with a friend the words you wrote. Explain to your friend why you chose those words to describe your feelings about mathematics.
2. Planning: List the reasons why you chose those words to describe your feelings about mathematics.
3. Writing: Write a few paragraphs that describes your feelings towards mathematics using those words and the reasons. Think of incidents or examples to support your reasons. Include the incidents or examples in your paragraphs. Share your thoughts with a friend and ask your friend to give you suggestions that could improve your paragraphs.
4. Editing: Review your writing to ensure capitals are used when necessary, words are spelled correctly, and appropriate punctuation is used throughout your paragraphs.
5. Publishing: Neatly write a final copy of your paragraphs.

Most of all, I hope through the use of the ideas found in this book teachers, home school providers, and parents find the beauty of mathematics and instill in children a love for learning and doing math. The books in the Math Fun series that are described in this blog and in previous blogs are available for download on your Mac or iPad through the iTunes iBook Store.

For more information about the Math Fun series, visit my website, Ventura Curriculum and Assessment Solutions.

Another Breakfast Time, Another Math Time

This morning, I had breakfast with my daughter, Emily and my grandsons, Jack and his brother Oliver. Oliver turned 2 years old in April and as you may recall Jack turned 4 years old in June. Emily made muffins for breakfast.

Emily put 4 muffins on a serving plate. She asked Jack, “How can you evenly share the muffins with Oliver?” With a sly little grin on his face, Jack put 2 muffins on Oliver’s plate and 2 muffins on his plate. Jack responded, “We both get 2 muffins.”

The opportunity arose. Before Jack and Oliver could take a bite, I put the muffins back on the serving plate. Jack and Oliver knew there was a math lesson coming. I asked, “If there is only one boy, how many muffins would that boy get?” Jack quickly responded with the correct answer, 4 muffins. Then I asked, “If there are 2 boys, how many muffins would the boys get?” Again, Jack responded with the correct answer, 2 muffins. I continued by asking, “If there are 4 people, how many muffins would each person get?” Jack handed each of us 1 muffin. Jack responded, “See, Grandma, we each get 1 muffin.”

Emily, a true daughter of a math teacher, extended the questioning by asking, “How many muffins would we need to put on the serving plate so each of us would get 2 muffins?” Jack counting by twos, pointed to Oliver and said 2; pointed to his mother and said 4, pointed to me and said 6, and finally pointed to himself and said 8. He knew he should count by twos to get the correct answer. Jack responded, “We will need 8 muffins, then we each can have 2 muffins!”

Finally, Emily asked if Daddy was here how many muffins do we need? Again Jack counting by twos, pointed to Oliver and said 2; pointed to his mother and said 4, pointed to me and said 6, pointed to himself and said 8, and then pointed to the front door and said 10. He verbalized his findings by saying, “Mommy, I counted by twos and we need 10 muffins if Daddy was here.”

Coffee was ready. Emily put the 4 muffins on the serving plate. Jack gave each person a muffin. Oliver gave each person a banana. I poured the freshly-squeezed orange juice. Together, we each enjoyed muffins, a banana, and a glass of freshly-squeezed orange juice.

Thank you for visiting my blog. I love sharing these math ideas with my grandchildren and with the readers. Please recommend my blog to your friends. You may also enjoy the series of interactive mathematics books that I have written called Math Fun. The books are available on your Mac or iPad through the iTunes iBook store.

Since my grandchildren are 6 years old and younger, they are enjoying  Math Fun, Kindergarten.

For more information, visit my website, Ventura Curriculum and Assessment Solutions.

Math Fun Coordinate Geometry: Interactive Books

In the Math Fun series, there are two books that focus on Coordinate Geometry. Both interactive books are aligned to the Common Core State Standards for Mathematics, one book is written to address the grade 5 standards and the other book addresses grade 6 standards.

The lesson plans, student activities, and online assessments in the interactive books are designed for ease of use by teachers, home school providers, and parents. The activities are intended to be used jointly with the app, Coordinate Geometry, published by Ventura Educational Systems.

With these interactive books, children begin their journey through coordinate geometry with the legend of Rene Descartes and the fly on the ceiling. Throughout the book, students individually, with a partner, or with the entire class, are offered a multitude of engaging opportunities to demonstrate their knowledge and understanding of the concepts by completing the worksheets, games, and online activities. To evaluate each child’s strengths and weakness of the concepts, there is an online assessment following each section.

Thank you for visiting my blog. I love sharing these math ideas with the readers. Please recommend my blog to your friends. The series of interactive mathematics books that I have written called Math Fun are available on your Mac or iPad through the iTunes iBook store. For more information, visit my website, Ventura Curriculum and Assessment Solutions.

Another Snack Time, Another Math Time

I enjoyed the morning with Rhys and his brother Archer. Rhys, my first grandchild, is now 6 years old. Archer, my most recent grandchild, turned 1 year old in April. With Rhys, I repeated the estimation activity, Breakfast Time, Math Time, that I did with Jack yesterday. He first printed his name, Rhys, on the sheet of paper. Since it was snack time, he used the fruit snacks to cover the letters in his name.

He discovered that it took 7 fruit snacks to cover the letter R and 5 fruit snacks to cover the letter h. I asked Rhys, “How many fruit snacks do you think it will take to cover the letter y?” He thought and then said, “I think it will take less than it took for the letter R.” I continued the questioning by asking Rhys if it would take more, less, or the same number to cover the letter y as it took to cover the letter h.  He said he thought it would take more. This was the moment to ask Rhys what number is less than 7 and more than 5. A number line was the perfect resource for Rhys to use to visually determine the number that is less than 7 and more than 5. He responded, “I think it will take 6.” He was correct; it did take 6 fruit snacks to cover the letter y. He then estimated that it would take only 3 fruit snacks to cover the letter s. He was correct again.

Under each letter, Rhys recorded the number of fruit snacks it took to cover the letter. His next task was to find the total number of fruit snacks it took to cover all the letters in his name. I wanted to use this activity to provide Rhys with strategies he could use to find the sum of four addends. The data Rhys collected in this activity was perfect to present the strategies Making Tens, Decomposing Numbers, and Making Doubles.

The first strategy I introduced to Rhys was friendly numbers. Sums of 10, making tens, are one type of friendly numbers. So I asked Rhys to find two friendly numbers that add up to 10. He examined the four numbers and then responded that 7 and 3 add up to 10, using his fingers to prove his answer.

The second and third strategies I presented to Rhys was decomposing numbers and adding by making doubles. I asked Rhys what is 5 and 5. He quickly and confidently responded 10. Then I asked what is 5 and 5 and 1 more. He thought and responded 11. I explained to Rhys that he could break up  (decompose numbers) 6 into 5 and 1. Rhys then recognized that he could add 5 and 6 by adding the double 5 and 5 and 1 more to arrive at the sum of 11.

Finally, Rhys needed to add 10 and 11. Again he used the strategies of adding by decomposing a number and by making a double. He was able to decompose 11 into 10 and 1. He added the double 10 and 10 and then added 1 more to arrive at the sum of 21. Rhys then asked if he was done with the math activity and if he could eat the fruit snacks. He is such a cutie. He did enjoy the fruit snacks along with an apple bar.

Thank you for visiting my blog. I love sharing these math ideas with my grandchildren and with the readers. Please recommend my blog to your friends. You may also enjoy the series of interactive mathematics books that I have written called Math Fun. The books are available on your Mac or iPad through the iTunes iBook store. Since my grandchildren are 6 years old and younger, they are enjoying  Math Fun, Kindergarten. For more information, visit my website, Ventura Curriculum and Assessment Solutions.

Breakfast Time, Math Time

Jack comes to my house each Monday morning with his brother Oliver. They spend the day with me. Breakfast is always a special time for us. We light the LED candles on the table and have a candlelight breakfast. We are counting the weeks until Jack’s mommy has her third baby boy. We started counting backwards from 25. I have two cubes with the numbers on it. Each Monday morning Jack changes the cube. This weeks it is 07! Just 7 more weeks and grandchild number 7 will be born.

The activity this week was not about counting backwards from 25. It centered on estimation skills and number sense. Jack’s task, this morning, was to determine the number of Cheerios it would take to cover the letters in his name. Jack first wrote his name on a piece of paper. Then he estimated the number of Cheerios it would take to cover the letter J. Jack estimated 20 Cheerios. He carefully covered the letter J and counted the Cheerios. Jack discovered it only took 12 Cheerios. He said that his guess was too many.

I then asked Jack, “Do you think it will take more, less, or the same number of Cheerios to cover the letter A?” He thought for awhile and responded that it would take more. He covered the letter A and counted the Cheerios. He found that it took the same number of Cheerios to cover the letter A as it took to cover the letter J.

Now the letter C. I asked Jack, “Do you think it will take more, less, or the same number of Cheerios to cover the letter C?” He responded that it would take less Cheerios. He justified his answer by describing the contrast between the formation of the letter A and the formation of the letter C. Jack’s reasoning was sound, his explanation was valid, and his answer was correct; it only took 9 Cheerios to cover the letter C. He was very proud of himself.

Jack told me that it would take more Cheerios to cover the letter K than it did to cover the letter C. He also decided that it would take more Cheerios to cover the letter K than it did to cover the letter A and the letter J. Jack determined that he would need more than 9 and more than 12 Cheerios to cover the letter K. It took 22 Cheerios to cover the letter K. Jack was correct again. 

Jack recorded his work – some of his numbers on the chart are written backwards. To the reader the 2  may look like a 5. On this occasion, I chose not to correct the formation of the numbers 2 and 9 and the letter J. Jack was intrigued with the activity. Following the activity he munched on a bowl of Cheerios and a banana and drank a glass of orange juice.

Since Jack just turned 4, I did not ask him to find the total number of Cheerios it took to cover the letters in his name by finding the sum of the 4 numbers. I did keep his chart that recorded the number of Cheerios for each letter. As a follow-up activity, I would like Jack to repeat the activity with grapes. Grapes are larger than Cheerios so Jack should realize that it would take less grapes than Cheerios to cover the letters.

Thank you for visiting my blog. I hope you enjoy reading about my mathematical adventures with Jack. Please recommend it to your friends. You may also be interested in the series of interactive mathematics books that I have written called Math Fun. The books are available on your Mac or iPad through the iTunes iBook store. Since my grandchildren are 6 years old and younger, they are enjoying  Math Fun, Kindergarten. For more information, visit my website, Ventura Curriculum and Assessment Solutions.