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Multiplication Fact fluency Built on Understanding.pptx

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2023 Mathematics Framework

At its meeting on July 12, 2023, the State Board of Education (SBE) adopted the Mathematics Framework for California Public Schools: Kindergarten Through Grade Twelve ( Mathematics Framework). The framework is important guidance designed to help educators align classroom teaching with California's rigorous math learning standards.

The Mathematics Framework reflects input from California parents, educators, students, and others who commented during the two 60-day field review periods that were held in 2021 and 2022.

California is committed to achieving excellence in math teaching and learning through curriculum and instructional approaches grounded in research and reflective of best practices across the globe. The Mathematics Framework provides guidance for mathematics learning for all students at all levels of math-including calculus-and ensures students have a wide variety of options including pursuing Science, Technology, Engineering, and Mathematics (STEM) in college and career.

Frequently Asked Questions
Information about the draftMathematics Framework.

Schedule of Significant Events for the Revision of the Mathematics Framework
At its meeting on July 13, 2022, SBE revised the Schedule of Significant Events (Timeline) for the Revision ofMathematics Framework. The Timeline was originally approved by the SBE on May 8, 2019, and was previously revised on September 11, 2019, May 7, 2020, July 14, 2021, and November 3, 2021.

A professionally-edited and designed PDF version of the framework will be posted at a later date. The content will not substantively change from the version posted below.

Curriculum Framework and Evaluation Criteria Committee

At their January 08, 2020, meeting the State Board of Education appointed 20 members to the Mathematics Curriculum Framework and Evaluation Criteria Committee (Mathematics CFCC) to assist in the development of the Mathematics Framework.

The Mathematics CFCC Meetings and Notices

Focus Groups

Pursuant to the California Code of Regulations, Title 5, Section 9511(c), the California Department of Education (CDE) convened four focus groups across California.

Listserv

Additional Resources

2013 Mathematics Framework

Assembly Bill 250 (Chapter 608, Statutes of 2011) called for the revision of the Mathematics Framework to align with the California Common Core State Standards for Mathematics.

Video: Overview of the Mathematics Framework (Dated 26-Feb-2015)
This video for teachers, administrators, and other educators provides an overview of the Mathematics Framework and how it supports implementation of the California Common Core State Standards for Mathematics.

Common Core State Standards for Mathematics (PDF; 3MB)
Links to the standards adopted by the California State Board of Education in August 2010 (Modified January 2013 Publication Version).

Common Core State Standards (CCSS) Initiative
The multi-state initiative released the CCSS on June 2, 2010. The initiative site includes information about the development and research behind the standards, appendices, the states that have adopted the CCSS, and frequently asked questions.

Appendix A
Designing High School Mathematics Courses Based on the CCSS.

2005 Mathematics Framework (Available on request)
The Framework was adopted by the State Board of Education on March 9, 2005.
*To order a copy of this framework please contact CDE Press.

Content Standards
Links to downloads of all Content Standards.

All Curriculum Frameworks
Links to downloads of all Curriculum Frameworks.

Questions: Curriculum Frameworks and Instructional Resources Division | CFIRD@cde.ca.gov | 916-319-0881

Last Reviewed: Friday, October 20, 2023

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Curriculum frameworks provide guidance to educators, parents, and publishers, to support implementing California content standards.

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Zoom is the leader in modern enterprise video communications, with an easy, reliable cloud platform for video and audio conferencing, chat, and webinars across mobile, desktop, and room systems. Zoom Rooms is the original software-based conference room solution used around the world in board, conference, huddle, and training rooms, as well as executive offices and classrooms. Founded in 2011, Zoom helps businesses and organizations bring their teams together in a frictionless environment to get more done.

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A Chair for My Mother by Vera B. Williams | Children's Read Aloud Story

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When it comes to explaining the basics of multiplication, many kids are thrown into the vat of multiplication facts and asked to memorize them, having absolutely no idea of what multiplication really is all about.

The definition is a great place to start and with this Graph Grid Multiplication Game, your students will be understanding what it means in no time at all!

Grab these few supplies, and you are on your way:

1. First off, place a sheet of graph paper between two or more kids. You can download our graph paper here, or use your own (see below for more information).

2. One after another, students roll the pair of dice. (These 10-sided dice are super cool! I love this set of 100 multi-sided dice.)

3. Students look at the two numbers rolled and create a grid. For example, if the student rolls a 3 and a 4, they draw a grid that is 3 high and 4 wide, or 4 high and 3 wide. The box is then labeled with the number and the answer. If students do not know the answer, they can count the squares. This is just fine as this action helps kids understand that multiplication is area and repeated addition!

4. Students color in their grid and/or place their initials inside. Players take turns rolling the dice and making grids.

5. They continue playing until a player rolls numbers that equal a grid that cannot be drawn on paper. If there are more than two players, play continues until each player rolls two numbers that do not fit.

6. Students count the number of squares in the grid to determine the winner. The winner has the most squares!

Want to see the game played?

,

Notes: You can use the more common 6-sided dice, or you can invest in some 9 and 12-sided dice. They are perfect for this game. You can find them here.

You may use the graph paper you have at a home, but beware: The number of squares in your graph paper could significantly change the length of your game! We suggest using this free PDF 25X25 graph paper.

For beginners, you might want to consider this 20X20 PDF graph paper or even this 15X15 PDF graph paper.

And for extended learning, we present to you:

This Array Math Art Activity will give students more time to practice multiplication. Students roll the dice and list all the different grids (or fact families) that can be formed using those two numbers. Repeat 15 times, then trace all the different grids on the paper, overlapping fact families. Color in your grids, and you have yourself some art worthy of the fridge! For a more complete explanation: Multiplication Array Art Activity.

If multiplication understanding is already mastered, then it's time to move on to this super fun competitive version of Multiplication War! Your students will forget they are practicing their times tables in no time!

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The Graph Grid Multiplication Game and Video

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This graph grid game is the perfect multiplication game for beginners!

# data[].attributes.attachment_link.readable_text
When it comes to explaining the basics of multiplication, many kids are thrown into the vat of multiplication facts and asked to memorize them, having absolutely no idea of what multiplication really is all about.

The definition is a great place to start and with this Graph Grid Multiplication Game, your students will be understanding what it means in no time at all!

Grab these few supplies, and you are on your way:

1. First off, place a sheet of graph paper between two or more kids. You can download our graph paper here, or use your own (see below for more information).

2. One after another, students roll the pair of dice. (These 10-sided dice are super cool! I love this set of 100 multi-sided dice.)

3. Students look at the two numbers rolled and create a grid. For example, if the student rolls a 3 and a 4, they draw a grid that is 3 high and 4 wide, or 4 high and 3 wide. The box is then labeled with the number and the answer. If students do not know the answer, they can count the squares. This is just fine as this action helps kids understand that multiplication is area and repeated addition!

4. Students color in their grid and/or place their initials inside. Players take turns rolling the dice and making grids.

5. They continue playing until a player rolls numbers that equal a grid that cannot be drawn on paper. If there are more than two players, play continues until each player rolls two numbers that do not fit.

6. Students count the number of squares in the grid to determine the winner. The winner has the most squares!

Want to see the game played?

,

Notes: You can use the more common 6-sided dice, or you can invest in some 9 and 12-sided dice. They are perfect for this game. You can find them here.

You may use the graph paper you have at a home, but beware: The number of squares in your graph paper could significantly change the length of your game! We suggest using this free PDF 25X25 graph paper.

For beginners, you might want to consider this 20X20 PDF graph paper or even this 15X15 PDF graph paper.

And for extended learning, we present to you:

This Array Math Art Activity will give students more time to practice multiplication. Students roll the dice and list all the different grids (or fact families) that can be formed using those two numbers. Repeat 15 times, then trace all the different grids on the paper, overlapping fact families. Color in your grids, and you have yourself some art worthy of the fridge! For a more complete explanation: Multiplication Array Art Activity.

If multiplication understanding is already mastered, then it's time to move on to this super fun competitive version of Multiplication War! Your students will forget they are practicing their times tables in no time!

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The Graph Grid Multiplication Game and Video

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This graph grid game is the perfect multiplication game for beginners!

# data[].attributes.attachment_link.readable_text
For long term multiplication success, it is imperative that kids understand multiplication. Many mistakenly think that if only kids will memorize their facts, they will be on their way and ready to move on. Not so! Kids need ample time to explore the different avenues of multiplication. Building multiplication arrays is a great place to start! When kids understand that 3X4 and 2X6 both equal 12, yet look different on paper, they start to use multiplication as an application when solving math equations and not just something to memorize.

This game is simple and gives students a chance to be creative! With a roll of dice, students will create multiplication problems, then find all the fact families of each array.

1 page of graph paper

a pair of dice

ruler and pencil

included PDF worksheet or blank paper

colored pencils or markers

1. Roll the dice. Consider the two numbers rolled as a multiplication problem and determine its product. Write the problem and answer on the worksheet. Repeat 14 more times, listing the multiplication problem and answer for each.

2. After numbers are rolled, students go through each problem and list the other ways that that product can be represented. For instance: 8 X 5 = 40, and so does 4 X 10 and 2 X 20.

3. When finished, grab a pencil and ruler and sketch out all the different arrays listed on the paper, making sure each family of facts are overlapping. Arrays can also overlap other problems listed. Be creative!

4. Color the arrays any way you choose!

When finished, each fact family is drawn and colored on graph paper.

Every student will have a different outcome. So fun!

You can download this Multiplication Array Art Worksheet, or have your students sketch something similar on a lined sheet of paper. You can also use this free graph paper printable:

Follow these simple instructions to create your own array math art!

All you need:

For more practice understanding the meaning and function of multiplication, try this interactive Graph Grid Multiplication Game!

Its perfect for kids who are just learning about multiplication.

And for those kids who need help recalling their times tables, Multiplication War is an excellent game. Try this version here!

# data[].attributes.attachment_link.description
For long term multiplication success, it is imperative that kids understand multiplication. Many mistakenly think that if only kids will memorize their facts, they will be on their way and ready to move on. Not so! Kids need ample time to explore the different avenues of multiplication.

# data[].attributes.attachment_link.readable_text
For long term multiplication success, it is imperative that kids understand multiplication. Many mistakenly think that if only kids will memorize their facts, they will be on their way and ready to move on. Not so! Kids need ample time to explore the different avenues of multiplication. Building multiplication arrays is a great place to start! When kids understand that 3X4 and 2X6 both equal 12, yet look different on paper, they start to use multiplication as an application when solving math equations and not just something to memorize.

This game is simple and gives students a chance to be creative! With a roll of dice, students will create multiplication problems, then find all the fact families of each array.

1 page of graph paper

a pair of dice

ruler and pencil

included PDF worksheet or blank paper

colored pencils or markers

1. Roll the dice. Consider the two numbers rolled as a multiplication problem and determine its product. Write the problem and answer on the worksheet. Repeat 14 more times, listing the multiplication problem and answer for each.

2. After numbers are rolled, students go through each problem and list the other ways that that product can be represented. For instance: 8 X 5 = 40, and so does 4 X 10 and 2 X 20.

3. When finished, grab a pencil and ruler and sketch out all the different arrays listed on the paper, making sure each family of facts are overlapping. Arrays can also overlap other problems listed. Be creative!

4. Color the arrays any way you choose!

When finished, each fact family is drawn and colored on graph paper.

Every student will have a different outcome. So fun!

You can download this Multiplication Array Art Worksheet, or have your students sketch something similar on a lined sheet of paper. You can also use this free graph paper printable:

Follow these simple instructions to create your own array math art!

All you need:

For more practice understanding the meaning and function of multiplication, try this interactive Graph Grid Multiplication Game!

Its perfect for kids who are just learning about multiplication.

And for those kids who need help recalling their times tables, Multiplication War is an excellent game. Try this version here!

# data[].attributes.attachment_link.description
For long term multiplication success, it is imperative that kids understand multiplication. Many mistakenly think that if only kids will memorize their facts, they will be on their way and ready to move on. Not so! Kids need ample time to explore the different avenues of multiplication.

# data[].attributes.attachment_link.readable_text
Multiplication War is a card game that has been around since I can remember and, since I am now 40-years-old, that is debatably a long time. ;) But I'm still young next to this long-loved game.

Card games are the fool proof way to get kids learning math because kids love to ditch the paper and pencil now and again.

Check out this quick video tutorial, or scroll down further to read the directions.
Multiplication War Card Game: How to Play

1. Remove the Jacks, Kings and Queens from a regular deck of cards.

2. Shuffle.

3. Players place cards face down in a pile.

4. At the count of three, both players flip over their first card.

5. The first person to say the product of the 2 cards receives both cards and puts them in a separate pile.

6. If both players say the answer at the same time, the cards are put in the middle of the table.

7. The next player to win the "flip" gets the cards in the middle of the table in addition to the cards just played.

8. The winner is the person with the most cards at the end of play.

Other Variations:

1. Each kid turns over two cards and multiplies his or her own cards together. Whoever has the highest product, wins both sets of cards. The winner has the most cards at the end.

2. Do not remove the Joker, Jack, Queen and King in the deck. Instead, assign the following values to them:

Play continues as outlined above, or play your favorite version.

3. Fraction War: Aces are 1, Jack is 10, Queen is 11, and King is 12. Students turn over two cards. The first card is the denominator, the second number is the numerator. Whoever has the largest fraction wins!

4. Decimal War: Take out all face cards. Aces are 1. Players turn over three cards. The first card is the whole number, the second number is the tenths, and the third number is the hundredths. If kids are just learning decimals, just have them draw two cards: the first is the whole number, while the second number is the tenths.

5. Guess the Card: For this game, you will need three players. Shuffle the deck of cards, removing the face cards. Aces are worth 1. Two of the players sit facing each other. Deal the cards evenly between the two players. Players place their stack of cards face down in front of them. The third player sits so that he or she can see the players. At the count of three, the two players facing each other flip over their card and press it to their foreheads, being careful to not see their own card. The third player looks at both cards and calls out the product of the two numbers. Looking at their opponents card, players try to be the first to call out the number on their own card (by figuring out what the missing addend is). The winner takes both cards. For the next round, players rotate and continue until all cards are used. http://www.tjed.org/wp-content/uploads/2015/04/Simple-games-to-play-at-h...

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Multiplication War is a card game that has been around since I can remember and, since I am now 40-years-old, that is debatably a long time. ;) But I'm still young next to this long-loved game. Card games are the fool proof way to get kids learning math because kids love to ditch the paper and pencil now and again.

# data[].attributes.attachment_link.readable_text
Multiplication War is a card game that has been around since I can remember and, since I am now 40-years-old, that is debatably a long time. ;) But I'm still young next to this long-loved game.

Card games are the fool proof way to get kids learning math because kids love to ditch the paper and pencil now and again.

Check out this quick video tutorial, or scroll down further to read the directions.
Multiplication War Card Game: How to Play

1. Remove the Jacks, Kings and Queens from a regular deck of cards.

2. Shuffle.

3. Players place cards face down in a pile.

4. At the count of three, both players flip over their first card.

5. The first person to say the product of the 2 cards receives both cards and puts them in a separate pile.

6. If both players say the answer at the same time, the cards are put in the middle of the table.

7. The next player to win the "flip" gets the cards in the middle of the table in addition to the cards just played.

8. The winner is the person with the most cards at the end of play.

Other Variations:

1. Each kid turns over two cards and multiplies his or her own cards together. Whoever has the highest product, wins both sets of cards. The winner has the most cards at the end.

2. Do not remove the Joker, Jack, Queen and King in the deck. Instead, assign the following values to them:

Play continues as outlined above, or play your favorite version.

3. Fraction War: Aces are 1, Jack is 10, Queen is 11, and King is 12. Students turn over two cards. The first card is the denominator, the second number is the numerator. Whoever has the largest fraction wins!

4. Decimal War: Take out all face cards. Aces are 1. Players turn over three cards. The first card is the whole number, the second number is the tenths, and the third number is the hundredths. If kids are just learning decimals, just have them draw two cards: the first is the whole number, while the second number is the tenths.

5. Guess the Card: For this game, you will need three players. Shuffle the deck of cards, removing the face cards. Aces are worth 1. Two of the players sit facing each other. Deal the cards evenly between the two players. Players place their stack of cards face down in front of them. The third player sits so that he or she can see the players. At the count of three, the two players facing each other flip over their card and press it to their foreheads, being careful to not see their own card. The third player looks at both cards and calls out the product of the two numbers. Looking at their opponents card, players try to be the first to call out the number on their own card (by figuring out what the missing addend is). The winner takes both cards. For the next round, players rotate and continue until all cards are used. http://www.tjed.org/wp-content/uploads/2015/04/Simple-games-to-play-at-h...

# data[].attributes.attachment_link.description
Multiplication War is a card game that has been around since I can remember and, since I am now 40-years-old, that is debatably a long time. ;) But I'm still young next to this long-loved game. Card games are the fool proof way to get kids learning math because kids love to ditch the paper and pencil now and again.

# data[].attributes.attachment_link.readable_text
Multiplication War is a card game that has been around since I can remember and, since I am now 40-years-old, that is debatably a long time. ;) But I'm still young next to this long-loved game.

Card games are the fool proof way to get kids learning math because kids love to ditch the paper and pencil now and again.

Check out this quick video tutorial, or scroll down further to read the directions.
Multiplication War Card Game: How to Play

1. Remove the Jacks, Kings and Queens from a regular deck of cards.

2. Shuffle.

3. Players place cards face down in a pile.

4. At the count of three, both players flip over their first card.

5. The first person to say the product of the 2 cards receives both cards and puts them in a separate pile.

6. If both players say the answer at the same time, the cards are put in the middle of the table.

7. The next player to win the "flip" gets the cards in the middle of the table in addition to the cards just played.

8. The winner is the person with the most cards at the end of play.

Other Variations:

1. Each kid turns over two cards and multiplies his or her own cards together. Whoever has the highest product, wins both sets of cards. The winner has the most cards at the end.

2. Do not remove the Joker, Jack, Queen and King in the deck. Instead, assign the following values to them:

Play continues as outlined above, or play your favorite version.

3. Fraction War: Aces are 1, Jack is 10, Queen is 11, and King is 12. Students turn over two cards. The first card is the denominator, the second number is the numerator. Whoever has the largest fraction wins!

4. Decimal War: Take out all face cards. Aces are 1. Players turn over three cards. The first card is the whole number, the second number is the tenths, and the third number is the hundredths. If kids are just learning decimals, just have them draw two cards: the first is the whole number, while the second number is the tenths.

5. Guess the Card: For this game, you will need three players. Shuffle the deck of cards, removing the face cards. Aces are worth 1. Two of the players sit facing each other. Deal the cards evenly between the two players. Players place their stack of cards face down in front of them. The third player sits so that he or she can see the players. At the count of three, the two players facing each other flip over their card and press it to their foreheads, being careful to not see their own card. The third player looks at both cards and calls out the product of the two numbers. Looking at their opponents card, players try to be the first to call out the number on their own card (by figuring out what the missing addend is). The winner takes both cards. For the next round, players rotate and continue until all cards are used. http://www.tjed.org/wp-content/uploads/2015/04/Simple-games-to-play-at-h...

# data[].attributes.attachment_link.description
Multiplication War is a card game that has been around since I can remember and, since I am now 40-years-old, that is debatably a long time. ;) But I'm still young next to this long-loved game. Card games are the fool proof way to get kids learning math because kids love to ditch the paper and pencil now and again.

# data[].attributes.attachment_link.readable_text
Multiplication

Auto-Scored Quizzes

Expanded reporting features

Mobile friendly

Picture hint option

Large equation input box

Automatically scored and timed

Enter answer with keyboard or touch pad

MULTIPLICATION Equation Family Quizzes

(All equation for the fact group)

MULTIPLICATION Up Through Quizzes

(All equation UP THROUGH the fact group)

The "up-through" quizzes for the tens, elevens, and twelves do not include all of the equations. They include the top 40 equations.

Quiz Navigator - Take a customized quiz with all of the equations up through the fact you choose below.

Shaded Facts are Repeats

(Self-correcting quizzes for the tens, elevens, and twelves are in development.)

Membership Makes Auto-Scoring Quizzes even MORE AMAZING

Quizzes tracked for easy reporting

Quiz filtering to spot patterns

Growth, accuracy, and fluency reports

All ads removed so quizzes display full screen

Learn More about Membership

More Membership Features

Intuitive Dashboard

Amazing Lessons

Memory Activities

"Smart" Games

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Test yourself on any of the multiplication facts in the times tables on Multiplication.com. Answer the questions at your own pace and see how you did at the end of the quiz.

# data[].attributes.attachment_link.readable_text
Multiplication

Auto-Scored Quizzes

Expanded reporting features

Mobile friendly

Picture hint option

Large equation input box

Automatically scored and timed

Enter answer with keyboard or touch pad

MULTIPLICATION Equation Family Quizzes

(All equation for the fact group)

MULTIPLICATION Up Through Quizzes

(All equation UP THROUGH the fact group)

The "up-through" quizzes for the tens, elevens, and twelves do not include all of the equations. They include the top 40 equations.

Quiz Navigator - Take a customized quiz with all of the equations up through the fact you choose below.

Shaded Facts are Repeats

(Self-correcting quizzes for the tens, elevens, and twelves are in development.)

Membership Makes Auto-Scoring Quizzes even MORE AMAZING

Quizzes tracked for easy reporting

Quiz filtering to spot patterns

Growth, accuracy, and fluency reports

All ads removed so quizzes display full screen

Learn More about Membership

More Membership Features

Intuitive Dashboard

Amazing Lessons

Memory Activities

"Smart" Games

# data[].attributes.attachment_link.description
Test yourself on any of the multiplication facts in the times tables on Multiplication.com. Answer the questions at your own pace and see how you did at the end of the quiz.