# data[].attributes.body
Students follow their own path based on diagnostic results. These lessons are determined by a Diagnostic Assessment to determine where gaps should be filled in.

# data[].attributes.attachment_link.description
Log in to i-Ready®, online assessment and instruction that helps teachers provide all students a path to proficiency and growth in reading and mathematics.

# data[].attributes.body
Students will play learning games to support content.

# data[].attributes.attachment_link.description
Log in to i-Ready®, online assessment and instruction that helps teachers provide all students a path to proficiency and growth in reading and mathematics.

# data[].attributes.body
Students have access to digital math tools to support learning.

# data[].attributes.attachment_link.description
Log in to i-Ready®, online assessment and instruction that helps teachers provide all students a path to proficiency and growth in reading and mathematics.

# data[].attributes.body
Practice addition fluency.

# data[].attributes.attachment_link.readable_text
View the research behind our ESSA Tier IV evidence

XtraMath worked with LeanLab Education to document the connections between using XtraMath and improving outcomes for students primarily in grades K-6.

Download our Logic Model to discover the research and evidence that demonstrates how using XtraMath enhances students' learning and performance, leading to better outcomes for both students and teachers.XtraMath worked with LeanLab Education to document the connections between using XtraMath and improving outcomes for students primarily in grades K-6.
Download our Logic Model

# data[].attributes.attachment_link.title
XtraMath - 10 minutes a day for math fact fluency

# data[].attributes.attachment_link.description
XtraMath is a free program that helps students master addition, subtraction, multiplication, and division facts.

# data[].attributes.body
Practice subtraction fluency.

# data[].attributes.attachment_link.readable_text
View the research behind our ESSA Tier IV evidence

XtraMath worked with LeanLab Education to document the connections between using XtraMath and improving outcomes for students primarily in grades K-6.

Download our Logic Model to discover the research and evidence that demonstrates how using XtraMath enhances students' learning and performance, leading to better outcomes for both students and teachers.XtraMath worked with LeanLab Education to document the connections between using XtraMath and improving outcomes for students primarily in grades K-6.
Download our Logic Model

# data[].attributes.attachment_link.title
XtraMath - 10 minutes a day for math fact fluency

# data[].attributes.attachment_link.description
XtraMath is a free program that helps students master addition, subtraction, multiplication, and division facts.

# data[].attributes.body
Practice multiplication fluency.

# data[].attributes.attachment_link.readable_text
View the research behind our ESSA Tier IV evidence

XtraMath worked with LeanLab Education to document the connections between using XtraMath and improving outcomes for students primarily in grades K-6.

Download our Logic Model to discover the research and evidence that demonstrates how using XtraMath enhances students' learning and performance, leading to better outcomes for both students and teachers.XtraMath worked with LeanLab Education to document the connections between using XtraMath and improving outcomes for students primarily in grades K-6.
Download our Logic Model

# data[].attributes.attachment_link.title
XtraMath - 10 minutes a day for math fact fluency

# data[].attributes.attachment_link.description
XtraMath is a free program that helps students master addition, subtraction, multiplication, and division facts.

# data[].attributes.body
Factor numbers using a tree diagram.

# data[].attributes.attachment_link.readable_text
Number & Operations (All Grade Bands)

Virtual manipulatives for Number & Operations.
Number & Operations (Grades Pre-K - 2)Number & Operations (Grades 3 - 5)Number & Operations (Grades 6 - 8)Number & Operations (Grades 9 - 12)

# data[].attributes.attachment_link.description
Number & Operations (All Grade Bands) Virtual manipulatives for Number & Operations. Number & Operations (Grades Pre-K - 2) Number & Operations (Grades 3 - 5) Number & Operations (Grades 6 - 8) Number & Operations (Grades 9 - 12)

# data[].attributes.body
Use bars to show addition, subtraction, multiplication, and division on a number line.

# data[].attributes.attachment_link.readable_text
Number & Operations (All Grade Bands)

Virtual manipulatives for Number & Operations.
Number & Operations (Grades Pre-K - 2)Number & Operations (Grades 3 - 5)Number & Operations (Grades 6 - 8)Number & Operations (Grades 9 - 12)

# data[].attributes.attachment_link.description
Number & Operations (All Grade Bands) Virtual manipulatives for Number & Operations. Number & Operations (Grades Pre-K - 2) Number & Operations (Grades 3 - 5) Number & Operations (Grades 6 - 8) Number & Operations (Grades 9 - 12)

# data[].attributes.body
Visualize the multiplication of two numbers as an area.

# data[].attributes.attachment_link.readable_text
Number & Operations (All Grade Bands)

Virtual manipulatives for Number & Operations.
Number & Operations (Grades Pre-K - 2)Number & Operations (Grades 3 - 5)Number & Operations (Grades 6 - 8)Number & Operations (Grades 9 - 12)

# data[].attributes.attachment_link.description
Number & Operations (All Grade Bands) Virtual manipulatives for Number & Operations. Number & Operations (Grades Pre-K - 2) Number & Operations (Grades 3 - 5) Number & Operations (Grades 6 - 8) Number & Operations (Grades 9 - 12)

# data[].attributes.body
Visualize and practice multiplying integers using an area representation.

# data[].attributes.attachment_link.readable_text
Number & Operations (All Grade Bands)

Virtual manipulatives for Number & Operations.
Number & Operations (Grades Pre-K - 2)Number & Operations (Grades 3 - 5)Number & Operations (Grades 6 - 8)Number & Operations (Grades 9 - 12)

# data[].attributes.attachment_link.description
Number & Operations (All Grade Bands) Virtual manipulatives for Number & Operations. Number & Operations (Grades Pre-K - 2) Number & Operations (Grades 3 - 5) Number & Operations (Grades 6 - 8) Number & Operations (Grades 9 - 12)

# data[].attributes.headline
Multiplying 1-digit numbers by multiples of 10, 100, and 1,000

# data[].attributes.subject
Multiplying 1-digit numbers by multiples of 10, 100, and 1,000

# data[].attributes.body
Watch the video to support learning.

# data[].attributes.attachment_link.title
Multiplying 1-digit numbers by multiples of 10, 100, and 1000 | Math | 4th grade | Khan Academy

# data[].attributes.headline
Using area model and properties to multiply

# data[].attributes.subject
Using area model and properties to multiply

# data[].attributes.body
Watch the video to support learning.

# data[].attributes.attachment_link.title
More ways to think about multiplying | Multiplication and division | 4th grade | Khan Academy

# data[].attributes.headline
Multiplying 3-digit by 1-digit numbers with regrouping

# data[].attributes.subject
Multiplying 3-digit by 1-digit numbers with regrouping

# data[].attributes.body
Watch this video to support learning.

# data[].attributes.attachment_link.title
Multiplying: 3 digits times 1 digit (with carrying) | Arithmetic | Khan Academy

# data[].attributes.headline
Multiplying 2-digit numbers with area models

# data[].attributes.subject
Multiplying 2-digit numbers with area models

# data[].attributes.body
Watch these videos and complete the practice to support learning.

# data[].attributes.attachment_link.readable_text
So I'm going to multiply 16 times 27. I'm going to do it using something called an area model. And the whole point of an area model is to really understand what's going on in the multiplication process. So 16, you can represent literally as 10 plus 6. This 1 is in the tens place. It represents one 10. So we can represent that as 10 plus 6. Let me do the 6 in that same green color. 10 plus 6. And let me mark off 10 and 6 here. So this is 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. So this part in blue, that's the 10. So I'm representing-- I've gone 10 slashes, or I'm representing 10 boxes right over there. And then the 6, which I want to do in that green color, the sixth, let's mark off 6 boxes. 1, 2, 3, 4, 5, 6. So 16 is this whole length. The blue part is the 10. The green part is the 6. The 10 comes from the one in the tens. This is literally 1 10 and this is literally 6 1s. Now let's think about 27. Well, we already know that the 2 in the 10s place is representing 20. So let's count off 20. So it's 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 15, 16 17, 18, 19. 20. So up until that point right over here, this line right over here has a length of 20. But we're not just talking about 20. We're talking about 27. So it's 20 plus 7. So let's count off 7 here, 1, 2, 3, 4, 5, 6, 7. Now if we look at the total number. So if we have 16 times 27, the product 16 times 27, what gives you the area of a 16 by 27 rectangle. So let me draw that. So it's 16-- this is a width of 16. Let's bring a little line down right over here-- and then the height of my rectangle, the way I've drawn it is 27. This is l, 2, 3, 4, 5, 6, 7. So the area of this rectangle is going to be 16 times 27, the area of this entire rectangle. Now, we could do is break it up by parts, because it'll be easier to compute, and we can see what part of the area those different products represent. So, for example, we can think about what 10-- so let me separate out the sections. So let me draw it. So this section is 10 wide. And then let me draw a section like this. So we could figure out the areas of each of these sections, and then the area of the entire rectangle, which is going to be this product, is going to be the area of all of these rectangles combined. So we could first think about it-- well, let's think about what 20 times 10 is. Well 20 times 10 is a fairly straightforward thing. It's going to be 200. You could think of as 2 times 1, and you have two 0's there. Or you probably know in your head 20 times 10 is just going to be-- you're going to add a 0 here. So it's going to be 200. So 20 times 10 is 200. And let me highlight that in. So you have-- that's not the color I wanted to use-- let me use this blue right here. So that's the blue from the 10. Let me put some orange in there from the 20 to make it clear that this is the product of both of those numbers. So 20 times 10 is 200. Now what's 20 times 6? Well 2 times 6 is 12, plus you have this 0 here. So this right over here is going to be 120. And it has the orange in it. So this is a 20. And then let me put some green in for the 6. 20 times the 6. Now what's the area of this section right over here? Well, it's 7 high and it is 10 wide. So it's going to be 7 times 10 or 70. I'll have an area of 70 square units. So let me do it in this purple, and I'll thrown some blue in there, too. It's kind of a fun art project. I'll throw some blue in there too. And then finally, what's the area of this little section right over here? It's 7 high and it's 6 wide. So it's going to be 7 times 6 or 42 square units of area. Let me color it in. So I got some magenta in there, and then I got some green in there right over there. So what's the area of this entire thing going to be? Well, it's going to be the 200 plus the 120 plus-- let me do it this way-- it's going to be 200 plus 120 plus 70 plus 42. When you add that up, you get, let's see, in the ones place, you get a 2. Then you get 2 tens plus 7 tens is 9 tens, plus 4 tens, is 13 tens, which is the same thing as 3 tens and 1 hundred. And then this is a 4. Did I add that up right? Let's see, this will be 11. Yup, that looks right. So this is 432. So this is going to be equal to 432. And you might be saying, hey, Sal, why did we go through all of this business? I've seen before that if I take 16-- I could take 16 times 27 like this. You probably learned this type of a process. 16 times 27. Then you say, OK, let's start with the 7 in the ones place and you do 7 times 6 is 42. And you carry the 4. You're really just putting the 4 in the tens place because it's a 40. But right when you did that 7 times 6, we essentially calculated this right over there. And then when you multiply the 7 times the 1, you really multiplying 7 times 10, and then you're adding the 4 from the 42. So when you do the 7 times this 1. This is you're actually calculating this area. And then when you carry it when you add this carried 4, and put it right down here. You're essentially taking the sum of both of these things, because you're multiplying 7 times the 16 to get this area. So let's just do it. 7 times 1 is 7 plus 4 is 11. So 112, what you just figured out right over here, is this area Right over here. So 7 times the 10 or the 70, plus 7 times 6, the 42. Now when you go into the tens place you've probably always said, oh, you know, I just throw a 0 down there. But why do you throw a 0 down there? Because this 2 is representing 10. So if you multiply 2 times the 6, and you put a 12 and put a 2 down and carry the 1. That wouldn't be right. This is a 20. So that's why you put the 0 there. So let's scratch this out so we don't get confused. 2 times 6 is 12. So we're used to carrying the 2 down here and carrying the 1. But notice we're really thinking about 20 times 60 is 120. Just doing that we just calculated that right over there. And then we do 20 times 10 is 200. But then we had that one from the 120. So this is going to be 300. So what we just did when we multiplied the 2 times the 16, we just calculated this total area. We did the 20 times the 6 to get that. And then we had the 20 times a 10 to get that. When we did the 20 times the 6, we carried this 1 into the hundreds place. And so we added it all together and got 320. And then this step right over here, you're literally just finding the combined area-- the area of this plus the area of that the area. So that's going to get us to--- we deserve a drum roll now. 2 plus 0 is 2. 1 plus 2 is 3. 1 plus 3 is 4.

# data[].attributes.attachment_link.title
Multiplying with area model: 16 x 27 (video) | Khan Academy

# data[].attributes.attachment_link.description
Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

# data[].attributes.headline
Multiply 2-digit numbers using partial products

# data[].attributes.subject
Multiply 2-digit numbers using partial products

# data[].attributes.body
Watch these videos and complete practice to support learning.

# data[].attributes.attachment_link.title
Multiplying two 2-digit numbers using partial products (video) | Khan Academy

# data[].attributes.attachment_link.description
Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

# data[].attributes.body
Play games to support learning.

# data[].attributes.body
Complete practice to support learning.

# data[].attributes.headline
Multiply two-digit by two-digit numbers with partial products

# data[].attributes.subject
Multiply two-digit by two-digit numbers with partial products

# data[].attributes.body
Complete practice to support learning.

# data[].attributes.headline
Multiply 1-digit numbers by 3-digit or 4-digit numbers

# data[].attributes.subject
Multiply 1-digit numbers by 3-digit or 4-digit numbers

# data[].attributes.body
Practice to support learning.

# data[].attributes.attachment_link.title
IXL | Multiply 1-digit numbers by 3-digit or 4-digit numbers | 4th grade math

# data[].attributes.attachment_link.description
Improve your math knowledge with free questions in "Multiply 1-digit numbers by 3-digit or 4-digit numbers" and thousands of other math skills.

# data[].attributes.headline
 Multiply 2-digit numbers by 2-digit numbers using area models

# data[].attributes.subject
 Multiply 2-digit numbers by 2-digit numbers using area models

# data[].attributes.body
Practice to support learning.

# data[].attributes.attachment_link.title
IXL | Multiply 2-digit numbers by 2-digit numbers: choose the area model | 4th grade math

# data[].attributes.attachment_link.description
Improve your math knowledge with free questions in "Multiply 2-digit numbers by 2-digit numbers: choose the area model" and thousands of other math skills.

# data[].attributes.body
Practice to support learning.

# data[].attributes.attachment_link.title
IXL | Box multiplication | 4th grade math

# data[].attributes.attachment_link.description
Improve your math knowledge with free questions in “Box multiplication” and thousands of other math skills.

# data[].attributes.headline
4th Grade Multiplication and Division Game

# data[].attributes.subject
4th Grade Multiplication and Division Game

# data[].attributes.body
Play games to support learning.

# data[].attributes.body
Play games to support learning.

# data[].attributes.body
Play games to support learning.

# data[].attributes.body
Watch video and complete activities to support learning.

# data[].attributes.attachment_link.description
Tim and Moby are at the zoo, and need to use simple multiplication skills in order to feed the animals. Factor 6,000 peanuts times 3,000 bananas...

# data[].attributes.body
Play game to support learning.

# data[].attributes.attachment_link.title
Sortify: Multiplication - GameUp - BrainPOP.

# data[].attributes.attachment_link.description
In this free online math game, students practice multiplication and division by sorting numerals into multiples and factors of given numbers.

# data[].attributes.body
Play game to support learning.

# data[].attributes.attachment_link.title
Multiplication Blocks - GameUp - BrainPOP.

# data[].attributes.attachment_link.description
In this free mental math game, students test the speed and accuracy of their multiplication skills by quickly choosing factors that multiply to a target product.

# data[].attributes.body
Worksheets to support fluency practice.

# data[].attributes.body
Support multiplication fluency with error analysis.

# data[].attributes.body
Support multiplication fluency with a game.

# data[].attributes.body
Play games to support learning.

# data[].attributes.attachment_link.readable_text
Mental Math - practice multiplying numbers

Common Core Connection for Grades 3 and 4

Apply properties of operations as strategies to multiply.
Fluently multiply within 100
Find all factor pairs for a whole number in the range 1-100.
Recognize that a whole number is a multiple of each of its factors.

# data[].attributes.attachment_link.description
Play Factor Pair Up at Math Playground.com! Capture products in a line before your opponent does.

# data[].attributes.body
Use the multiplication chart to support learning.

# data[].attributes.attachment_link.readable_text
Mental Math - visualize multiplication patterns

Common Core Connections - Grades 3 and 4

Understand properties of multiplication.
Multiply within 100.
Identify arithmetic patterns.
Look for and make use of structure.

# data[].attributes.attachment_link.title
Interactive Multiplication Chart | Math Playground

# data[].attributes.attachment_link.description
Interactive Multiplication Chart at Math Playground.com! Explore factors, multiples, products, square numbers, multiplication patterns, math facts and more.

# data[].attributes.body
Play games to support learning.

# data[].attributes.attachment_link.readable_text
Problem Solving
Number Sense

Common Core Connection for Grades 3-5

Represent and solve problems involving multiplication and division.
Multiply and divide within 100.
Gain familiarity with factors and multiples.
Write and interpret numerical expressions.

# data[].attributes.attachment_link.title
Professor X and the FactorBots | Math Playground

# data[].attributes.attachment_link.description
Play Professor X and the FactorBots at MathPlayground.com! Solve number puzzles to win the game.