{"type":"default","seo":{"title":"Teaching Multiplication with Arrays in Math | HMH","description":"By teaching multiplication with arrays in math, you can help students better understand multiplication concepts by enabling them to visualize the computation process.","headercode":"","ogtitle":"Teaching Multiplication with Arrays in Math","ogdescription":"Help students visualize multiplication by showing them how to represent the concept using arrays.","ogimage":"https://s3.amazonaws.com/int-hmhco-vmg-craftcms-public/seo/teaching-multiplication-with-arrays-in-math-hero.jpg","seosettings":{"noIndexNoFollow":false,"showGtm":true},"keywords":"","canonical":""},"redirect":[],"entrysettings":{"includeinsearch":true,"showglobalmessaging":true},"globalsettings":{"standardheader":true,"standardfooter":true},"url":"/blog/teaching-multiplication-with-arrays-in-math","id":74884,"title":"Teaching Multiplication with Arrays in Math","slug":"teaching-multiplication-with-arrays-in-math","bodycontainer":[{"type":"copy","headline":null,"richtext":"
Students in Grades 3+ can more readily develop an understanding of multiplication when they see it visually. For example, they can picture a marching band arranged in equal rows or chairs set up evenly in an auditorium. In both cases, they are visualizing rows and columns. An arrangement of objects, pictures, or numbers in rows and columns is called an array. Arrays are useful representations of multiplication concepts (among other ideas in mathematics).
\n
This array has 4 rows and 3 columns. It can also be described as a 4 by 3 array. The word \"by\" is often represented with a multiplication cross: 4 × 3.
Notice that the rows in each array are equal in length. Think of the rows as equal groups. Your students should have already used equal groups to multiply (2.OA.C.4).
","subheadline":null,"alignment":"left"},{"type":"media","color":"transparent","backgroundshape":"rectangle","mediadisplay":"fillgrid","headline":null,"subheadline":null,"media":{"type":"image","caption":null,"image":"https://s3.amazonaws.com/int-hmhco-vmg-craftcms-public/blog/multiply-two-groups-of-six.png","height":386,"width":800,"title":"Multiply two groups of six","alignment":"not-set","asLightbox":false,"style":"not-set","transforms":{"large":{"image":"https://s3.amazonaws.com/int-hmhco-vmg-craftcms-public/_transforms/blog/_large/multiply-two-groups-of-six.png","height":463,"width":960,"title":"Multiply two groups of six"},"medium":{"image":"https://s3.amazonaws.com/int-hmhco-vmg-craftcms-public/_transforms/blog/_medium/multiply-two-groups-of-six.png","height":309,"width":640,"title":"Multiply two groups of six"},"small":{"image":"https://s3.amazonaws.com/int-hmhco-vmg-craftcms-public/_transforms/blog/_small/multiply-two-groups-of-six.png","height":154,"width":320,"title":"Multiply two groups of six"},"xlarge":{"image":"https://s3.amazonaws.com/int-hmhco-vmg-craftcms-public/_transforms/blog/_xlarge/multiply-two-groups-of-six.png","height":618,"width":1280,"title":"Multiply two groups of six"}},"color":" background-transparent","display":" display-fillgrid","mediasize":"xlarge"}},{"type":"copy","headline":null,"richtext":"
If you arrange the equal groups in rows, you form an array.
","subheadline":null,"alignment":"left"},{"type":"media","color":"transparent","backgroundshape":"rectangle","mediadisplay":"fillgrid","headline":null,"subheadline":null,"media":{"type":"image","caption":null,"image":"https://s3.amazonaws.com/int-hmhco-vmg-craftcms-public/blog/multiply-two-rows-five-columns.png","height":298,"width":800,"title":"Multiply two rows five columns","alignment":"not-set","asLightbox":false,"style":"not-set","transforms":{"large":{"image":"https://s3.amazonaws.com/int-hmhco-vmg-craftcms-public/_transforms/blog/_large/multiply-two-rows-five-columns.png","height":358,"width":960,"title":"Multiply two rows five columns"},"medium":{"image":"https://s3.amazonaws.com/int-hmhco-vmg-craftcms-public/_transforms/blog/_medium/multiply-two-rows-five-columns.png","height":238,"width":640,"title":"Multiply two rows five columns"},"small":{"image":"https://s3.amazonaws.com/int-hmhco-vmg-craftcms-public/_transforms/blog/_small/multiply-two-rows-five-columns.png","height":119,"width":320,"title":"Multiply two rows five columns"},"xlarge":{"image":"https://s3.amazonaws.com/int-hmhco-vmg-craftcms-public/_transforms/blog/_xlarge/multiply-two-rows-five-columns.png","height":477,"width":1280,"title":"Multiply two rows five columns"}},"color":" background-transparent","display":" display-fillgrid","mediasize":"xlarge"}},{"type":"copy","headline":null,"richtext":"
When you show students the connection between equal groups and arrays, students can visualize how to use arrays to multiply. They will use arrays again later to divide.
\n
Look at the multiplication sentence that describes the array below. The numbers in multiplication sentences have special names.
","subheadline":null,"alignment":"left"},{"type":"media","color":"transparent","backgroundshape":"rectangle","mediadisplay":"fillgrid","headline":null,"subheadline":null,"media":{"type":"image","caption":null,"image":"https://s3.amazonaws.com/int-hmhco-vmg-craftcms-public/blog/multipliaction-with-arrays-rows-columns-update.png","height":454,"width":800,"title":"Multipliaction with arrays rows columns update","alignment":"not-set","asLightbox":false,"style":"not-set","transforms":{"large":{"image":"https://s3.amazonaws.com/int-hmhco-vmg-craftcms-public/_transforms/blog/_large/multipliaction-with-arrays-rows-columns-update.png","height":545,"width":960,"title":"Multipliaction with arrays rows columns update"},"medium":{"image":"https://s3.amazonaws.com/int-hmhco-vmg-craftcms-public/_transforms/blog/_medium/multipliaction-with-arrays-rows-columns-update.png","height":363,"width":640,"title":"Multipliaction with arrays rows columns update"},"small":{"image":"https://s3.amazonaws.com/int-hmhco-vmg-craftcms-public/_transforms/blog/_small/multipliaction-with-arrays-rows-columns-update.png","height":182,"width":320,"title":"Multipliaction with arrays rows columns update"},"xlarge":{"image":"https://s3.amazonaws.com/int-hmhco-vmg-craftcms-public/_transforms/blog/_xlarge/multipliaction-with-arrays-rows-columns-update.png","height":726,"width":1280,"title":"Multipliaction with arrays rows columns update"}},"color":" background-transparent","display":" display-fillgrid","mediasize":"xlarge"}},{"type":"copy","headline":null,"richtext":"
The numbers that are multiplied are called factors. The result of multiplying the factors is called the product.
\n
Now look at what happens to the factors and product in the multiplication sentence when the array is turned on its side.
","subheadline":null,"alignment":"left"},{"type":"media","color":"transparent","backgroundshape":"rectangle","mediadisplay":"fillgrid","headline":null,"subheadline":null,"media":{"type":"image","caption":null,"image":"https://s3.amazonaws.com/int-hmhco-vmg-craftcms-public/blog/multiply-using-three-rows-of-six.png","height":357,"width":800,"title":"Multiply using three rows of six","alignment":"not-set","asLightbox":false,"style":"not-set","transforms":{"large":{"image":"https://s3.amazonaws.com/int-hmhco-vmg-craftcms-public/_transforms/blog/_large/multiply-using-three-rows-of-six.png","height":428,"width":960,"title":"Multiply using three rows of six"},"medium":{"image":"https://s3.amazonaws.com/int-hmhco-vmg-craftcms-public/_transforms/blog/_medium/multiply-using-three-rows-of-six.png","height":286,"width":640,"title":"Multiply using three rows of six"},"small":{"image":"https://s3.amazonaws.com/int-hmhco-vmg-craftcms-public/_transforms/blog/_small/multiply-using-three-rows-of-six.png","height":143,"width":320,"title":"Multiply using three rows of six"},"xlarge":{"image":"https://s3.amazonaws.com/int-hmhco-vmg-craftcms-public/_transforms/blog/_xlarge/multiply-using-three-rows-of-six.png","height":571,"width":1280,"title":"Multiply using three rows of six"}},"color":" background-transparent","display":" display-fillgrid","mediasize":"xlarge"}},{"type":"copy","headline":null,"richtext":"
The order of the factors changed, but the product stayed the same. This is in fact always the case and a feature that has piqued the interest of mathematicians for centuries. You can change the order of factors, but the product stays the same, a mathematical property known as the Commutative Property of Multiplication. Students should be familiar with the commutative property because they have already seen it applied to addition (1.OA.B.3).
\n
Help students realize that by applying the commutative property, they know twice as many multiplication facts. For example, if they know 8 × 5 = 40, then they also know 5 × 8 = 40.
\n
***
\n
Looking for more free math lessons and activities for elementary school students? Be sure to explore our Free Teaching Resources portal.
Get our FREE guide \"Optimizing the Math Classroom: 6 Best Practices.\"
","color":"pale-orange","displaydropdown":"stickycta","mediadisplay":"","subheadline":null,"cta":[{"linktype":"pill","url":"https://www.hmhco.com/forms/6-best-practices-to-optimize-math-classrooms","linkurl":"https://www.hmhco.com/forms/6-best-practices-to-optimize-math-classrooms","linktext":"Download","opennewwindow":false,"className":["button","pill","small"],"index":0}]}],"postDate":"2024-08-15T10:35:00-04:00","postUpdatedDate":"2024-12-30T14:47:56-05:00","section":"blog","duration":"2","media":{"type":"image","caption":null,"image":"https://s3.amazonaws.com/int-hmhco-vmg-craftcms-public/seo/teaching-multiplication-with-arrays-in-math-hero.jpg","height":450,"width":800,"title":"Teaching multiplication with arrays in math hero","alignment":"not-set","asLightbox":false,"style":"not-set","transforms":{"large":{"image":"https://s3.amazonaws.com/int-hmhco-vmg-craftcms-public/_transforms/seo/_large/teaching-multiplication-with-arrays-in-math-hero.jpg","height":540,"width":960,"title":"Teaching multiplication with arrays in math hero"},"medium":{"image":"https://s3.amazonaws.com/int-hmhco-vmg-craftcms-public/_transforms/seo/_medium/teaching-multiplication-with-arrays-in-math-hero.jpg","height":360,"width":640,"title":"Teaching multiplication with arrays in math hero"},"small":{"image":"https://s3.amazonaws.com/int-hmhco-vmg-craftcms-public/_transforms/seo/_small/teaching-multiplication-with-arrays-in-math-hero.jpg","height":180,"width":320,"title":"Teaching multiplication with arrays in math hero"},"xlarge":{"image":"https://s3.amazonaws.com/int-hmhco-vmg-craftcms-public/_transforms/seo/_xlarge/teaching-multiplication-with-arrays-in-math-hero.jpg","height":720,"width":1280,"title":"Teaching multiplication with arrays in math hero"}},"mediasize":"large","isHero":true},"textLabel":"
","url":"https://web-delivery-v1.int.webnp.hmhco.com/people/richard-blankman","media":{"type":"image","caption":null,"image":"https://s3.amazonaws.com/int-hmhco-vmg-craftcms-public/people/RichardHeadshotUpdated.png","height":756,"width":756,"title":"Richard Blankman Blog 800X800 3","alignment":"not-set","asLightbox":false,"style":"not-set","transforms":{"large":{"image":"https://s3.amazonaws.com/int-hmhco-vmg-craftcms-public/_transforms/people/_large/RichardHeadshotUpdated.png","height":960,"width":960,"title":"Richard Blankman Blog 800X800 3"},"medium":{"image":"https://s3.amazonaws.com/int-hmhco-vmg-craftcms-public/_transforms/people/_medium/RichardHeadshotUpdated.png","height":640,"width":640,"title":"Richard Blankman Blog 800X800 3"},"small":{"image":"https://s3.amazonaws.com/int-hmhco-vmg-craftcms-public/_transforms/people/_small/RichardHeadshotUpdated.png","height":320,"width":320,"title":"Richard Blankman Blog 800X800 3"},"xlarge":{"image":"https://s3.amazonaws.com/int-hmhco-vmg-craftcms-public/_transforms/people/_xlarge/RichardHeadshotUpdated.png","height":1280,"width":1280,"title":"Richard Blankman Blog 800X800 3"}},"mediasize":"medium"}}],"contributors":[],"tags":[{"title":"Activities & Lessons","slug":"activities-lessons"},{"title":"Math","slug":"math"},{"title":"Grades 3-5","slug":"grades-3-5"},{"title":"Grades 1-2","slug":"grades-1-2"}],"sidebarcontent":{"headline":"
Math Best Practices Guide
","richtext":"
Get our FREE guide \"Optimizing the Math Classroom: 6 Best Practices.\"
Download our free activities calendar for fun lessons to do with your class, plus engaging ways to commemorate and celebrate events throughout the year.
Download our free activities calendar for fun lessons to do with your class, plus engaging ways to commemorate and celebrate events throughout the year.
Get our free administrator’s guide to building a positive school culture, filled with practical advice, real-world examples, and resources for further exploration.
Download our free activities calendar for fun lessons to do with your class, plus engaging ways to commemorate and celebrate events throughout the year.
Get our free administrator’s guide to building a positive school culture, filled with practical advice, real-world examples, and resources for further exploration.
Students in Grades 3+ can more readily develop an understanding of multiplication when they see it visually. For example, they can picture a marching band arranged in equal rows or chairs set up evenly in an auditorium. In both cases, they are visualizing rows and columns. An arrangement of objects, pictures, or numbers in rows and columns is called an array. Arrays are useful representations of multiplication concepts (among other ideas in mathematics).
This array has 4 rows and 3 columns. It can also be described as a 4 by 3 array. The word "by" is often represented with a multiplication cross: 4 × 3.
This array has 5 rows and 4 columns. It is a 5 by 4 array.
Notice that the rows in each array are equal in length. Think of the rows as equal groups. Your students should have already used equal groups to multiply (2.OA.C.4).
If you arrange the equal groups in rows, you form an array.
When you show students the connection between equal groups and arrays, students can visualize how to use arrays to multiply. They will use arrays again later to divide.
Look at the multiplication sentence that describes the array below. The numbers in multiplication sentences have special names.
The numbers that are multiplied are called factors. The result of multiplying the factors is called the product.
Now look at what happens to the factors and product in the multiplication sentence when the array is turned on its side.
The order of the factors changed, but the product stayed the same. This is in fact always the case and a feature that has piqued the interest of mathematicians for centuries. You can change the order of factors, but the product stays the same, a mathematical property known as the Commutative Property of Multiplication. Students should be familiar with the commutative property because they have already seen it applied to addition (1.OA.B.3).
Help students realize that by applying the commutative property, they know twice as many multiplication facts. For example, if they know 8 × 5 = 40, then they also know 5 × 8 = 40.
***
Looking for more free math lessons and activities for elementary school students? Be sure to explore our Free Teaching Resources portal.
Get our FREE guide "Optimizing the Math Classroom: 6 Best Practices."
