How many different ways can you represent 82 using tens and ones?

Does 4 tens and 8 ones have the same value as 3 tens and 18 ones? Explain your thinking.

Do 2 tens and 6 ones have the same value as 2 ones and 6 tens? Use models and/or hundreds chart to help explain your answer.

A two-digit number has more tens than ones. What could the number be? What is another possibility?

The sum of the digits of a two-digit number is12. Use a hundred chart, what could the number be? What is another possibility?

How are the numbers 30 and 35 alike? How are they different?

Kendra made a two-digit number with a 6 in the ones place. What possible numbers could she have made?

About the Math

The concept of ten is a foundational skill in primary mathematics. Students must be able to compose ten in order to add and subtract as well as understand the value of a number. Understanding the composition of a two-digit number is equally important. Students need ample practice so that understanding is intuitive rather than rote or memorized.

There are many different models that can be used to develop the concept. Models for grouping incude: Beans and small paper cups (for groups of 10), Linking cubes, and/or Digi-blocks. Essential vocabulary for this standard includes: place value, digit, one, ten, and hundred(online dictionary, HCPSS Vocabulary Cards).

Pregrouped models include: Base-ten blocks, five and ten-frames, and place value mats.
Virtual base ten blocks , Chip Abacus, and hundred charts are good electronic resources.

The Illustrative Mathematics tasks below demonstrate expectation for this standard.

Rich Tasks for Multiple Means of Engagement, Expression, and Representation (UDL)

1. Ten and Some More (VandeWalle, K-3, p 55). Use a simple two-part mat, and have children count out ten counters onto one side.
Next have them put five counters on the other side. Together count all of the counters by ones. Chorus the combination, "Ten and
five is fifteen." Turn the mat around, "Five and ten is fifteen." Repeat with other numbers in a random order but without changing the
10 side of that mat.

Rich Problems

Choose a number between 1 and 10. Show that number in as many ways as you can. Choose a number between 20 and 30. Show that number in as many ways as you can. (Small, Good Questions, Great Ways to Differentiate Mathematics Instruction, p 40).

## Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:

## B. The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.

## Quarter 1

Quarter 2B. The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.

B. The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.

This includes representing 100 with a "flat" base ten block (in quarter 2).

This includes representing 100 with a "flat" base ten block (in quarter 2).

This includes representing 100 with a "flat" base ten block (in quarter 2).

## Increasing Rigor

The concept of ten is a foundational skill in primary mathematics. Students must be able to compose ten in order to add and subtract as well as understand the value of a number. Understanding the composition of a two-digit number is equally important. Students need ample practice so that understanding is intuitive rather than rote or memorized.About the MathThere are many different models that can be used to develop the concept. Models for grouping incude: Beans and small paper cups (for groups of 10), Linking cubes, and/or Digi-blocks. Essential vocabulary for this standard includes:

place value, digit, one, ten,andhundred(online dictionary, HCPSS Vocabulary Cards).Pregrouped models include: Base-ten blocks, five and ten-frames, and place value mats.

Virtual base ten blocks , Chip Abacus, and hundred charts are good electronic resources.

The Illustrative Mathematics tasks below demonstrate expectation for this standard.

Rich Tasks for Multiple Means of Engagement, Expression, and Representation (UDL)Next have them put five counters on the other side. Together count all of the counters by ones. Chorus the combination, "Ten and

five is fifteen." Turn the mat around, "Five and ten is fifteen." Repeat with other numbers in a random order but without changing the

10 side of that mat.

Choose a number between 1 and 10. Show that number in as many ways as you can. Choose a number between 20 and 30. Show that number in as many ways as you can. (Small, Good Questions, Great Ways to Differentiate Mathematics Instruction, p 40).Rich ProblemsPrint Resources:Math by All Means Place Value 1-2

(56-71)

Math Connections K-3

(7, 32, 70)

Mental Math in the Primary Grades

(15-16)

Nimble with Numbers 1-2

(104)

Web ResourcesGames and CentersLessonsStudent ResourcesVideo SegmentsMy Double Ten-Frame Riddle

Teens on the Ten Frame

Make 10 Bundles

Base Ten Concentration (2 Digit)

Representing Two Digit Numbers with Base 10 Blocks

Printable GamesTens and Ones Game

Online GamesZap

Hundred Board Logic

Guess My Number

Mystery Number (Game/Lesson Seed)Constructing Tens and Ones

Numbers in the Teens

Instructional Ideas

Teaching Teen Numbers

Teen Number Instructional Idea

Interactive Hundred ChartBase Ten Blocks

Numbers to 20 on the TenFrame

Numbers to 20 on the MathRack

PrintablesHundred ChartTeens on the Ten Frame Book Template

Teacher guide for virtual manipulatives 1.NBT.2

## Questions/Comments:

Contact John SanGiovanni at jsangiovanni@hcpss.org.Use and Sharing of HCPSS Website and Resources:Howard County Public Schools Office of Elementary Mathematics Curricular Projects has licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.