Compose and decompose numbers from 11 to 19 into ten ones and some further, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.

Progression of Skills

Enduring Understanding

Understanding place value leads to number sense and efficient strategies for computing.

Kindergarteners need to understand the idea of a ten so they can develop the strategy of adding onto 10 to add within 20 in Grade 1. Students need to construct their own base-ten ideas about quantities and their symbols by connecting to counting by ones. They should use a variety of manipulatives to model and connect equivalent representations for the numbers 11 to19. For instance, to represent 13, students can count by ones and show 13 beans. They can anchor to five and show one group of 5 beans and 8 beans or anchor to ten and show one group of 10 beans and 3 beans. Students need to eventually see a ten as different from 10 ones.

After the students are familiar with counting up to 19 objects by ones, have them explore different ways to group the objects that will make counting easier. Have them estimate before they count and group. Discuss their groupings and lead students to conclude that grouping by ten is desirable. 10 ones make 1 ten makes students wonder how something that means a lot of things can be one thing. They do not see that there are 10 single objects represented on the item for ten in pregrouped materials, such as the rod in base-ten blocks. Students then attach words to materials and groups without knowing what they represent. Eventually they need to see the rod as a ten that they did not group themselves. Students need to first use groupable materials to represent numbers 11 to 19 because a group of ten such as a bundle of 10 straws or a cup of 10 beans makes more sense than a ten in pregrouped materials.

Kindergarteners should use proportional base-ten models, where a group of ten is physically 10 times larger than the model for a one. Nonproportional models such as an abacus and money should not be used at this grade level. Students should impose their base-ten concepts on a model made from groupable and pregroupable materials (see Resources/Tools). Students can transition from groupable to pregroupable materials by leaving a group of ten intact to be reused as a pregrouped item. When using pregrouped materials, students should reflect on the ten-to-one relationships in the materials, such as the “tenness” of the rod in base-ten blocks. After many experiences with pregrouped materials, students can use dots and a stick (one tally mark) to record singles and a ten.

Encourage students to use base-ten language to describe quantities between 11 and 19. At the beginning, students do not need to use ones for the singles. Some of the base-ten language that is acceptable for describing quantities such as18 includes one ten and eight, a bundle and eight, a rod and 8 singles and ten and eight more. Write the horizontal equation 18 = 10 + 8 and connect it to base-ten language. Encourage, but do not require, students to write equations to represent quantities.

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

Rich Problem:

Activity 2.26 Ten and Some More (pg. 55) (add pdf)

## Compose and decompose numbers from 11 to 19 into ten ones and some further, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.

Understanding place value leads to number sense and efficient strategies for computing.Enduring Understanding

How does a digit's position affect it's value?Essential Questions

compose, decompose, tens place, ones place, equaitonVocabulary

Kindergarteners need to understand the idea of a ten so they can develop the strategy of adding onto 10 to add within 20 in Grade 1. Students need to construct their own base-ten ideas about quantities and their symbols by connecting to counting by ones. They should use a variety of manipulatives to model and connect equivalent representations for the numbers 11 to19. For instance, to represent 13, students can count by ones and show 13 beans. They can anchor to five and show one group of 5 beans and 8 beans or anchor to ten and show one group of 10 beans and 3 beans. Students need to eventually see a ten as different from 10 ones.About the MathAfter the students are familiar with counting up to 19 objects by ones, have them explore different ways to group the objects that will make counting easier. Have them estimate before they count and group. Discuss their groupings and lead students to conclude that grouping by ten is desirable. 10 ones make 1 ten makes students wonder how something that means a lot of things can be one thing. They do not see that there are 10 single objects represented on the item for ten in pregrouped materials, such as the rod in base-ten blocks. Students then attach words to materials and groups without knowing what they represent. Eventually they need to see the rod as a ten that they did not group themselves. Students need to first use groupable materials to represent numbers 11 to 19 because a group of ten such as a bundle of 10 straws or a cup of 10 beans makes more sense than a ten in pregrouped materials.

Kindergarteners should use proportional base-ten models, where a group of ten is physically 10 times larger than the model for a one. Nonproportional models such as an abacus and money should not be used at this grade level. Students should impose their base-ten concepts on a model made from groupable and pregroupable materials (see Resources/Tools). Students can transition from groupable to pregroupable materials by leaving a group of ten intact to be reused as a pregrouped item. When using pregrouped materials, students should reflect on the ten-to-one relationships in the materials, such as the “tenness” of the rod in base-ten blocks. After many experiences with pregrouped materials, students can use dots and a stick (one tally mark) to record singles and a ten.

Encourage students to use base-ten language to describe quantities between 11 and 19. At the beginning, students do not need to use ones for the singles. Some of the base-ten language that is acceptable for describing quantities such as18 includes one ten and eight, a bundle and eight, a rod and 8 singles and ten and eight more. Write the horizontal equation 18 = 10 + 8 and connect it to base-ten language. Encourage, but do not require, students to write equations to represent quantities.

Rich Tasks for Multiple Means of Engagement, Expression, and Representation (UDL)Rich Problem:- Activity 2.26 Ten and Some More (pg. 55) (add pdf)

*MSDE/CMS:LessonsPlace Value Foundation

Using a Rekenrek to Build and Understand Place Value

Teens on the Ten FrameOnline ResourcesTeens on the Ten Frame Book

Tens and Ones with Unifix Cubes

My Double Ten-Frame Riddle

Teens on the rekenrek*NEW*

Strips of Connected Squares (ablongman)

Five frames and Ten frames (ablongman)

Place Value Mat for Ten frames (ablongman)

Teacher Created MaterialsNena Hupp (Worthington Elementary) • Show a Number Different Way

Beans glued to popsicle sticks are good models for tens and ones.Instructional ResourcesOther models include linking cubes

Print Resources:Investigations Lessons that Support the Standard:Common Core Alignment## Questions/Comments:

Contact John SanGiovanni at jsangiovanni@hcpss.org.