Standard K.NBT.1: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

About the Math

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.

Ability to use concrete materials (e.g., Unifix cubes, snap cubes, Digi-blocks, base ten blocks, etc.) to represent the combination of one ten and ones for each number

Ability to record the representations of 11 through 19 in pictures, numbers, and/or equations

Instructional Resources

Beans glued to popsicle sticks are good models for tens and ones.
Other models include linking cubes, digi-blocks, and plastic chains.

Students have difficulty with ten as a singular word that means 10 things. For many students, the understanding that a group of 10 things can be replaced by a single object and they both represent 10 is confusing. Help students develop the sense of 10 by first using groupable materials then replacing the group with an object or representing 10. Watch for and address the issue of attaching words to materials and groups without knowing what they represent. If this misconception is not addressed early on it can cause additional issues when working with numbers 11-19 and beyond.

Print Resources

Math Intervention: Building Number Power with Formative Assessments, Differentiation, and Games, PreK-2

Standard K.NBT.1: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

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.

## Essential Skills and Knowledge (from MSDE Common Core Frameworks)

Beans glued to popsicle sticks are good models for tens and ones.Instructional ResourcesOther models include linking cubes, digi-blocks, and plastic chains.

Teens on the Ten FrameOnline ResourcesTeens on the Ten Frame Book

Tens and Ones with Unifix Cubes

My Double Ten-Frame Riddle

Strips of Connected Squares (ablongman)

Five frames and Ten frames (ablongman)

Place Value Mat for Ten frames (ablongman)

Lessons, Lesson Seeds, Instructional ActivitiesTiny Tens, Math Intervention: Building Number Power with Formative Assessments, Differentiation, and Games (81-83)Teacher Created MaterialsFormative Assessments

Students have difficulty with ten as a singular word that means 10 things. For many students, the understanding that a group of 10 things can be replaced by a single object and they both represent 10 is confusing. Help students develop the sense of 10 by first using groupable materials then replacing the group with an object or representing 10. Watch for and address the issue of attaching words to materials and groups without knowing what they represent. If this misconception is not addressed early on it can cause additional issues when working with numbers 11-19 and beyond.Common Misconceptions

Math Intervention: Building Number Power with Formative Assessments, Differentiation, and Games, PreK-2Print Resources- Match and Claim (pg. 66-68) Match and Claim.pdf
- Tiny Tens (pg. 81-83) Tiny Tens.pdf

Teaching Student-Centered Mathematics- Activity 2.26 Ten and Some More (pg. 55) (add pdf)

Developing Number Concepts Book 2: Addition and Subtraction

Quarter 1 Quarter 2 Quarter 3 Quarter 4Investigations AlignmentUnit 6: 5A.3, 5A.4, 5A.5