Students will develop strategies for composing and decomposing numbers to reach decade numbers and subtract from decade numbers. Students will: 
- use their understanding of making ten and twenty to add to and subtract from decade numbers. 
- decompose numbers 1–10 to help them reach decade numbers.

- How are mathematical representations of relationships made? 
- What are some applications for expressions, equations, and inequalities in the quantification, modeling, solving, and/or analysis of mathematical situations?
- How can the study of mathematics aid in clear communication?
- How can recognizing repetition or regularity help you solve problems faster? 
- How do we represent, compare, quantify, and model numbers using mathematics?

- Sum: The result of addition.

- numeral cards 11–100 
- Counters 
- deca-number cube (one per pair) 
- ten-frames for students who need visual support 
- copies of the Hop to It game board (M-2-3-2_Hop to It) 
- copies of the Hop from 60 game board (M-2-3-2_Hop from 60) 
- copies of the Hopping Assessment (M-2-3-2_Hopping Assessment)

- Student progress will be evaluated through observations made during whole-class discussions, small-group work, and student interaction.
- The hop-forward-and-backward-from-decades assessment (M-2-3-2_Hopping Assessment) can be used as a formative assessment as well as a review of the strategies that students learned in Lesson 2.

Explicit instruction, modeling, scaffolding, and active engagement 
W: Provide students with ten frames if they require a visual aid for creating numbers to and from the decades. 
H: Ask students to help you arrive at a decade number to assist you in solving a real-world problem in class. 
E: Skip-count the decade numbers by tens with the class. After that, ask the class to choose the number that corresponds to the closest decade by calling out a few two-digit numbers. 
R: Allow students to play the Hop to It game in pairs. Students can write their equations on their whiteboards or in their math notebooks. 
E: As an informal assessment, observe student discussions. As you reach the decade number, have pairs talk about the different approaches they took. 
T: Assign students a goal number to mentally solve on a daily or frequent basis. If students require additional practice, they can use ten-frames to work in small groups and discuss the best strategy to use to accomplish their objectives. Ask students to hop back from a decade number if they're ready. 
O: The purpose of this lesson is to help students comprehend place value and the composition and decomposition of numbers. 

"There are numerous applications for the knowledge we possess regarding ten and twenty-plus numbers. I need twenty pencils, for instance, but I only have 13. How many more pencils would I require?"

Allow students time to think. Before you ask for ideas, ask them to think, pair, and share.

"How can understanding what goes with 13 to create 20 aid in understanding what goes with 23 to create 30? Or 43 to get 50?"

Present both the number cards and the Hop to It game board (M-2-3-2_Hop to It). Inform students that they will be playing a game to help them practice hopping to decade numbers. 

Mix up the numeral cards. Place one card out at a time and ask students what decade number comes after that. Say, for instance, "I have 52; what is the decade number I would look forward to?" after setting out a 52-number card. (60) After hearing back, find out how they identified it. Find out how many hops it would take to reach sixty. Demonstrate how they would use the counters to mark their hops on the game board.

Change the numeral card each time you repeat the exercise a few more times. Distribute the materials and assign students to pairs once they have a firm understanding of the task.

Allow enough time so that students can participate in this game in pairs. When they appear to be doing well, gather the class to talk about the observations they made while engaging in the game.

(This next section can be performed the day after or the same day.) Find out from the students what they did in the Hop to It game (maybe from the previous day). Give the answers time. Instruct students to round numbers to the closest decade number using what they learned about making ten. Inform them that going forward, they will be utilizing their knowledge of making ten to hop back.

"I had to give back three of the twenty books I owned to the library. How many books are left in my collection? So, I know that 3 + 7 = 10, so 10 - 3 = 7; 20 is 10 greater than 10, so 7 + 10 = 17. That indicates that I am down to 17 books."

"I made thirty cupcakes, six of which I gave to my mom. Let's get started try this one. How many cupcakes do I still have? How can I resolve this one?" Give students time to think, pair, and share before answering the question. As needed, provide students with guidance. (I know that 10 – 6 = 4 is equal to 6 + 4 = 10, and since 30 is 20 more than 10, so 4 + 20 = 24. This indicates that 24 cupcakes remain.)

"I want you to try this with your partner now: Out of the 40 computers in the library, five are broken. How many computers are in use right now?" Let students work in pairs and groups while keeping an eye on them and offering assistance when needed. Choose one pair to share. (Since 10 – 5 = 5, we know that 5 + 5 = 10, and since 40 is 30 more than 10, 5 + 30 = 35. Thus, 35 computers are operational.)

Inform the students that Hop from 60 is the name of the game they will be playing next. Give out the Hop from 60 game board (M-2-3-2_Hop from 60). Using the deca-number cube and their understanding of 10 and 20, they will hop from 60 to 60 without counting.

Following the hop, they will place a counter on the number they land on. The objective is to achieve a "blackout" on the board, meaning that all of the counters are in place.

Monitoring student responses during discussions and group projects can be used as informal assessments to guide instruction.

To evaluate students' progress, utilize the M-2-3-2_Hopping Assessment paper-and-pencil assessment. To make sure students are using non-counting strategies, it should be administered in small groups.

Extension:

To fulfill your students' needs throughout the year, employ the techniques and activities provided below.

Routine: Students can practice jumping to and from decade numbers by hopping forward and backward. When they transition to two-digit addition and subtraction, this will be helpful.

Small Group: Additional practice and small-group instruction will help students who require opportunities for further learning. To assist students with other decade numbers, provide them with an empty ten-frame so they can see the divisions and combinations of 10. To improve their factual fluency for these base numbers, they might need to play a variation of hop to 10 or hop from 10. Make sure they can utilize these figures with ease and flexibility before advancing to the higher decades, as they will probably start counting backward or forward.

Expansion: When they're ready, students can practice jumping forward and backward in time. When they draw the number 54, for instance, and roll the deca-number cube, they obtain a 9. They could calculate which number they would land on if they hopped forward and which number they would land on if they hopped backward. Students would say that 54 + 6 = 60, and then 60 + 3 (the remainder from the 9) = 63, using the decade numbers as landmarks. In other words, 54 – 4 = 50; 50 – 5 (left from 9) = 45.