“We use what we know about making numbers to ten and 20 in many different ways. For example, I have 13 pencils but I need 20 pencils. How many more pencils would I need? ”
Allow time for students to think. Then have them think-pair-share their thoughts before you ask for ideas.
“How can knowing what goes with 13 to make 20 help me to know what goes with 23 to make 30? Or 43 to make 50?”
Display the Hop to It game board (M-2-3-2_Hop to It.docx) and the numeral cards. Tell students they will be playing a game that will help them practice what they know about hopping to decade numbers.
Mix up the numeral cards. Place one card out at a time and ask students what is the next decade number after that number. For example if you place a 52 numeral card out, say: “I have 52; what is the decade number I would hop forward to?” (60) Wait for responses and ask how they know. Ask how many hops it would take to get to 60. Model how they would mark their hops on the game board with the counters.
Repeat the activity a few more times, changing the numeral card each time. Once students understand this activity, distribute the materials and pair students.
Allow adequate time for students to play this game in pairs. When they seem to be doing well, call the class together to discuss what they noticed while playing the game.
(This next portion can be played the same day or the following day.) Ask the class what they did in the Hop to It game (perhaps the day before). Allow time for responses. Tell students that they used what they knew about making ten to hop numbers up to their nearest decade number. Tell them that now they will be using what they know about making ten to hop back.
“I had 20 books but I had to return three of them to the library. How many books do I have left? Well, I know that 3 + 7 = 10, so I know that 10 – 3 = 7; 20 is 10 more than 10, so 7 + 10 = 17. That means I have 17 books left.”
“Let’s try this one: I made 30 cupcakes and gave 6 of them to my mom. How many cupcakes do I have left? What can I do to solve this one?” Allow students to think-pair-share before responding to the question. Guide students as needed. (I know that 6 + 4 = 10, so 10 – 6 = 4; 30 is 20 more than 10, so 4 + 20 = 24. That means there are 24 cupcakes left.)
“Now I would like you and your partner to try this one: There are 40 computers at the library, but 5 of them are broken. How many computers are working?” Allow students to think-pair-share and monitor them to assist as needed. Choose one pair to share out. (We know that 5 + 5 = 10, so 10 – 5 = 5; 40 is 30 more than 10, so 5 + 30 = 35. That means 35 computers are working.)
Tell students the next game they will play is called Hop from 60. Distribute the Hop from 60 game board (M-2-3-2_Hop from 60.docx). They will roll the deca-number cube and use what they know about 10 and 20 to hop from 60 without counting.
They will put a counter on the number they would land on after the hop. The goal is to have a “blackout” on the board (i.e., the board is completely filled with counters).
Monitoring student responses during discussions and partner work can be used as informal assessments to guide instruction.
A paper-and-pencil assessment may be used (M-2-3-2_Hopping Assessment.docx) to assess students’ progress. It should be given in a small-group setting to be sure students are using noncounting strategies.
Extension:
Use the activities and strategies listed below to meet the needs of your students during the year.
- Routine: As a morning routine students can practice hopping forward and backward to and from decade numbers. This will help when they move to two-digit by two-digit addition and subtraction.
- Small Group: For students who need opportunities for additional learning, more practice and small-group instruction will be beneficial. Give students an empty ten-frame to help them visualize the combinations and partitions of 10 to help with other decade numbers. They may need to play a version of hop to 10 or hop from 10 in order to build their fact fluency for these base numbers. Ensure that they use these numbers fluently and flexibly before moving to the higher decades, or they will most likely resort to counting on/back.
- Expansion: Students who are ready can practice expansions of hopping across and back decades. For example, they draw the number 54 and roll the deca-number cube and get a 9. They could figure out what number they would land on if they hopped forward, and what number they would land on if they hopped backwards. Students would use the decade numbers as landmarks so they would say 54 + 6 is 60, and then 60 + 3 (that’s left from the 9) = 63. Or 54 – 4 = 50; then 50 – 5 (left from the 9) is 45.
