Double Digit +-
This module is the same concepts as the Double-Digit Addition and Double-Digit Subtraction modules. However, this switches back and forth between the two concepts each day.
This ability to switch the thinking and overall concept quickly is very important as the student learns more and more math concepts. Again, the student is working on mental calculation and is trying to get faster and faster day by day.
OVERVIEW & PURPOSE
Week five of the 2nd Grade CountFast program focuses the general strategies for subtracting double-digit numbers with quick mental calculation. (Subtraction with ‘borrowing’ or ‘trading in’, and subtraction with no borrowing.) Card decks should go home with students each day for additional practice with a parent at home. Each week, a new deck is introduced and the previous deck is for the student to keep at home for continued practice.
- NCTM Standard: develop fluency with basic number combinations for addition and subtraction
- NCTM Standard: understand the effects of adding and subtracting whole numbers
Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
- Develop strategies for fluency in solving double-digit subtraction equations by understanding the process of ‘borrowing’ or ‘trading in’ when needed.
One Double-Digit Subtraction card deck for each student. This deck is for school and home use. Discuss routine and expectations for taking home the deck and returning it to school each day.
Double-Digit Subtraction – Day 1
Teacher Model/Direct: Introduce students to this week’s card deck. Today you will work with the yellow cards in the pack. The problems on the cards are written horizontally. Discuss/demonstrate with students how these same problems are written vertically, lining up the ones and tens columns as learned in 1st Grade. Review the process of subtracting the one’s column first, and then subtracting the ten’s column. When looking at the horizontal representation of the problems (on the cards), show students that they can look quickly at the numbers in the one’s position of each number to determine if the one’s will subtract without needing to borrow from the tens group. For all of the yellow cards, the one’s digits calculations do not require any ‘borrowing’ or ‘trading’.
Of course, there are other methods students can use for quick mental calculation. Some students may find it faster to decompose the numbers and subtract those smaller parts. (23 – 11 can be thought of as 20 – 10 – 3 – 1, or 20 – 10 -4, or 23 – 10 – 1). Encourage students to use the fastest mental calculation method for his/her way of thinking.
Student Activity: Partner up students and have each pair use one deck to work with. Ask them to take out the yellow cards. Students turn over one card at a time and see which partner can solve the problem the fastest, being sure to explain to his/her partner how he/she arrived at the answer.
Home Activity: Students will practice solving the problems on the YELLOW cards with a parent as quickly as possible.
Double-Digit Subtraction – Day 2
Teacher Model/Direct: Review the concept of subtracting double-digit numbers when there is no need to ‘borrow’ or ‘trade in’. Today, look at the BLUE set of cards in the deck with students. Guide them to notice that on each blue card, the answer when subtracting the digits in the one’s place equals zero. This makes it quick and easy to subtract the numbers in the ten’s place and add a zero on the end to get the final difference. For example, 31 – 11 can be solved quickly by noticing that the one’s digits (1 – 1) will equal 0. This just leaves subtraction of the ten’s digits (3 – 1 which equals 2) and then add a 0 after that answer (2) to get 20 as a final difference.
Student Activity: Repeat the activity from Day 1, using the BLUE cards in the deck. Students should encourage partners to speak through the process to each other and celebrate each other’s successes.
Home Activity: Students will practice quick mental calculation of the blue cards with parents.
Double-Digit Subtraction – Day 3
Teacher Model/Direct: Review the strategies learned on Days 1 and 2. Today, use the GREEN/GOLD cards in the deck to quickly subtract numbers when there is a need to ‘borrow’ or ‘trade in’ to get the answer. Re-teach what it looks like when the problems are written vertically instead of horizontally the way they are on the cards. Review the subtraction concept of the top (or first) number being how much we HAVE to start with. The bottom (or second) number is what we are taking AWAY. Sometimes there are not enough ones in the top (or first) number to subtract the bottom (or second) number. AND – we know that Commutative Property does not work for subtraction, so we cannot just transpose the numbers to make it ‘easier’. Review borrowing or trading in from the tens group to look at the original number differently without changing its value. (42 – 29 requires a trade-in because we cannot take 9 ones away from 2 ones. We must rewrite 42 as 3 tens and 12 ones in order to subtract.) This lesson may take three days to fully teach so that students can do this process mentally.
Some students will look at the problems differently (such as 42 – 29 can be solved by subtracting 20 from 42, then subtracting 9 more; OR subtracting 30 from 42, then adding one back on). Encourage students to use a method that is FASTEST for the way he/she thinks.
Student Activity: Partner students and have them use the GREEN/GOLD cards from the deck to take turns quickly mentally subtracting double-digit numbers using ‘trading in’ or ‘decomposing’. Students should encourage each other to speak through the process used and to celebrate each other’s successes.
Home Activity: Students will practice quick mental calculation of the GREEN/GOLD cards with parents.
Double-Digit Subtraction – Days 4 and 5
For days 4 and 5, review the three mental calculation strategies and practice with each of the color sets. Students can even mix up the color sets, and explain which strategy was used to solve each problem as they compete with their partners. Students will do the same at home with parents on these days. You may wish to use these days to continue working with the concept of trading in.
For an added challenge, students can play a bracket-style tournament in which all of the yellow, blue, and green/gold cards are mixed together. Partners can turn one card over at a time, much like they did with the CountFast 12 game, and see who ‘wins’ each card by solving the problem the fastest. Winners move on to the next round/opponent and those eliminated should cheer on those still competing. Celebrate together the accomplishments of this challenging week!