OVERVIEW & PURPOSE
Week four of the 2nd Grade CountFast program focuses two general strategies for adding double-digit numbers with quick mental calculation. (Addition with no carrying over, addition with carrying forward). Students will also learn how to quickly solve problems that add up to a multiple of 10. 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 addition equations using the ‘carry forward’ and ‘no carrying’ concepts.
One Double-Digit Addition 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 Addition – 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 addition process of adding the one’s column first, and then adding 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 add up to more than 9, or less than 10. If so, there will be no need to ‘carry over’ or ‘bundle’ into the ten’s place. For all of the yellow cards, the one’s digits calculations do not require any ‘carry over’ or ‘bundling’.
Of course, there are other methods students can use for quick mental calculation. Some students may find it faster to decompose the numbers and add together those smaller parts. (11 + 12 can be thought of as 10 + 1 + 10 + 2, or 10 + 10 + 1 + 2). 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. For example, 11 + 12 = 23 can be explained in this way: “Two tens and three ones make twenty-three. I did not need to carry over.”
Home Activity: Students will practice solving the problems on the YELLOW cards with a parent as quickly as possible.
Double-Digit Addition – Day 2
Teacher Model/Direct: Review the concept of adding double-digit numbers that require no bundling or carry-over. Today, use the BLUE cards in the deck to quickly add numbers in which the one’s digits add up to 10. Teach students that if the one’s digits add up to exactly 10, they can quickly solve the problem by carrying 1 into the ten’s group, adding the ten’s digits, and putting a zero behind that number for the final answer. For example, 25 + 45 can be solved by quickly noticing that the two 5’s in the one’s places add up to exactly 10. Add 1 to the ten’s digits (1 + 2 + 4 =7) and then put a zero behind that 7 to make a total of 70. Practice this thought process several times together. With repetition of the process, students will get faster and faster mentally calculating what they see with their eyes. Say the process out loud together with each blue card.
Student Activity: Repeat the activity from Day 1, using the BLUE cards in the deck and using the carry-over strategy when the one’s digits total exactly 10. Students should encourage 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 Addition – Day 3
Teacher Model/Direct: Review the strategies learned on Days 1 and 2. Today, use the PINK cards in the deck to quickly add numbers in which the one’s digits add up to more than 10, requiring carry-over to the ten’s place. Teach students the quick way to mentally calculate these problems by adding the one’s digits, (which will equal more than 10) and holding the ending digit of that answer in their mind. Then add the ten’s place digits, remembering to add 1 for the carry-over. For example, the problem 18 + 25 can be solved quickly by noticing that 8 ones and 5 ones make 13. Hold the ‘3’ in your mind while adding the 1 ten and 2 tens – and adding in one more ten for the carry-over to get a total of 4. Mentally, place the 4 (tens) in front of the 3 (ones) you were holding in your mind for a final answer of 43. Practice this thought process several times together. With repetition of the process, students will get faster and faster mentally calculating what they see with their eyes. Say the process out loud together with each PINK card.
Student Activity: Partner students and have them use the PINK cards from the deck to take turns quickly solving problems involving carry-over. Students should encourage each other to speak through the process and to celebrate each other’s successes.
Home Activity: Students will practice quick mental calculation of the PINK cards with parents.
Double-Digit Addition – 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.
For an added challenge, students can play a bracket-style tournament in which all of the yellow, blue, and pink 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!