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Developing Number Fact Fluency. 2. Fluency: Key Behaviors. Students who are fluent use number facts without being prompted Flexibility Efficiency Accuracy. Knowledge of sums to 10 is critical for success with addition and subtraction of multi-digit numbers. 3.
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2 Fluency: Key Behaviors • Students who are fluent use number facts without being prompted • Flexibility • Efficiency • Accuracy • Knowledge of sums to 10 is critical for success with addition and subtraction of multi-digit numbers
3 Developing Fact Fluency Expectations: • By end of grade 1, fluency with addition and related subtraction facts to 10 • By end of grade 2, fluency with addition and related subtraction facts to 20 Evidence: • Exactly what does it mean to be fluent with number facts?
4 Meaningful Fact Mastery According to Van de Walle, for fact mastery children need… • A strong understanding of number relationships and of the operations • Efficient strategies for fact retrieval through practice • Drill in the use and selection of those strategies once they have been developed
Meaningful Fact Mastery A strong understanding of number relationships and of the operations 5 54 can be 5 tens and 4 ones When I add these, I’ll have more. 8 is more Than 5
Meaningful Fact Mastery Efficient strategies for fact retrieval through practice 6 I know all my plus ones. See… 6 + 1 = 7 8 + 1 = 9 3 + 1 = 4 And I know 25 + 1 = 26 250 + 1 = 251 1 million + 1 = 1 million and 1
Meaningful Fact Mastery Drill in the use and selection of those strategies once they have been developed 7 Eight horses and 9 cows… How many animals? I know that 8 + 8 is 16. So 8 + 9 is 17 animals !
Meaningful Fact Strategies One-more-than and two-more-than Counting up or counting back Facts with zero Doubles and near doubles Make ten facts Fact families Commutative property Compensation part-part whole 8
9 Assessment is the Key • Determining each student’s understanding of number combinations • Knowing which facts each child has not yet learned and reassessing weekly to encourage students to move on • Helping students take responsibility for learning facts • Informing parents with specifics
10 Combinations of 7
Process for Assessment • Gathering information about students’ understanding can be informal (next slide) as teachers stop beside a child to talk or more structured (next few slides) • Assessments can utilize counters (as next slides) or involve only symbols (as when students flash answers on individual white or chalk boards) • Information can be gathered orally or written
Process for Assessment • How many red cubes? • How many yellow cubes? • How many in both hands? • If I give you one more yellow cube, how many would there be? • If I take away one red cube, how many would be left? • How many more are needed to make 8?
13 Process for Assessment: Additive Task Briefly show 8 counters and say, “I have 8 counters” Then cover the counters
14 Additive Task With the 8 counters covered, briefly show 5 more counters Say, “Now I’ve added 5 more”
15 Additive Task With the 5 counters also covered, ask “How many counters altogether?”
16 Additive Task “How many counters altogether?” If a child quickly answers correctly, ask the student how he/she figured out the total
17 Additive Task “How many counters altogether?” If a child cannot answer correctly, uncover the 5 markers and see if he can count on from 8
18 Additive Task “How many counters altogether?” If a child cannot count on from 8 with the visual cue, uncover the 8 markers and see if he can count the total
Keeping Track • Choose a format that makes sense to you: cards on a key ring, individual student pages, group checklists • Keep students and parents updated on progress learning facts
Developing Fact Fluency Instructional Strategies include… Teacher directed, whole class lessons Small group activities and drills Individual explorations and tasks Games Class Pairs Individuals 20
6 21 Part-Part-Whole Activities • Spill the Counters • Cover Up • Missing-Part Cards
Drop and Decide Drop 6 counters on the workspace Are there more reds than yellows? Are there more yellows than reds? Are there the same number of reds as yellows? Record the results on a recording sheet using a tally Continue to drop all 6 counters and record
Drop and Decide…Day 2 Prepare index cards labeled 2 through 12 Students select a card from the pile and use the number as their target number Play in pairs until 20 tallies are recorded on their answer sheet Discuss how counters look for different tally marks Teams play additional rounds if necessary to use all index cards 24
Drop and Decide Drop 6 counters on the workspace Are there more reds than yellows? Are there more yellows than reds? Are there the same number of reds as yellows? Record the results on the recording sheet by using a tally Continue to drop all 6 counters and record 25
Drop and Decide...Day 3 26 Even Numbers 2 Yes 1+1 3 No 4 Yes 2+2 5 No 6 Yes 3+3 7 No
Subitizing • Determining the number in a collection of items which are typically in a spatial relationship • Determining the total immediately • Determining the total without counting
Quick Images How many did you see? How did you figure out the number of faces?
Quick Images How many did you see? How did you figure out the number of stars?
Break Down…Show Down Play in small groups Build a 10 tower of snap cubes and place it behind your back One player says “Break Down” and each player breaks their tower into two parts Taking turns, players show their two tower parts and combinations they made
Break Down… Combine the two towers from the right hands of both players and say the sum Is the sum of the two towers more or less than ten? Combine the two towers from the left hands Is the sum of the two towers more or less than ten? 33
Hiding Dots Place 10 circle stickers on a 3-by-10 inch strip of tagboard or cardstock Cut an envelope from top to bottom so that dots can be hidden when the strip is placed inside the envelope 34
Hiding Dots…Student Responses Show student the strip with ten dots and then slide it into the envelop “If the paper clip is on the 6th dot and there are 10 dots in all, how many are hidden?” 35
Real Counting On Game Partners need cards with 1-7, a die, a cup, and counters Player 1 takes a number card from the stack and places that number of counters in the cup, placing the card beside the cup 36 4
Real Counting On Game Player 2 rolls the die and places that many counters next to the cup Together they decide how many counters in all and record. Players reverse rolls and continue play 37 4
38 Arithmetic Rack • Designed to: • Develop computation skills • Solve contextual problems • Focus on: • Seeing the quantity of five as a whole • Seeing the quantity of ten as a whole
Solo* Make 10 • Step 1:Make a deck with 4 sets of 1 to 10 cards • Step 2:Student deals 4 cards face up • Step 3:Student removes “10” cards and sums of ten • Step 4:Each time cards are removed,student replaces them with the top card(s) from the remaining deck • Continue game until all cards in the deck are used • Object is to have as few cards left as possible in one “trip” through the deck * Student works alone
11 - 3 = 7 + 5 = Number Talks… • Give students opportunities to solve in different ways and explain their thinking • Are appropriate for all grades • Support students in making sense of mathematics • Are good examples of 5-minute math
1 • Each student has a gameboard • Take turns rolling 2 dice and adding or subtracting • Capture one spot per turn • If no sums are available, student just passes the dice along to the next player Capture! 8 12 4 2 7 5 6 8 9 7 11 9 10 3 5
Zero, My Hero • Deck consists of 4 sets of 1 to 9 cards plus at least 4 wild cards; students work in pairs • Step 1: Leader turns 3 cards face up and pairs attempt to use ALL cards in one or more equations to reach zero • Step 2: If no solution is found, leader turns up a fourth card • Step 3: If no solution is found, turn cards face down and repeat steps 1 and 2 • Team to first reach zero wins the round 6 - 3 = 3 3 + 2 = 5 5 - 5 = 0
43 As Students Play, Think About : • How can you know the strategies that students would use in playing the games? • Why is conversation about these games important in building fluency with addition and subtraction facts? • What is the “return” on the investment of math time in assuring that students know well sums and differences to10?
Final Thoughts Who is doing the thinking in your classroom? Do you encourage students to do only what makes sense to them? Are you practicing “Talk less, Listen more”?
