Rocket Math Randi Saulter & Don Crawford, Ph.D. (2006)

Relevant Educational Theory Accuracy: we can do them correctly if we take our time and concentrate

Fluency: we can go quickly without making mistakes

Automaticity: we can go quickly without errors without much conscious attention (obligatory; you can’t not do it!)

Introduction of New Facts Facts are introduced at a rate of 2 facts and their reverses per sheet. When too many are being learned/practiced at once, “proactive and retroactive inhibition” (i.e. confusion!) develops (see p. 6 and 25)

Why is Automaticity important? Math facts are for service of higher and more complex math problems Automaticity improves ability to learn and retain higher order math skills because students won’t be distracted by trying to remember math facts. Careless errors aren’t necessarily careless; they stem from lack of automaticity.

Notebook Introduction Each section has its own page numbers: P. 14, 15, “Nutshell” Workshop handouts Rocket Math Coversheet / Teacher directions p. 1 – 40 Each set of probes (+, -, x, /) Answer keys for each set

Table of Contents 3rd page of Teacher directions Read as FAQs

Materials to copy (keep in each student’s folder) Rocket Chart p. 30 Writing Speed Test p. 31 Goal Sheet p. 32 Individual Student Graph p. 33 Placement Probes p. 41, 73, 105, 137 (only on the day you are going to give placement test)

What you need: Hanging File crates (4) Files A-Z per crate; Files 1-5 per crate for 2-minute timings Folders, 1 per student A designated place for student folders Answer Key packets in color Homework Packet

Answer Keys Practice sheet answer key Test answer key (daily test) Two-minute timing answer key Make several (one for each student using that operation) Use a different color for each operation

Math Fact Crate Contents In each crate (+, -, x, /), each folder, A-Z, should have 25 – 30 copies in each sheet so they are available when students need them

Order of Instruction Before grade 4: Addition Subtraction (not until Addition is mastered!) Multiplication Division (not until Multiplication is mastered!) See page 6 of teacher directions for an explanation of why

Grade 4 and up: Multiplication Division (not until Multiplication is mastered!) Addition Subtraction (not until Addition is mastered!) Multiplication is a priority for 4th grade and up because it is essential for understanding fractions and ratios (p.7)

Assessment/placement Writing Speed Test Goal Sheet Placement probes

Writing Speed Test Ultimate fluency goal: 40 correct problems per minute For non-fluent writers, the goal will be the number of problems they can write in one minute. Students who cannot write at least 24 numbers per minute should not be placed in Rocket Math

Students’ goals increase as their writing speed increases, i. e Students’ goals increase as their writing speed increases, i.e. when a student exceeds his goal on a probe, that score becomes his new goal (be sure they would be able to maintain that speed before increasing goal; see p. 10 for explanation).

Important to raise goals so that children can’t pass a set of facts they are hesitant on. (p.10). If students are hesitant, but get to move up, they end up with too many facts to “learn” at the same time and won’t become automatic.

Imperative that students start and stop exactly on time Passing: Placement Probes Timed: 15 seconds 4 probes per operation Imperative that students start and stop exactly on time Passing: No skipping No errors (p. 11-12)

Goal Sheet Writing speed score 15 second placement probe 1 minute daily test 2 minute annual goal

Student passes 15-second timing for a part (A-F, G-L, etc.): Give next 15 second timing place in the first sequence that was not passed.

If student exceeds goal on a portion of the placement test, the goal is raised! The next 15-second test must be as fast as the previous one in order to pass it. (p. 12-13)

WARNING!! Students who do not pass any timings within the first week should either be moved back to a lower part of the sequence or have a re-test of their writing speed.

Student Practice Procedures Teach practice procedures! One student has Practice Answer Key and is the Checker Practicing student has the practice sheet and reads each problem aloud and says the answer (not just the answer) Timed practice: 2 minutes! (p. 16)

Student Practice Procedures Checker watches Key and listens for hesitations or mistakes. (Teach this vocabulary and model it) Correction Procedures: Imperative! Even a slight hesitation gets the correction procedure!

Correction Procedure Checker interrupts and immediately gives the correct answer Checker asks practicing student to repeat the fact and the correct answer 3 times Checker has practicing student back up 3 problems and begin again from there.

Correction Procedure If the practicing student has any hesitation or error, the correction procedure is repeated. (see p. 15 for examples) This is not punishment; students will not develop fluency if they have to “figure out” the facts.

Student Practice Procedures After first student practices, switch roles. Another 2-minute timed practice Students do not have to be on the same set or same operation.

“How do I teach the procedures so students practice the right way?”

Steps to teach the practice procedure (p. 17) Model in front of class Post correction procedures and teach them verbally Explain what a “hesitation” is (2 or more seconds)

4. Take the role of the checker and have a student be the “practicing student” 5. Have the practicing student make a “pretend mistake” and model the 3 steps of the correction procedure

6. Now take the role of the “practicing” student 6. Now take the role of the “practicing” student. Make both hesitations and errors, making sure the student follows the correction procedures exactly. 7. All students need to have a turn being the Checker and mastering the correction procedures.

Practice the procedures for 5-7 minutes per day before starting the program. Students should show mastery of correction procedures before working in pairs. (p. 17)

Management Establish the routine at the outset Assign A and B partners; announce who starts today Be firm with the timer: 2 minutes only for practice “Pencils up! Ready for daily timing test!”

2 minutes for each partner practice 1 minute timing You are finished with Rocket Math for the day!

Daily Teacher Preparation You need to: Check papers daily Fill their folders w/sheets Keep crates full of sheets

Passing a set of facts Consider defining “passing” as 2 or 3 days consecutively of meeting the goal, especially with the students who have the most difficulty.

Homework?? Only after students have learned the “right way” to practice (i.e. say the whole problem and the answer) A few minutes is plenty Send a sample parent letter to explain procedure (p. 34)

How to conduct the daily test Provide golf pencils (no erasing!) “Pencils in the air when ready!” Use a timer All students are doing their own tests; doesn’t have to be the same operation

Monitor closely to ensure they start and stop exactly on time Collect folders and tests of students who say they passed Check papers only of those who say they passed (they know what their goal was!)

Put new practice sheets in folder for next day clean copy of same one if they did not pass copy of next set of facts in alphabetic sequence if they did pass You can train students to put their own new sheets in or create a system

The Rocket Chart! Every day the student is timed, he/she writes the date of the try on the Rocket Chart When he/she passes, they color the appropriate square on the Rocket Chart; they don’t do this until you have checked their paper.

Intervention If a student does not pass the same level in 6 tries Try testing the student orally (for testing they only say answers, not the whole problem) If the student can say 40 answers in one minute, he/she is fluent; adjust writing goal.

Usually, not progressing means the student is not practicing the right way (doesn’t say whole problem out loud or skips correction procedure when they are hesitant). Have the teacher be this student’s partner for a couple of weeks. Consider rewards/recognition to increase motivation

Lack of motivation is most often the result of failing to progress, rather than the cause. Observe the student during the timing: are they on-task? Are they gazing around or looking at the clock? If practicing with the student doesn’t help, they may have moved ahead too quickly. Back up until you find a letter they can pass (p. 22)

Be proactive in preventing students from avoiding all their practice by announcing a policy at the outset that “6 tries and then you have to move back” – it is better to pre-correct than have to fix it later.

Progress Monitoring Use the 2-minute timings once every week or 2 weeks These results go on the Individual Student Graphs Eventually they will be able to answer 80 in 2 minutes with no hesitations, skips or errors.

Before starting 2-minute test, have students look at their graph for previous “best;” their goal is to meet/beat their previous “best.” Do your own correcting for progress monitoring for IEP data (contrary to the directions on p. 24)

Refer to your manual for questions and review