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Multiplication–Learning Computation
After becoming fluent with multiplication facts the best way for students to retain the knowledge of those facts is by doing multiplication computation. If students have not been taught multiplication computation, this program breaks it down into small, easy-to-learn steps that are numbered in a teaching sequence that leaves nothing to chance.
Note that the number for each skill gives the grade level as well as indicating the teaching sequence. Skill 3b is a 3rd grade skill and after skill 3e is learned the next in the sequence is skill 4a. The sequence of skills is drawn from M. Stein, D. Kinder, J. Silbert, and D. W. Carnine, (2006) Designing Effective Mathematics Instruction: A Direct Instruction Approach (4th Edition) Pearson Education: Columbus, OH.
(3b) Multiplying 1-digit times 2-digit; no renaming
(3c) Multiplying 1-digit times 2-digit; carrying
(3d) Multiplying 1-digit times 2-digit, written horizontally.
(3e) Reading and writing thousands numbers, using commas.
(4a) Multiplying 1-digit times 3-digit
(4b) Multiplying 1-digit times 3-digit; zero in tens column
(4c) Multiplying 1 digit times 3 digit, written horizontally
(4d) Multiplying 2-digits times 2-digits.
(4e) Multiplying 2-digits times 3-digits.
(5a) Multiplying 3-digits times 3-digits.
(5b) Multiplying 3-digits times 3-digits; zero in tens column of multiplier.
For each skill there is a suggested Teaching Script giving the teacher/tutor/parent consistent (across all the skills we use the same explanation) language of instruction on how to do the skill. The script helps walk the student through the computation process. For the teacher, in addition to the script, there are answer keys for the five worksheets provided for each skill.
Each worksheet is composed of two parts. The top has examples of the skill being learned that can be worked by following the script. After working through those examples with the teacher the student is then asked to work some review problems of addition problems that are already known. The student is asked to do as many as possible in 3 minutes—a kind of sprint. If all is well the student should be able to do all the problems or nearly all of them, but finishing is not required. Three minutes of review is sufficient for one day.
There are five worksheets for each skill. Gradually as the student learns the skill the teacher/tutor/parent can provide progressively less help and the student should be able to do the problems without any guidance by the end of the five worksheets. There are suggestions for how to give less help in the teaching scripts.
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Addition—Learning Computation
After becoming fluent with addition facts the best way for students to retain the knowledge of those facts is by doing addition computation. If students have not been taught addition computation, this program breaks it down into small, easy-to-learn steps that are numbered in a teaching sequence that leaves nothing to chance.
Note that the number for each skill gives the grade level as well as indicating the teaching sequence. Skill 2a is a 2nd grade skill and after skill 2f is learned the next in the sequence is skill 3a. The sequence of skills is drawn from M. Stein, D. Kinder, J. Silbert, and D. W. Carnine, (2006) Designing Effective Mathematics Instruction: A Direct Instruction Approach (4th Edition) Pearson Education: Columbus, OH.
(1b) Adding 1-, or 2-digit numbers; no renaming
(2a) Adding three single-digit numbers
(2b-c) Adding 3-digit numbers; no renaming
(2c) Adding 3-digits to 1 or more digits; no renaming
(2d) Adding three 1- or 2-digit numbers; no renaming
(2e) Adding two 2-digit numbers, renaming 1s to 10s
(2f) Adding 3-digit numbers, renaming 1s to 10s
(3a) Adding a 1-digit number to a teen number, under 20
(3b) Adding two 2- or 3-digit numbers; renaming 10s to 100s
(3c) Adding 3-digit numbers; renaming twice
(3d) Adding three 2-digit numbers; renaming sums under 20
(3e) Adding four multi-digit numbers; renaming, sums under 20
(4a) Adding a 1-digit number to a teen number, over 20
(4b) Adding three 2-digit numbers, sums over 20
(4c) Adding four or five multi-digit numbers, sums over 20
For each skill there is a suggested Teaching Script giving the teacher/tutor/parent consistent (across all the skills we use the same explanation) language of instruction on how to do the skill. The script helps walk the student through the computation process. For the teacher, in addition to the script, there are answer keys for the five worksheets provided for each skill.
Each worksheet is composed of two parts. The top has examples of the skill being learned that can be worked by following the script. After working through those examples with the teacher the student is then asked to work some review problems of addition problems that are already known. The student is asked to do as many as possible in 3 minutes—a kind of sprint. If all is well the student should be able to do all the problems or nearly all of them, but finishing is not required. Three minutes of review is sufficient for one day.
There are five worksheets for each skill. Gradually as the student learns the skill the teacher/tutor/parent can provide progressively less help and the student should be able to do the problems without any guidance by the end of the five worksheets. There are suggestions for how to give less help in the teaching scripts.
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Dictating Sentences is spelling with a twist. Instead of spelling one word at a time, in Dictating Sentences (now part of the Universal Level Rocket Math Worksheet Program) students are asked to write an entire sentence from memory. They work in pairs and their tutor has the student repeat the sentence until it is learned. Then the student has to write the whole sentence from memory. It turns out this is considerably harder than writing words on a spelling test, so it is challenging practice, and does a lot to help students develop automaticity with spelling.
If you have to stop and think of the spelling of a word while you are trying to write, it distracts you from thinking about what you are trying to write. Students are more successful and better able to show what they know and better able to focus on learning when their tool skills have developed to the level of automaticity.
Daily practice develops automaticity. Developing automaticity with math facts and with spelling requires a lot of practice. Daily practice is best and a few minutes a day is optimal. That is why Rocket Math is designed the way it is–to provide that daily practice. So Dictating Sentences gives each member of the pair ten minutes a day of practice writing sentences composed of words they know how to spell.
Working in pairs. As you know from Rocket Math practice, students enjoy working in pairs. And when one partner has an answer key the practice can be checked and corrected. Sound research shows that immediate correction and editing of misspelled words is the fastest way to learn the correct spelling, so that’s what we have the student tutor do. After each sentence is written every word is checked and practiced again until it is correct.
Mastery learning. The program is structure so that all the words are learned to the level of automaticy. Students keep working on a sentence until it can be written without any errors. They work on the same lesson for as many days as is needed for them to spelling every word perfectly in all three sentences. Each sentence persists for two or three lessons, so that the student is required to write it from memory and spell every word perfectly for several days in a row.
500 Most common words. Dictating sentences systematically practices the 500 most common words that students need in their writing. It includes all of Rebecca Sitton’s 400 Core Words. It also includes the 340 words that children most need for writing according to writing researchers Harris and Graham. When students know these words to the level of automaticity, they will be able to write fluently and easily.
Earning points by being correct and going fast. Students earn two points for every word that is spelling correctly the first time. Every word on which there is an error is worked on until it too can be spelled correctly, earning one point. The faster students go during their ten minutes, the more points they can earn. Students graph the amount of points earned and try to beat their own score from previous days. Teams can be set up and competition for the glory of being on the winning team can enhance the motivation.
Individual Placement. There is a placement test. Students begin at the level where they first make a mistake. Student partners do not need to be at the same level, so every student can be individually placed at the level of success.
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Four Problem Types to Learn
Learning to Subtract Integers displays problems on a vertical number line and then teaches students two rules about how to solve problems in which you subtract positive and negative numbers.
Rule 1: When you subtract a positive number, go DOWN.
Rule 2: When you subtract a negative number, go UP.Doing problems on the vertical number line is more intuitively appealing because UP is more and DOWN is always less. This makes crossing zero a little easier to comprehend.
Students learn how these two rules play out with two types of problems: when starting with a positive number and when starting with a negative number. Students gradually learn all four types of problems. On each worksheet they see how to solve each problem type using the number line working with their partner. Then students learn to recognize the pattern of each problem type by orally answering several examples of each type with their partner (going around the outside of the page). You will probably not be surprised that there is a one-minute test on each set. Students are to be 100% accurate and to meet or beat their goal from the special writing speed test for Learning to Subtract integers (the fastest goal is only 28 problems in a minute).
4 online lessons teach students how each type of problem is solved and why it is correct.
(1) Subtract Integers Set A Positive subtract a positive
(2) Subtract Integers Set B Positive subtract a negative
(3) Subtract Integers Set G Negative subtract a negative
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Mixed Integers displays problems on a vertical number line and then teaches students two rules about how to solve problems that add or subtract positive and negative numbers.
Rule 1: When you add a positive number OR subtract a negative number, go UP.
Rule 2: When you subtract a positive number OR add a negative number, go DOWN.Students learn how these rules play out when starting with a positive number and a negative number, gradually learn these two variations of all four types of problems. They learn to solve a problem type using the number line and then to recognize the pattern of each problem type by working several examples of each type. This practice gives them a chance to build fluency with each problem type as they work with their partner on the top half of the page. You will probably not be surprised that there is a one-minute test on each set. The goals are slightly different than before. Students are to be 100% accurate and to meet or beat their goal from the special writing speed test for mixed integers.
8 online lessons teach students how each type of problem is solved and why it is correct.
(1) Mixed Integers Set A1 Positive add a positive
(2) Mixed Integers Set A2 Positive subtract a positive
(3) Mixed Integers Set D Negative add a positive
(4) Mixed Integers Set G Negative subtract a positive
(5) Mixed Integers Set J Negative subtract a negative
(6) Mixed Integers Set M Positive subtract a negative
(7) Mixed Integers Set P Positive add a negative
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