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These are the basic single digit Addition facts 1s through 9s. Each of the 26 levels, A through Z, introduces two facts and their reverses. You can see in the picture above of Set B, I have outlined the new facts in red.
Students practice orally with a partner, reading and answering the facts going around the outside of the sheet. The partner has the answer key. Then the two students switch roles. After practice everyone takes a one minute test on the facts in the box–which are only the facts learned up to this level. Each student has individual goals based on writing speed, but no one can pass a level if there are any errors. You must give the special Writing Speed Test to set individual goals for your students.
Students should be able to pass a level in a week, if they practice the right way. To the right you can see the sequence of facts that will be learned in the Addition 1s-9s program. The program uses the four forms–that can be found in the forms and information drawer.
The most succinct way to be introduced to this program is this 8 minute video.
These are the basic single digit Multiplication facts 1s through 9s. Each of the 26 levels, A through Z, introduces two facts and their reverses. You can see in the picture above of Set C, I have outlined the new facts in red.
Students practice orally with a partner, reading and answering the facts going around the outside of the sheet. The partner has the answer key. Then the two students switch roles. After practice everyone takes a one minute test on the facts in the box–which are only the facts learned up to this level. Each student has individual goals based on writing speed, but no one can pass a level if there are any errors. You must give the special Writing Speed Test to set individual goals for your students.
Students should be able to pass a level in a week, if they practice the right way. To the right you can see the sequence of facts that will be learned in the Multiplication 1s-9s program. The program uses the four forms–that can be found in the forms and information drawer.
The most succinct way to be introduced to this program is this 8 minute video.
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After becoming fluent with subtraction facts the best way for students to retain the knowledge of those facts is by doing subtraction computation. If students have not been taught subtraction computation, Subtraction–Learning Computation breaks it down into 18 small, easy-to-learn steps that are numbered in a teaching sequence that leaves nothing to chance. Even better the instructional materials include an assessment of all the skills in subtraction computation in order, so you can test the knowledge of the student(s) before beginning instruction to see where to start. You can use this assessment to find very specific “holes” in student skills and then have the exact problems and explanation to fill that hole.
Note that the number for each skill gives the grade level as well as indicating the teaching sequence. Skill 3b is a 3^{rd} grade skill and after skill 3g is learned the next in the sequence, skill 4a is best taught in fourth grade. Minor changes have been made, but for the most part, 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 (4^{th} Edition) Pearson Education: Columbus, OH.
(1b) Subtract from 2 digits; no renaming.
(2a) Subtract from 2digits; renaming required.
(2b) Subtract from 3 digits; borrow from 10s.
(3a) Subtract from 3 digits; borrow from 100s.
(3b) Subtract from 3 digits; borrow either place.
(3c) Subtract tens minus one facts.
(3d) Subtract from 3 digits; zero in 10s; borrow 10s or 100s.
(3e) Read and write thousands numbers, use commas.
(3f) Subtract from 4 digits; borrow from 1000s.
(3g) Subtract from 4 digits; borrow once or more.
(4a) Subtract from 4 digits; zero in 10s or 100s column
(4b) Subtract from 4 digits; zero in 10s column, 1 in 100s.
(4c) Subtract hundreds minus one facts.
(4d) Subtract from 4 digits; zero in 10s and 100s column.
(4e) Subtract 1, 2, or 3 digits from 1,000.
(4f) Subtract 5 and 6 digits with borrowing.
(5a) Subtract thousands minus one facts.
(5b) Subtract from a number with four zeroes.
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. My favorite part is the rule students are taught for when to borrow (often confusing for students): Bigger bottom borrows. Simple, easy-to-remember and consistently correct. 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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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
(4) Subtract Integers Set L Negative subtract a positive
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Be ready to start right away. Here is all you need to organize a Tournament set of 15 Race for the Stars games. Game boards and their matching pieces store easily in the seven hanging file folders with labels for the color-coded levels of the game and directions.
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