# Pacing

## How long should a lesson take?

Think Math! was designed for 60-minute math lessons, every day, plus additional time, separate from the math lesson, forheadline stories (10 to 15 minutes) and mental math (10 to 15 minutes of "recycled" time that otherwise tends to get lost during the day). Improved learning in mathematics requires good teaching, good materials, and adequate time.

- For more about setting up a daily schedule, see Think Math! class schedule.
- During the first year of implementation, some lessons might take longer, requiring occasional spreading over two days. For more about first year issues, see first year of implementation, teachers and first year of implementation, students).

There are three essential elements in a day's work. If possible, it is best to do these at separate times during the day.

- Headline Story develops those all-important problem solving skills required in short answer questions, open responses, and interpreting word problems. Research shows that this is far more effective at teaching those skills to children than explicit training in problem solving strategy and test prep. Schedule 10 to 15 minutes for this daily for when the children are fresh and alert. First thing in the morning is great.

- The Headline Story for each lesson is given in the Teacher Guide, part 1 Daily Activities for each lesson.

- Skills Practice and Review also requires 10 or 15 minutes a day. This is a good activity in the spaces before or after lunch, before going to or just after returning from a specialist, between other subjects to provide a short change-of-pace...

- The Skills Practice and Review activity for each lesson is given in the Teacher Guide, part 1 Daily Activities for each lesson.

- Teach and Practice is the main body of the lesson, and is designed to take an hour.

- Specific activities, along with suggested times, are given in the Teacher Guide, part 2 Teach and Practice.

Note: The 1, 2, 3 of the teacher guide structure for each lesson are misleading. Parts 1 and 2 are essential elements of the day. Part 3 Differentiated Instruction, is not a separate "part" of the lesson. That section of the teacher guide suggests ideas for modifications or optional extras that teachers may use for differentiation. These ideas are valuable and may be used in many ways that do not compete for time with the main elements of mathematics. Some are options for teacher use while students are doing independent work. Some (including the Write Math that appears at the end of section 2, but has no time allocated to it) can be incorporated in other times during the day.

## If my students have not all mastered the content of a lesson, should I repeat, or should I move on?

Of course, you must use your discretion as the teacher: all classes are different. But Think Math! was designed knowing that students learn at different rates, and so it gives students many opportunities to catch an idea in a later lesson that they did not fully catch the first time around. In general, a pace that is quite lively -- quick, confident in children's ability to learn, but not pushed or rushed or anxious -- is best.

When to move on: If most of the students have most of the idea in a lesson, then moving on is better than stagnating for three reasons.

Going slowly

- can be boring and defeating;
- puts off other essential content; and
- delays the opportunity for students to get a second shot at the current content in some subsequent lesson.

All lessons were tested both with advanced children and with classes that are seriously behind. Teachers who prepare the lesson well and teach it as designed (with attention to their own students, of course) usually find that they and the students succeed well.

When to repeat or stretch a lesson: Straight repetition with more examples is generally not helpful. Extending a lesson over more time is sometimes useful when a substantial number of the children seem "right on the verge" of a real breakthrough and will have the "high" of understanding something really well if given just a bit more time.

Some days just don't work, no matter how well the same activity might have worked at some other time or with some other group. For whatever reason, that lesson did not match those children (or your preferred teaching style) at that time. When that happens, merely repeating the lesson, unless you adjust substantially, will probably not help anyway. If an adjustment is obvious, you might try that. Otherwise, do what's necessary to keep it light, so that neither you nor the children feel "at fault," and just move on.

## Pacing lessons to fit the year

**The whole year: 136 lessons for a 180-day year---** To improve children's mathematical learning, school need to devote enough time, but the designers of *Think Math!* knew that no school, anywhere, actually has all 180 school days in their school year. Field trips, surprise assemblies, pre-holiday parties, teacher-absences (and discomfort handing a "real" lesson to a sub), testing, and so on, cut the actual time by over 20%.^{[1]} As a result, *Think Math!* contains no more than 136 lessons in any grade (except 2nd, with 144), and no more than 114 before testing.

**At the rate of one lesson per day, as we recommend, it should be possible for any class to finish the entire grade in a year.**

*First year---*With support in the school, this is possible*even the first year*. Without support, this is harder the first year, especially in 5th grade. In a school that was so behind to begin with and had been failing AYP for so long that it was threatened with closure, all teachers were able to get to at least the critical number of lessons before testing during the first year of implementation*and*made AYP for the first time in six years. The teachers had good math coaching, and needed it, but did the teaching themselves, and the kids did the learning!

## Covering all essential topics before the state test

**Will the essential topics be covered by March? Yes.** *Think Math!* was designed to meet state-test *dates* as well as content coverage. That is one reason why the rich, enjoyable, and valuable material in grade 5's chapters 12, 13, 14, and 15 come at the end of the year and not earlier. This content is important for 5th grade learners but can wait for post-March study.

**Before the test: 105 to 113 lessons---** High-stakes tests come quite early in some states. Accordingly, *Think Math!* is designed so that the first roughly 105-113 lessons cover all requirements for the tests.

Even in the first year of implementation, if a district devotes an hour per day to mathematics, and does not take away from that time for testing, test-prep, or "supplementing," and does not overly extend the length of lessons, they will get through all of required material before March. One school that did that -- a school that had been failing for so long that it was already in its state's "corrective action" category -- made AYP in math, in all subcategories, and is no longer threatened with immediate corrective action. The program works, *if it is used*.

*First year---*Especially during the first year, we recommend schools be very thoughtful about not losing lesson-time early in the year. Seecontrolling the quantity of work per lesson (below) for information about controlling the length of a lesson. If a school knows from the start that it cannot successfully teach 105 one-hour lessons, it might (the first year) sacrifice the problem-solving lessons, which have excellent problems but without which we've still had excellent results. But rearranging or omitting chapters in order to "get it all in" is not advised as a strategy for success. In particular, the first chapter is important; do not skip it. We are working on listing other possible abridgments for the first year, and will add them to this site under first-year issues when they are ready.

**After the test: something lively and worthwhile to do---** The arrangement of lessons also accounts for the after-testing months, when Spring is in bloom, Summer is approaching, the dreaded test is over, and students and teachers are drained and *need* something lively and worthwhile to do. The last two to three chapters in every grade (in 5th grade, for example, the last three) are *not needed before the test*. Using fifth grade as an example, if state testing came so early that a full third of instructional time (60 days) comes during or after the test, that still leaves 120 days for only 105 lessons. Most testing schedules leave 130 to 140 days for that 105 lessons. That allows some lessons to take more than a period, as long as not too many periods are lost.

Students are refreshed by the new material and yet, despite its apparently "enrichment" not-on-the-test status, it is designed to reinforce the ideas learned that year. Grade 5's chapter 12, for example, refreshes and strengthens all the geometric learning students have done earlier.

**The last three chapters of 5th grade---** In the special case of 5th grade, the next grades are not under our wing anyway. The last three chapters of that grade build a strong foundation for algebra (and probability), getting the children ready for high-school in a way that is appropriate even in 5th grade (where they are) but is uncommon in middle school (which is why we do it now, while we've got them). This is, of course, "not critical" in the sense that the kids can go on to 6th grade without them. But they are worth trying to do because they are so helpful to kids in later grades.

And, because schools, in order to meet their pre-March concerns, need to get through chapters 1-11 anyway, they have a lot of time after the tests, and these other chapters fill that need.

**Number of "essential" lessons in each grade---** The following table lists the total number of lessons in each grade and the number that are "critical" before the test (or to be totally prepared for the following year). The columns represent the grade, the total number of lessons in that grade, the "critical" lessons (needed for that year's test, if any, and all that is needed for success in the following year), and the lessons available for after testing time.

Grade Total "critical" after-test 1 134 105-115 19 to 29 2 144 125-131 13 to 19 3 136 111 25 4 136 113 23 5 136 105 31

*In grades 1 and 2*, in which the testing stakes are lower, two numbers are listed under "critical." These indicate how many lessons are needed during the*whole year*. The lower figure is the number of lessons that constitute adequate preparation to make optimal progress in the following year; the higher figure is the number of lessons to strive for. Of course, depending on the circumstances of one's students, one can strive for all the lessons, but that is hard to achieve the first year. If the grades have testing, their*tests cover considerably less material*than that. For example, state testing in grade 2 is not likely to require multiplication and division.

A case example:Worried that grade 5 fractions and decimals would not be learned by March, some districts sorted the chapters by topics: multiplication and division (chapters 2, 5, 8 and 3, in that order), then some fractions and decimals (first chapter 7 from grade 4, then chapters 11 and 7 from grade 5), and then geometry (chapters 9 and 10). Curricula can be designed that way, but there are also good reasons for the choicesThink Math!made. (See more about those choices in the previous section.)Think Math!develops mathematical ideas, and thenusesthem for a while, giving them time to solidify, before cycling back to extend them. This builds mastery and confidence. Rearranging the chapters destroys this structure, leaving students without prerequisite knowledge and requisite practice.This plan also skips chapters 1, 4 (fractions!), and 6 entirely. Even with students who are

underperforming,seriouslybelow grade level -- in fact, perhapswayespeciallywith these students -- there should be no need to skip so much. In a seriously under-performing school, one that had not achieved AYP for years and was under threat of restructuring, fifth grade was taught to children (and by teachers) who had never seenThink Math!before. They added the Gr4 Ch7 fractions chapter, but otherwise taught in order, skipping nothing. Students improveddramaticallyon the state tests.Part of the reason that

Think Math!students become so good is thatThink Math!gets them thinking. Skipping and rearranging means that ideas don't unfold logically, but are treated as isolated things to know (sometimes without the prerequisites). That defeats thinking.

There is no need to worry about timing for March.If a school teachesalllessons from chapter 1 through chapter 11 in order, that still totals only 105 lessons. In a 180-day school year, if time is spentin the curriculum, and not diverted to testing and test-prep and other things that take timeawayfrom the learning, this accounts for only 105 days, leaving 75 post-March days, a very safe margin. This even leaves room to add Gr4 Ch7 before Gr5 Ch4, often a good idea for students who have never hadThink Math!before. Some teachers find it hard, the first year, to move at the rate of a lesson a day (though some donot), but unless the students areexceptionallybehind, they can usually do at least 4 lessons a week. For students who are not already seriously behind, there should be no difficulty doing 5/wk.

## Controlling the quantity of work per lesson

Using *all* the materials for *every* lesson is overkill. The teacher guide has a 1...2...3 structure -- 1) Daily Activities, 2) Teach and Practice, and 3) Differentiated Instruction. But these are not "three steps" to complete: time is allocated only for (1) and (2); while section 3 has a different purpose. The differentiated instruction ideas help them do (1) and (2) sensitively, but are not "another thing to do" (that is, not a Step 3). If teachers do the lesson parts in steps (1) and (2), and students use only the LAB and Practice books (and extensions, for those who are eager), that's a solid background for the tests and for the next grade. Spiral Review is extra, if there's time. (During the first year, that may be hard, but it is never part of lesson time: it is excellent for "extra" time in class, which there often is.) We've also seen teachers taking extra lesson time to explain how to do items in the Spiral Review because their students have not yet had that material that year (e.g., in the beginning of a year). No extra time should be taken for that.

## This looks too hard for my kids. The pace seems ambitious. Is this practical?

This is a very common perception *before* teaching with *Think Math!*. The pace *is* ambitious, but very practical. All teachers have found, *after* they've used the materials for a half year with their students, that students can achieve far more than their own past performance would predict. Even those students who started way behind in their skill and understanding grab hold and make rapid progress, succeeding well.