Daily Practice and Problems

The Daily Practice and Problems (DPP) is a set of short exercises that provides a structure for ongoing review and study of math concepts, skills, and math facts. To support this daily routine, at least two DPP items are included for each class session. The first item for a lesson is always a Bit and the others will be either Tasks, Challenges, or Bits. Nine icons designate the subject matter of the DPP items.

Algebra
Computation
Data
Geometry
Math Facts
Measurement
Money
Number Sense
Time

Unit 1 Daily Practice Problems A-X

Choose a practice problem here
A Triangle Sums 1 B Addition Practice C Triangle Sums 2 D Counting Squares E Triangle Sums 3 F Counting Rectangles G Reading Time H More Addition Practice I Time 1 J Variables and Values K Time 2 L Tom's and Tim's Savings M Count Your Change N Counting Cars O Addition Test: Doubles, 2s, 3s P Sharing Pennies Q Addition Test: More Addition Facts R Measuring S Measurement: Could Be
or Crazy? T Favorite Sandwiches U Median V Best Guess W Which Two Add Up? X Points on a Graph DPP Teacher Notes

Students will need: rulers, Centimeter Graph Paper, and calculators readily available.

 

The Daily Practice and Problems items provide a structure for distributed practice to:

  • systematically study basic math facts and practice computation;
  • develop concepts and skills such as number sense, mental math, telling time, and working with money; and
  • review topics from earlier units, presenting concepts in new contexts and linking ideas from unit to unit.

There are three types of items: Bits, Tasks, and Challenges. Bits are short and should take no more than five minutes to complete. They usually provide practice with a skill or the basic math facts. Tasks take about ten minutes to complete. Challenges usually take longer to complete and the problems are more thought-provoking. Use them to stretch students' problem-solving and reasoning skills.

Problem of the Week

A DPP item that can serve as the Problem of the Week will be identified for every week of the unit and will always be a Task or a Challenge. The intention is that students be given a problem that allows time for thoughtful consideration of the strategies they are developing. Such a problem may require more reflection, maybe some trial and error, and may not be immediately solvable at first glance. At the end of the week, students can share their strategies. The following DPP items in this unit can each serve as a Problem of the Week:

Challenge F in Lesson 2
Task N in Lesson 4

Review and Assessment of the Math Facts

Students have been developing strategies for solving the math facts since their early years and are fairly close to gaining or have gained proficiency. Students are expected to demonstrate fluency with the math facts according to the following timetable:

  • By the end of second grade: addition and subtraction facts
  • By the end of third grade: multiplication facts
  • By the end of fourth grade: division facts

Many of the DPP items for this first unit of fourth grade review the addition facts. DPP items for Unit 2 review the subtraction facts. DPP items for Unit 3 begin a systematic review of the multiplication facts.

Use DPP items O and Q to assess students' fluency with the addition facts.

The first assessment, Addition Facts Quiz: Doubles, 2s, and 3s, contains those addition facts that can be solved using counting-on strategies and using doubles. The second test, Addition Facts Quiz: More Addition Facts, contains those facts that can be solved making tens, using tens, and reasoning from known facts.

These short assessments are less threatening and as effective as longer tests. Tests that include a small number of facts give teachers, students, and parents the information needed to continue learning and practicing the facts efficiently. The goal of the math facts assessment program is to determine the degree to which students can find answers to facts problems quickly and accurately and whether they can retain this skill over time.