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Posted Sun Aug 19 18:54:48 PDT 2012 by Yordan Krastev (Yordan Krastev).

Hunter College, Manhattan, New YORK

Materials Required: Dry eras board, markers, place value chart

Activity Time: 30min

Concepts Taught: Subtraction and Addition

Yordan Krastev

Teaching points to consider:

When regrouping three addend problems, many students find it especially difficult to `` keep the place while copying or computing problems of this type``. Even if they know how to do the regrouping, the three addends problem becomes a 4 addend problem because of the regrouping. Many students forget to write the one on top and add the 1 with the 3 other numbers.

Activities:

1. Approach column addition step by step. Before writing the final sum, the student fills in the blank line to the right of the problem with the sum of the first two addends. Use green for the first two addends and their answer line, red for the arrow and the last addend. This way students are more likely to remember to solve for the ``ones`` column firsts, and then for the `` tens `` column.

2.- Visual activities help. Provide students with square centimeter paper and instruct the students to write one digit per square. Teach the students to color-highlight a column before adding it.

Subtraction of whole numbers:

Teaching points to consider:

When subtracting with regrouping, many students tend to subtract the smaller from the larger number, regardless of the position within the problem. Teach the `` take away`` model which implies to subtract like units, if there are not enough, make a trade. The model follows the following steps. First : prepare the students with sample regrouping problems demonstrating them with cards and 10- stack chips and loose chips. Ask the children to circle the problem if there aren`t enough and have them say `` take-away, trade and do not trade`` according to the numbers. The next step is to guide them through the process. For this goal the teacher helps them focus on a starting point in each problem. Ask them to read across the line and fill in the blanks while doing so. Eventually, they will internalize and make the process more automatic when they do it themselves. Teach them to subtract like units starting with the ``ones`` column. According to students` individual learning styles, teach step by step when computing or going thru the entire problem and noting where regrouping is necessary. Use graph paper to help students struggling with alignment.

Activities to consider:

1. Provide students with regrouping and non-regrouping examples . Ask students to circle the examples in which a `` trade `` must be made. Then ask them to complete the problems. Help as needed.

2. Use 100, 10 and 1 dollar bills. Model numbers such as 203 ,304 and elicit that these numbers can be shown and expressed by using 2 hundreds, no tens, and 3 or 4 ones.

Multiplication of whole numbers / one digit factors

Teaching point to consider:

Systematic review and integration of mental calculations and estimation strategies are important. As computational skills are expanded, the number of steps increases and accurate sequencing of the process becomes essential.

Sample sequence of Activities:

1. Use tens and ones to model a simple problem. Remind students that as in addition, it`s ``first the ones, then the tens- so we know whether to regroup or not.`` When solving for example 24x3 , we trade 10 ones for 1 ten, and write the 1 on top. When writing the 1 on top, cross out that number to avoid confusion with 2-digit factors when more than one carried digit is shown.

2. Relate to addition. The students will first solve an embedded addition problem and then a related multiplication problem. This activity is for them to see and practice the similarities and the differences between multiplication and addition.

3. Use color codes such as red to indicate multiplying