Crossed up hundreds board

Students will experience patterns and problem solving on the Hundreds Board.

A lesson plan for grade 3 Mathematics

By Karen Bartlett

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Learning outcomes

Students will practice addition skills with paper and pencil or using the calculator and problem solving with patterns. The possibilities with patterns are endless.

Teacher planning

Time required for lesson

45 minutes

Materials/resources

• Hundreds Boards
• calculators
• paper
• pencils

Pre-activities

Students should have had exposure to the Hundreds Board and understand the basic patterns on it.

Activities

This activity can be done as a calculator activity or a pencil and paper activity depending on the skill that the teacher would like to emphasize. The pattern is easier to see if a calculator is used.

1. Ask each student to choose a number on the Hundreds Board and add it four times. For the first number, students will be more successful if they choose a number in the middle of the Hundreds Board (ex: see Example 1, 46 + 46 + 46 + 46 = 184)
2. Next, add the four numbers that surround the original number-vertically and horizontally (36 + 47 + 56 + 45 = 184). This is a + (cross) formation.
3. Ask the students what is true about both the sums. (They are the same.) Why? (The numbers that surround the original number are one less, one more, ten less, and ten more and therefore balance out. The sum of the four numbers equals the sum of the original number.)
4. Ask the students if this same principle or pattern works for the next four numbers: vertically and horizontally (26 + 48 +66 + 44 = 184) Why? (This time it is two more, two less, twenty more, and twenty less.)
5. Ask the students what they predict the next sum will be if they continue in the same pattern. (16 +49 + 76 + 43 = 184)
6. Let the students try other numbers on the Hundreds Board to see if this holds true for them. (This produces practice, patterning, and problem solving all in one!)

Extension

Try this same theory in an X (diagonal) formation instead of a + (vertical- horizontal) formation. (34 + 37 + 57 + 55 = 183) Do the students see a similar pattern? (nine less, nine more, eleven less, eleven more) Great thinking! (See Example 2)

Assessment

As the students work independently or with partners doing this activity, the number patterns that were found will be recorded. The students will color a Hundreds Board to show their understanding of the patterns found. Students will also show computations to validate their patterns.