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Number Relationships

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Relationship cards are designed to help students understand addition and subtraction concepts in picture form before introducing abstract math notation. Instead of going directly to counting strategies to figure out addition or subtraction facts, students use these cards first to build an understanding of addition and subtraction relationships.

By using a special break apart picture called a number bond, students identify a part-part-whole relationship. Students learn that addition is the process of putting together the parts to make a whole and that subtraction is the opposite process of removing a part from the whole. Can they find the parts? Can they find the whole? Do they see an inverse relationship between addition and subtraction? Number relationship cards allow students to learn arithmetic based on number relationships and counting strategies.

First, build number bonds with concrete objects.

  • Draw a large number bond picture with no numbers in it on a small dry erase board.
  • Give the student some linking cubes or other objects to count. “Can you make two groups? Can you make one group of 5 and one group of 2? “(Use a different color object for each group). Ask the student to place each group in a “part” square.
  • The student should find the total using the counting on from the bigger part strategy. To count on correctly, the student may need to see a number line from 1 to 10.
  • After finding the total, point to each part and say, “5 and 2 make 7”. Then, push the total of 7 into the “whole” square.

Continue to practice only the “missing whole” number relationship cards. Do not introduce plus, minus or equal signs yet. Gradually remove the concrete objects and replace with pictures. The student should practice by drawing circles in each part. The student should write the number inside the part square underneath the circle pattern. Repeat the process used previously when modeling with concrete objects.

Finally, have the student write a number sentence with a plus sign and an equal sign. Note that writing number sentences is not developmentally expected until kindergarten or later. Emphasis is placed on conceptual understanding and effective counting.

After the student has a good understanding of “missing whole” cards, he or she should practice “missing part” cards.

A student should progress through the fact card arithmetic levels in the sequence below. He or she must have mastery of prior levels before progressing to the next level.

  1. Number Relationship Cards
  2. Addition through 10 Cards
  3. Subtraction through 10 Cards
  4. Addition through 20 Cards
  5. Subtraction through 20 Cards
  6. Multiplication Level 1 Cards
  7. Division Level 1 Cards
  8. Multiplication Level 2 Cards
  9. Division Level 2 Cards