Ideas for Teaching Number Sense Including Facts and Number Operations

1. Ideas for Teaching Number Sense Including Facts and Number Operations

2. Math Facts: Strategies for Helping Students Who Struggle 1. Emphasize number sense patterns and relationships – number lines. How many different ways can you total six using these yellow cubes? Write the equation. two cubes and four cubes (2 + 4 = 6) 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 four cubes and two cubes (4 + 2 = 6) How are the two representations similar? How are they different?

3. Math Facts: Strategies for Helping Students Who Struggle 1. Emphasize number sense patterns and relationships – number lines. How many different ways can you total six using these yellow cubes? Write the equation. two cubes and four cubes (2 + 4 = 6) 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 four cubes and two cubes (4 + 2 = 6) How are the two representations similar? How are they different?

4. Math Facts: Strategies for Helping Students Who Struggle 1. Emphasize number sense patterns and relationships – number frames A number frame can be used to help students make sense of number patterns that represent addition and subtraction facts. 10 line

5. Math Facts: Strategies for Helping Students Who Struggle 1. Emphasize number sense patterns and relationships Ten and four is fourteen A number frame can be used to help students make sense of number patterns that represent addition facts by providing them with visual reference points. Working with students on a regular basis to identify different patterns can help them to create more meaningful cognitive anchors for recalling certain fact combinations 10 line One and two is three

6. 2. Emphasize facts that are more easily remembered first – abstract recall

7. 3. Teach rules for multiplying facts (adapted from Mercer & Mercer, 2001) Once students master these rules only 15 facts are left to multiply: 3x3=9; 3x4=12 3x6=18 3x7=21 3x8=24 4x4=16 4x7=28 4x8=32 6x6=36 6x7=42 6x8=48 7x7=49 7x8=56 8x8=64

8. 3. Create unique ways to remember less familiar facts with your students. 6 4 2 Selecting facts that are difficult for students and engaging with them to create ways to make facts meaningful can be an important activity for stimulating students’ metacognitive thinking and relating something abstract and meaningless to something tangible and meaningful.

9. 3. Computation - teach low stress alternative algorithms (adapted from Mercer & Mercer, 2001)

10. 3. Computation - teach low stress alternative algorithms (adapted from Mercer & Mercer, 2001) 34 X 3 12 90 102 Answer: 361 This algorithm helps students who have difficulty with the multiplication process - determining the correct quotient number when dividing. Initially student tried “2” but after subtracting 42 from 75 found that “33” was greater than the divisor. So divides by one more (“1” is placed above “2” in the quotient). Student repeats this step until no more multiplication is needed.

11. Fraction Number Sense – Number Line The following set of slides demonstrate how a number line and concrete materials (fraction bars) can be used to help students develop number sense related to fractions. The questions below each representation are those a teacher might ask. The words in the light colored boxes are language teachers and students might use to describe the meaning of each new representation.

12. Number Line Example: Fractions 1 0 How many blocks are there between zero and one on the number line? Is each block the same size? Let’s compare them to find out. How could I do that?

13. Number Line Example: Fractions One of the four blocks is on top of the number line 1 0 How many blocks are there between zero and one on the number line? How many blocks are on top of the number line?

14. Number Line Example: Fractions I’m going to represent one of four blocks by writing one-fourth on the number line. 1 1/4 0 How many blocks are there between zero and one on the number line? How many blocks are on top of the number line?

15. Number Line Example: Fractions Now there are two of four blocks on the top of the number line. 0 1 1/4 How many total blocks are there between zero and one on the number line? How many blocks are on top of the number line?

16. Number Line Example: Fractions I’m going to represent two of four blocks by writing two-fourths on the number line. 1 1/4 2/4 0 How many total blocks are there between zero and one on the number line? How many blocks are on top of the number line?

17. Number Line Example: Fractions Now there are three of four blocks on the top of the number line. 1 1/4 2/4 0 How many total blocks are there between zero and one on the number line? How many blocks are on top of the number line?

18. Number Line Example: Fractions I’m going to represent three of four blocks by writing three-fourths on the number line. 3/4 1 1/4 2/4 0

19. Number Line Example: Fractions Now there are three of four blocks on the top of the number line. 3/4 1 1/4 2/4 0 How many total blocks are there between zero and one on the number line? How many blocks are on top of the number line?

20. Number Line Example: Fractions I’m going to represent three of four blocks by writing four-fourths on the number line. 3/4 1 1/4 2/4 0 4/4 Why do you think I wrote four-fourths underneath the number one on the number line?