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Students in fourth grade are encouraged
to see the relationship between
A fourth grader has to understand the unit
fraction and be able to apply this Parent Math
multiplication and division. Their task is understanding to addition and subtraction
to make sense of division and have a real
understanding of the concept, thereby
of fra

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Parent Math Strategy Guide
Grade 4
Multiplication & Division
Working with Fractions
Cobb County Schools
Students in fourth grade are encouraged to see the relationship between multiplication and division. Their task is to make sense of division and have a real understanding of the concept, thereby preparing for more complicated strategies in subsequent grades. One strategy that supports this is
multiplying up.
This student has used the
multiplying up
strategy to find the solution to 624 ÷ 6.
Students need to see fractions on a number line and apply this knowledge to different situations. A fourth grader should develop an understanding of a fraction as a number.
Grade 4 expectations when working with fractions are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
Students are exposed to various strategies to ensure a good foundation in number sense.
One strategy,
partial quotients,
began in grade 3 and continues in grade 4 with larger numbers. A fourth grader has to understand the unit fraction and be able to apply this understanding to addition and subtraction of fractions.
5 1 1 1 1 18 8 8 8 8 8
OR
etc
…
2 38 8
Understanding fraction equivalence is very important in grade 4. Students need to understand how an equivalent fraction is obtained.
=
23
812
The whole is the square, measured by area. The left drawing is divided into 3 rectangles of equal area, and the shaded region is 2 of the 3 equal pieces. The right drawing is divided into 3 x 4 small rectangles of equal area, and the shaded area comprises 2 x 4 of these and so it represents 2 x 4 =8
.
3 x 4 12
By the time students reach 4
th
grade, they have mastered addition and subtraction strategies. Students now understand the standard algorithm for addition and subtraction and are able to apply it fluently to solve real-world problems.
Fourth graders come to this grade level knowing multiplication facts from memory. Students can use strategies to help them with these facts:
8 x 9
could be seen as
OR
Math
8 x 10 = 80 80
–
8 = 72 8 x 5 = 40 8 x 4 = 32
72
Once students have understood the models and can apply the distributive property to these multiplication problems, they move to
partial products
.
800 180
240 54
40 9 20 6
Students draw
models and calculate the product.
4 9 x 2 6
800 240 180 + 54 1274
Fourth graders explore division by finding whole number quotients and remainders using strategies based on place value and the properties of operations. A strategy based on place value that is used to assist students with understanding division is
explicit trades
. In this example, the student had to trade 2 tens for 20 ones. This should be clearly explained using place value language. A strategy that helps students multiply numbers mentally is
doubling and halving.
Here the student halves one number and multiplies the other number by two to get a friendly number that is easy to work with mentally. A fourth grade student is familiar with building simple multiplication problems using base ten blocks. This drawing shows the problem
4 x 13
.
Students investigated working with the distributive property in grade 3.
(4 x 10) + (4 x 3)
40 + 12 = 52
Students now begin to work with the
area model of multiplication
using 2-digit x 2-digit numbers. Here a student has built a 12 x 23 area model that shows the product 276. Once again, the distributive property (based on the model) helps students understand multiplication.
12 x 23 = 276
(10 + 2) x (20 + 3)
(10 x 20) + (2 x 20) + (10 x 3) + (2 x 3)
200 + 40 + 30 + 6 = 276 10 + 3 4
4 x 10 4 x
3

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