I-CANyons Parent Toolkit for Fourth Grade Mathematics
Numbers and Operations - Fractions: I CAN...
StandardRecognize, create and use equivalent fractions
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Core StandardNF4.1 Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and
size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. |
In Other WordsStudents find equivalent fractions by multiplying or dividing the numerator (top) and denominator (bottom) by the same number. For example: 1/2 is equal to 3/6 because both 1 and 2 were multiplied by 3. The same is true of division. 4/12 is equivalent to 1/3 because 4 divided by 4 is 1 and 12 divided by 4 is 3. A nonexample would be: 1/2 is not equal to 2/6 because the 1 was multiplied by 2 and the 2 was multiplied by 3.
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If MasteredUsing larger, more difficult numbers, student explains why a fraction is
or is not equivalent to another fraction. For example: Is 36/150 equivalent to 1800/7500? Answer: Yes, both 36 and 150 were multiplied by 50. You could also click here to have your child play a game at iXL. |
If Not Yet MasteredThese links are to activities the student can do to help visualize equivalent fractions.
NLVM Equivalent Fractions Fractions Memory Game Softschools Fractions Game Study Jams Equivalent Fractions If you do not have internet access, use the attached colored fraction strips to help your child visualize the fractions. Cut out all of the fraction strips. If you cut on the black lines on each color you will get individual pieces. You can then have your child find all the equivalent fractions to 1/2 for example by having him/her put other pieces on top of the 1/2 strip until they are the same size. In this example, two of the 1/4 pieces will fit on top of the 1/2 strip so 2/4 is equal to 1/2. |
StandardAdd and subtract fractions with common denominators
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Core Standard NF4.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8. c. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. d. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem. |
In Other WordsStudents add or subtract fractions with the same denominators (bottom numbers). This is done by simply adding or subtracting the numerators. For example: 4/11 + 3/11 = 7/11 because 4 + 3 = 7. The pieces here are the same size so the pieces are simply being added together. The same is true of subtraction. Example: 9/10 - 5/10 = 4/10 because 9 - 5 = 4. In a mixed number, you have a whole number plus a fraction. For example: 2 1/2 is the same as 2 + 1/2. When adding or subtracting two mixed numbers, you add/subtract the whole fractions first, then move to the whole numbers. Example: 4 1/5 + 3 2/5 = 7 3/5. You would add 1/5 + 2/5 first to get 3/5. Then add 4 and 3 to get 7. Finally you add the two answers 7 and 3/5. If the two fractions add up to more than 1 whole, you simplify first then add in the whole numbers. For example: 3 3/5 + 1 4/5= 5 2/5. 3/5 + 4/5 = 7/5. 7/5 is the same as 1 2/5 since 1 group of 5 plus 2 more equals 7. You then add 1 2/5 + 3 + 1 = 5 2/5. When solving word problems it is helpful to draw a picture. Using a rectangle rather than a cirlce will help when dividing up the whole into equal sized pieces. If you draw both rectangles the same, you'll be able to easily add or subtract the number of pieces in both wholes.
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If MasteredIf mastered, help your student extend his/her skills by adding/subtracting larger mixed numbers for example 365 108/450 - 299 99/450. This will pull in other mathematical skills such as regrouping to subtract. You could also have your child play a game on adding fractions at Funschool.Kaboose.com
If your child gets bored with this, you could also push them to the next level which would be adding and subtracting fractions with unlike denominators. Examples of this can be found at StudyJams.com |
If Not Yet MasteredIf student has not yet mastered this concept, consider using the following links which will walk him/her through through the proper steps to add/subtract fractions.
StudyJams Adding Fractions CoolMath4Kids Adding Fractions |
StandardMultiply fractions by a whole number
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Core StandardNF4.4 Apply and extend previous understandings of multiplication to
multiply a fraction by a whole number. a. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4). b. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.) c. Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie? |
In Other WordsStudents multiply a whole number by a fraction. For example 5 x 2/3. Here you would change the whole number into a fraction by putting the whole number 5 over the denominator of 1. This can be done because you have 5 whole pieces. Next you multiply straight across. 5 x 2 and 1 x 3 to get an answer of 10/3. You then simplify the answer by going 10 divided by 3 to get 3 1/3. This whole process can be seen by watching the following YouTube video.
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If MasteredIf mastered, you can use larger numbers to extend their thinking. For example, you could do 24 x 12/19. This is done by putting 24 over 1 then multiplying straight across, 24 x 12 and 1 x 19. You will get 288/19. Then simplify by doing 288 divided by 19. You will get 15 3/19. Another idea could be to have your student play a math game at CoolMath4Kids.
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If Not Yet MasteredIf your student had not yet mastered this concept, the following YouTube video does a step by step walk through.
You can then have your child practice by playing a game at CoolMath4Kids.com |
StandardUse decimals to hundredths and compare with fractions
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Core StandardNF4.5 Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.4 For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. NF4.6Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram. NF4.7 Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.
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In Other WordsStudents are asked to write fractions as decimals and decimals as fractions. For example:3/10 as a decimal would be 0.3. 0.67 as a decimal would be 67/100. This is done by putting the place value as the denominator (bottom number). If the last number is in the tenths place (one number right of the decimal), the denominator is 10. If the last number is in the hundredths place (two numbers right of the decimal), the denominator is 100. If the number is already a fraction, the numerator is placed after the decimal with the last number in the correct place value. For example with 3/10, the 3 is placed in the tenths place (one number right of the decimal) to get the answer of 0.3 but with 3/100 the 3 is placed in the hundredths place value (two digits right of the decimal) because the denominator is hundredths. You would then put a 0 in the tenths place to get 0.03. The student should then be able to compare decimals and fractions by making both fractions or by making both decimals. Students do NOT have to convert fractions such as 3/8 to a decimal in the fourth grade.
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If MasteredIf mastered, student can teach a parent or sibling how to convert a fraction to a decimal and a decimal to a fraction. Student can do this with a variety of decimals/fractions. You could also have your child play the following game on converting fractions to decimals at SheppardSoftware.com
The student can also explain to a parent or child how to compare fractions and decimals by converting them both to fractions or decimal and then comparing the numerators (top numbers) or the numbers after the decimals. This is only true for fractions less than 1 whole. If the fraction is a mixed number, the whole number must also be compared. The attached pdf has decimal grid paper for tenths and hundredths which can be used to show why one decimal/fraction is larger than the other. |
If Not Yet MasteredIf not yet mastered, the parent can model for the child how to read the fraction or decimal and how that relates to the numbers shown. For example 3/10 is read as "three tenths" so the decimal is written with 3 in the tenths place (the number just right of the decimal). 0.05 is read "zero and five hundredths" so the 5 becomes the numerator (top number) over the denominator (bottom number) of 100. Both the decimal and the fraction are read the same way. The attached pdf can be used to help the student visually see why one decimal/fraction is larger than the other. Student can also play the following game at SheppardSoftware.com on converting fractions to decimals.
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StandardCompare fractions with like and unlike denominators
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Core StandardNF4.2 Compare two fractions with different numerators and different
denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. |
In Other WordsStudents are asked to compare fractions with the same denominators (bottom numbers) such as 3/4 and 1/4. The student should be able to identify that 3/4 is larger becase 3 out of 4 pieces is more than 1 out of 4 pieces. This is only true however if the whole is the same. If you are comparing 3/4 of one fun size candy bar to 1/4 of a king size candy bar, 3/4 may not be larger. When comparing fractions with unlike denominators, students need to make equivalent fractions by finding a common denominator. For example when comparing 2/6 to 7/12, students would need to find a common denominator. This is done by looking at the multiples of the denominators 6 and 12. Both 6 and 12 share the common multiple of 12, so 12 is going to be the new common denominator. To make 2/6 have a denominator of 12, you have to multiply the 2 and the 6 by 2 since 6 x 2 = 12. You will get the new equivalent fraction of 4/12. You can then compare 4/12 to 7/12 and see that 7/12 is larger than 4/12.
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If MasteredIf your child has mastered this concept, he/she should be able to explain to a sibling or parent how to compare fractions. The Arcademics.com website also has games to play on comparing fractions.
To review this concept with your child, please visit StudyJams |
If Not Yet MasteredIf your child has not yet mastered this concept, you can visit the StudyJams website for step by step directions.
If you do not have internet access you could print off the attached Colored Fraction Strips, cut them out and have your child lay the fraction strips side by side to compare them. While this may only work with a few examples, your child would have a visual of why 1/4 is smaller than 2/3. |
