Math Released Item Grade 4. How Are Both Equivalent 0273-M01241

Transcription

1 Math Released Item 2017 Grade 4 How Are Both Equivalent 0273-M01241

2 Anchor Set A1 A10 With Annotations

3 Prompt

4 0273-M01241 Rubric Part A Score Description 2 Student response includes the following 2 elements. Computation component = 1 point 40 o The student provides the equivalent fraction, 100 Reasoning component = 1 point o The student explains how the model can be used to show both fractions are equivalent. Note: The explanation should contain a comparison of the model in tenths (model on the left) to the model in hundredths (model on the right): Sample Student Response: I could use the model by knowing that 4 columns in the left model are equal to 4. If I were to look at the same four columns in the right model, 10 then there would be 40 blocks colored in. Note: Other valid explanations are acceptable. 1 Student response includes 1 of 2 elements 0 Student response is incorrect or irrelevant M01241 Rubric Part B Score Description 2 Student response includes the following 2 elements. Computation component = 1 point

5 o The student provides the correct sum, 90 Reasoning component = 1 point 100 o The student explains how to use the model to add fractions. Sample Student Response: I wrote 4 as right model. I then added that to Note: because there are 10 blocks in each column in the Other valid equations or explanations are acceptable. 1 Student response includes 1 of the 2 elements. 0 Student response is incorrect or irrelevant.

6 A1 Part A: Score Point 2 Part B: Score Point 2

7 Annotation Anchor Paper 1 Part A: Score Point 2 This response receives full credit. The response includes each of the two 40 An equivalent fraction is provided ( 100 is equal to 104 ). A correct explanation using the model to show how both fractions are equivalent is provided (because there are 100 in one row and 100 = 10 so if you keep the pattern going it would be 100 = 102, 100 = = 104 ). Each is equivalent to 10 so 100 is equivalent to 104. Note that the model is used in the explanation (there are 100 in one row and 100 = 1 10 ). Part B: Score Point 2 This response receives full credit. The response includes each of the two The correct sum is provided ( 9 10 ). A correct explanation on how to use the model to add the fractions is provided. The student begins using the model to reflect 10 4 (my first 50 step I colored in 4 rows for my 104 ). The next step is converting 100 to and reflecting this on the model (then I changed 100 to 10 and colored in 5 rows). Note that the conversion alone is not sufficient for credit. It is the conversion and the use of the model that earns credit. The sum is then found (I added = 9 10 ).

8 A2 Part A: Score Point 2 Part B: Score Point 2

9 Annotation Anchor Paper 2 Part A: Score Point 2 This response receives full credit. The response includes each of the two 40 An equivalent fraction is provided ( 100 ). A correct explanation using the model to show how both fractions are equivalent is provided (the fist model shows that ten cubes are equal to one long strip. so four long strips are equivalent to forty cubes). One column in the first model is equal to one column in the second model, which is ten cubes. Four columns in the first model are equal to four columns in the second model, which is forty cubes. Part B: Score Point 2 This response receives full credit. The response includes each of the two 90 The correct sum is provided ( 100 ). A correct explanation on how to use the model to add the fractions is provided (You could use the model to solve the fractions by seeing that ten cubes equal on strip so four strips equal forty cubes and I know = 90).

10 A3 Part A: Score Point 2 Part B: Score Point 1

11 Annotation Anchor Paper 3 Part A: Score Point 2 This response receives full credit. The response includes each of the two 40 An equivalent fraction is provided ( 100 ). A correct explanation using the model to show how both fractions are equivalent is provided (4 tens are equal to 40 ones). Note that the model is used in this explanation. Four of the columns in the first box is broken up into tenths and equals forty of the squares in the second box, which is broken up into hundredths. Part B: Score Point 1 This response receives partial credit. The response includes one of the two 90 The correct sum is provided ( 100 ). An insufficient explanation on how to use the models to add the fractions is provided (You can change 10 to = 100 ). While does equal 90, and while the student shows the conversion and correct addition of the 100 fractions, to receive credit for this element the student must explain or demonstrate the use of the model to convert and add the fractions. Contrast this explanation of use of the model to Part A. In Part A it is clear the student is using the model as they reference the equivalent sections of each model (4 tens, 40 ones).

12 A4 Part A: Score Point 1 Part B: Score Point 2

13 Annotation Anchor Paper 4 Part A: Score Point 1 This response receives partial credit. The response includes one of the two 40 An equivalent fraction is provided ( 100 ) The explanation (you can shade in the fraction and the convert one fraction and see if they re equivalent) provided is insufficient. Without a comparison of the models this explanation is too general and vague for credit. Part B: Score Point 2 This response receives full credit. The response includes each of the two 90 The correct sum is provided ( 100 ). A correct explanation on how to use the model to add the fractions is provided (You could use the model to solve the problem by coloring in what each fraction is and add them up. Each 10 out of 100 is 1 out of 10). Information on how to use the model is provided (Each 10 out of 100 is 1 out of 10) and is needed for credit to be earned.

14 A5 Part A: Score Point 2 Part B: Score Point 0

15 Annotation Anchor Paper 5 Part A: Score Point 2 This response receives full credit. The response includes each of the two 40 An equivalent fraction is provided ( 104 = 100 ). A correct explanation using the model to show how both fractions are equivalent is provided (four of and fourdy of one is equal to 10 ). Four columns in the first box is equal to forty squares in the second box or one column in the first box is equal to 10 squares in the second box. Part B: Score Point 0 This response receives no credit. The response includes none of the two No sum is provided. No explanation on how to use the model to add the fractions is provided. The 4 40 explanation explains why 10 and 100 are equivalent (they both take up 4 rows), but not how to solve 10 4 plus

16 A6 Part A: Score Point 1 Part B: Score Point 1

17 Annotation Anchor Paper 6 Part A: Score Point 1 This response receives partial credit. The response includes one of the two 40 An equivalent fraction is provided ( 100 ). The explanation provided is insufficient (just take out the zeros and thear you go) and is too general and vague for credit without the use of specific information from the model. Part B: Score Point 1 This response receives partial credit. The response includes one of the two The correct sum is provided ( 9 10 ). An insufficient explanation on how to use the models to add the fractions is provided ( = 10 just reduce the fraction). While does equal 9 10, use of the model to add the fractions is not demonstrated.

18 A7 Part A: Score Point 1 Part B: Score Point 0

19 Annotation Anchor Paper 7 Part A: Score Point 1 This response receives partial credit. The response includes one of the two 40 An equivalent fraction is provided ( 100 ). The explanation provided is insufficient. Use of the model is not demonstrated. Part B: Score Point 0 This response receives no credit. The response includes none of the two 54 An incorrect sum of the fractions is provided ( 100 ). The explanation provided is incorrect for adding the fractions and use of the model is not demonstrated.

20 A8 Part A: Score Point 0 Part B: Score Point 1

21 Annotation Anchor Paper 8 Part A: Score Point 0 This response receives no credit. The response includes none of the two 4 25 An incorrect equivalent fraction to 10 is provided ( 100 ) The explanation provided is incorrect. ( 100 fraction to 10 4 is found. ) is not how an equivalent Part B: Score Point 1 This response receives partial credit. The response includes one of the two The correct sum is provided ( 1000 ). 10 and 100 were correctly converted to fractions with a common denominator of An insufficient explanation on how to use the models to add the fractions is provided. In this response, 10 4 and were correctly converted to fractions with a common denominator of This is acceptable for adding the fractions, but use of the model is not provided.

22 A9 Part A: Score Point 0 Part B: Score Point 0

23 Annotation Anchor Paper 9 Part A: Score Point 0 This response receives no credit. The response includes none of the two 50 No correct equivalent fraction is provided. The response incorrectly states 100 is equivalent to 104. The explanation provided is incorrect. The two fractions provided are not equivalent. Part B: Score Point 0 This response receives no credit. The response includes none of the two No sum is provided. The explanation is vague and insufficient (you can add four of the ten sticks and 50 of the 100 cubes). The explanation does not solve the problem; the model would need to be shaded in or additional explanation given.

24 A10 Part A: Score Point 0 Part B: Score Point 0

25 Annotation Anchor Paper 10 Part A: Score Point 0 This response receives no credit. The response includes none of the two No equivalent fraction is provided. An insufficient explanation is provided (They are both equivalent because if you count them all together it will equal 100). It is unclear what is being referenced or what is being added. Part B: Score Point 0 This response receives no credit. The response includes none of the two An incorrect sum of the fractions is provided (9). An incorrect explanation on how to use the models to add the fractions is provided. ( ) does not equal ( 100 ) and use of the model is not demonstrated.

26 Practice Set P101 - P105 No Annotations Included

27 P101

28 P102

29 P103

30 P104

31 P105

32 Practice Set Paper Score P101 2,2 P102 1,1 P103 2,1 P104 2,2 P105 2,0