Level 4

Are these numbers equal? 3 thousands 12 hundreds 8 tens 8 ones 4000 + 288 This should be an automatic recognition. 3 thousand plus 12 hundred equals 4200. Then 88. 4N1

What number is this? Students should be able to name the number with no writing of parts. They should recognize that 43(100) = 4300, 11(10) = 110 and 3(1) = 3. The number is 4413. Four thousand, 4 hundred, thirteen. 4N1

What number is ten more 7 896 This should be automatic. 7906 4N3

What number is one hundred more 15 937 This should be automatic. 16037 4N3

Approximately where do the fractions go?               They sit between 0 and 1 in order. Student makes quick approximation for dividing the space into 4 parts. The 2 is a distractor. 4N8

Approximately where do the fractions go?       1 4 1 7 4 4 2 fourths is half way between 0 and 1. Two sevenths will be to the left as it is smaller. No need to make tic marks. Just quickly show which side of 2/4. 2/2 equals one or one whole. 4N8

0.32 Are they equal? How do you know? 2 tenths 12 hundredths 4N11 2 tenths, 12 hundredths is the same as 3 tenths, 2 hundredths and that is what the decimal notation says. Are they equal? How do you know? 4N11

Are they equal? How do you know? 4(0.1) 4(0.01) 3(0.1) 13(0.01) 4N11 Student quickly recognizes 44 hundredths does not equal 43 hundredths. 4N11

Describe this decimal two ways. Possibilities include: 5 tenths, 6 hundredths or 56 hundredths or 3 tenths, 26 hundredths or 46 hundredths, 1 tenth. Any of these can be written in decimal or in fraction notation. 4N9

Name this image as a decimal. I see 70 hundredths and 7 more hundredths. I see 4 tenths, 37 hundredths, I see 5 tenths, 2 tenths, 7 hundredths. However I describe it the image represent 77 hundredths or 7 tenths, 7 hundredths. 0.77 4N9

Name the decimal that would be 0.5 more.

Name the decimal that would be 0.05 more.

How are these decimals different? Which has the greatest value? 0.65 0.6 0.06 65 hundredths is more than 6 tenths which is 60 hundredths and the third one is only 6 hundredths 4N9

How much is one third of 12? 5N10 Students should recognize that ⅓ of a number is the same as dividing 12 by 3. This should be automatic. 5N10

How much is three fifths of 20? Student can explain one fifth of 20 is like 20÷5 which is 4. Then 3 fours is 12. 5N10

Name 2 decimals that fit between 0.3 and 0.4 Student will go to hundredths anything between 0.31 and 0.39. Thousandths is unlikely but possible. 5N10

Do these both represent 0.83? 7 tenths + 13 hundredths 83 hundredths Yes. 0.7 + 0.13 is 0.83 5N10

How do you know this is true without solving? 243 x 6 = (40x6) + (200x6) + (3x6) The student recognizes that 74 = 70+4 or 4 + 70 and 63 = 60 + 3 or 3 + 60 so you simply expanded the factors (Distribution Property) 5N10

If 6 x 7 = 42 Then 12 x 7 = ? Student is quick to fill in 96. Just double the product. Six became 12. In a diagram the side doubled. 5N10

What multiplication equation is this? Student recognizes (3+5) 9 = 8 x 9. Student might go on to say (3x9)+(5x9) but this is not an equation unles he or she balances it with = 27 + 45 or with = (3+5) 9 or with = 8 x 9 5N10

What are the ?s. Explain how you know. Student can use multiplication or division to find the missing factors are 4 and 5 because 4 x 4 = 16 and 4 x 5 = 20 or 16÷ 4 = 4 and 20 ÷ 4 = 5 5N10

Sam wants to share 9 books with 4 people. Will there be extra books? Yes, unless he rips a book apart 5N6

Sam has 30 books to place equally into 5 bookbags. How many in each bag? 5N6

The area is 24 square cm. True or false? 6 cm 4 cm 4 cm 6 cm True. Student is automatic with the understanding that 6 x 4 finds the area. Multiplication is area. (No stopping to build anything) 6 cm