8/6/2014. Today we will: Explore tasks and activities focused on the concept of decimals and various representations

Transcription

1 Today we will: Explore tasks and activities focused on the concept of decimals and various representations Drew Polly, UNC Charlotte Discuss strategies and ways to support students understanding of decimals 4 th grade teachers? 5 th grade teachers? School-based leaders? District leaders? Others? A pencil packaging company puts 10 pencils in a box, 10 boxes in a bin, and 10 bins in a basket. Draw what you think a box, a bin, and a basket, look like. Try to draw close to scale/size. Compare your drawing with your neighbor. 1

2 Slide 1 1 What progression will they look at? Will we have copied the parts of NBT needed? Amy Lehew, 1 I think we decided we don't have time for progressions. Marta Garcia, 2 This could take 20+ minutes. Would we rather have participants doing some of the math involved or creating a progression? Amy Lehew, 3 Is this too much info for this venue? Amy Lehew, 2 Delete this slide! Marta Garcia,

3 How much of a basket is filled up by 1 bin? How much of a basket is filled up by 1 basket? What was the math involved? What did you have to know? How much of a basket is filled up by 1 box? How much of a basket is filled up by 1 pencil? How many times more pencils can you put in a basket than a box? What was the math involved? What did you have to know? How many times more pencils can you put in a bin than a box? What fraction of pencils can you put in a box compared to a bin? What fraction of pencils can you put in a box compared to a basket? 2

4 4.NBT.1 Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. 5.NBT.1 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Draw an unmarked number line. Draw and label numbers that are: Greater than 20 and less than 30 Greater than 20 and less than 22 Greater than 20 and less than 21 Greater than 20 and less than 20.1 Greater than 20 and less than The places in between.. How do we typically represent decimals? Where do our students struggle with representing decimals? How do you typically help students understand decimals? 3

5 3/10 or 0.4 7/10 or /100 or /100 or 0.2 Based on your picture which is larger? How does your picture help you solve the task? Without creating representations how do you know which is larger? The following are times from the state championship 50 meter dash: Marvin: 6.9 seconds Tyrone: 6 and 8/10 seconds Bernie: 6 and 91/100 seconds Zeb: 6.83 seconds What was the order of the finish from fastest to slowest? What was the difference between the fastest and 2 nd place runners? What was the total time of all four runners? Steve was hurt and didn t run. His fastest time is faster than Ben but slower than Tyrone. What was Steve s fastest time? Grade level? How can we make it better fit 4 th grade? How can we make it better fit 5 th grade? Standards? Standards for mathematical practice? Differentiation strategies? 4

6 You want to mail the following boxes to your cousin for his birthday. Nerf football: grams Bouncy ball: 453 and 9/10 grams How much would the items in the box weigh if you mailed: 1 football and 1 bouncy ball 2 footballs and 1 bouncy ball 2 footballs and 2 bouncy balls You can mail up to 3 kg of items for a set price. If you want to mail at least 2 of each item, what is the most number of each item that you can mail? Grade level? How can we make it better fit 4 th grade? How can we make it better fit 5 th grade? Standards? Standards for mathematical practice? Differentiation strategies? What does fluency mean? With decimals what do we expect students to be fluent doing? Draw 6 number cards and turn them face up. Use 4 of the number cards to create 2 decimals _. _ + _. _ = Get a sum as close to 10.1 as possible. The distance from 10.1 is your score for the round. The lowest score is the goal! 5

7 Standards? Where do students typically struggle? Standards for practice? Modifications? Here are some real student responses to how many times greater is 4 x 100 than 4 x 10? Who is correct? A: 4 x 100 is 360 times bigger than 4 x 10 B: 4 x 100 is 90 times bigger than 4 x 10 C: : 4 x 100 is 10 times bigger than 4 x 10 D: : 4 x 100 is 100 times bigger than 4 x 10 5.NBT.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used 6

8 Remember 2 x 30 = 3 x 20.2 x 30 = 20 x x x 2 = x 2 = 40 3x2 = x 0.6 = x 0.6 = 12 3x 0.6 = x 2.6 (100 x 2) + (100 x 0.6) + (20 x 2) + (20 x 0.6) + (3 x 2) + (3 x 0.6) = What s the rule 20 x 30 2 x 3 Count the zeros What s the rule.2 x.3 2 x 3 Count the decimal places 7

9 Pick 6 cards Choose 4 cards to create 2 decimals _. _ x _. _ = 200 divided by 40 = 20 divided by 4 The product closest to 30 wins. Your distance from 30 is your score for the round. Play a few rounds. Explore and draw a picture for each 32 kilograms of straw shared between 8 famers 3.2 kilograms of straw shared between 8 famers.32 kilograms of straw shared between 8 famers modified from GA Common Core framework units We have grams of peanut butter to use to make sandwiches. If we put 0.3 grams on each sandwich, how many sandwiches can we make? I know that I can move the decimal in both numbers one spot to the right to make 99.9 divided by 3. I then just divided and got my answer We can make 33.3 sandwiches. What did Sally do mathematically when she moved the decimal? What does Sally understand about place value? 8

10 What s the rule 80,000 divided by 400 Just cross out the zeros What s the rule 8.88 divided by 0.4 Just move the decimal. How does the multiplication and division of decimals connect the base ten work from prior grades? Drew- drew.polly@uncc.edu Planning resources link! State-wide math add-on license NCCTM in October 9