I will start this part of the lesson by having the students sit in a circle. I will show them two dice. One of them will have the numbers 0, 10, 20, 30,..., 90. The other will have 0-9. I will role the dice and say the number that is created. Their job will be to determine the number that comes just after the number that is rolled. I will do this for a couple of minutes and then switch to stating the number that comes just before. The CCSS ask that students can be given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; and explain the reasoning used (CCSS.Math.Content.1.NBT.C.5). This activity is the beginning of establishing part of that ability and thinking.
I will again make a slight variation to the Start At/Stop At routine. I will take all of my Start At/Stop At cards (see section resource if you haven't used them in the past) and put them in one envelop. I will then explain the routine to the class.
Today, we will be changing our Start At/Stop At routine a little bit. We will no longer have the 1-15 in one basket and the 16-30 in the other. Instead, the cards will all be mixed together and we will choose a Start At Number and A Stop At Number from the basket.
Using the number line, I will mark the Start At number with a green dot (on a sticky note) and the Stop At number with a red dot. I will play this activity several times making sure that we practice both counting forward and backward on the number line.
*Before starting each round of counting, I will ask the students if we will be counting forwards or backwards on the number line? I want them to explain their thinking on this and to establish the meaning of forwards and backwards counting.
After each round I will write the two numbers on the white board and ask a student two write a < or > symbol to make a true statement (i.e. 14<28). The CCSS ask that students be able to compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. By adding this piece to this activity, the students will start to see that if we count forward to a number, the Start At Number will be less than that of the Stop At number we are counting to and vice versa.
To see a sample of this activity in action see the section resource.
I start by displaying the problem, 10 Rocks and Balls, on the document camera. This problem can be found in the resource section. I read the problem aloud and ask them if this reminds them of any other problem that we have done in the past? If no one responds, I remind them of the Apples and Bananas Problem that we did earlier in the year. I want them to remember that there was more than one possible solution to this problem.
I then tell them that today they will be solving a similar problem about rocks and marbles (my students are really into rocks right now and I know this will get their attention. Feel free to change it to what ever you would like, remembering that it should be objects that are easy to draw). I tell them that I want them to find as many combinations of rocks and balls as they can and record them on their paper. Once you have found all the combinations, I want you to use your paper to prove that you have them all. By recording their thinking, the students are being asked to model their thinking with mathematics (CCSS.Math.Practice.MP4). The CCSS ask that this practice start at an early age and may be as simple as writing an equation to record their thinking.
Make sure that there are counters available for students to use.
The idea behind this conversation is that I want a whole group conversation about how students found as many 2 addend combinations as possible, and how do they know they found them all.
I start by creating a chart that has three columns (see section resource). The first column is titled rocks, the 2nd is titled balls, and the third is titled total. I will ask the students for the combinations that they found and record them on the chart.
Jim found 6 rocks and 4 balls. I am going to write the 6 in the rocks column and then write the 4 in the balls column. I am now going to add a + sign between them because I am adding 4 balls to the 6 rocks. That made 10, so I am going to write 10 in the total column. I am going to write an = sign after the 6+4 because the total equals 10. CCSS ask that students use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem (CCSS.Math.Content.1.OA.A.1). By modeling this action, I am helping students gain a conceptual understanding of how an equation is developed.
I continue to call on students to give other examples, reminding them to check their sheets and not give combinations that have already been suggested. I continue until their are no more suggestions.
Wow!, We have found a lot of combinations of rocks and balls. Do you think that we have found all of the ways? Why do you think so?
What strategies did people use to find many combinations?
Continue until no more strategies are given and suggest that students try these strategies as they continue to work on combination problems in future lessons. I will leave this chart out so students can continue to add to this if new combinations are found.
There is an photo of the chart in the section resource.
I will roll a 20 sided die and roll the it. I will call out the number and ask the students to write the number. I will remind them that I am looking for numbers that are not reversed. I will collect their paper at the end and review for any reversals.