Since we mastered double-digit addition, it's time to move on to double-digit subtraction. Subtraction is ALWAYS much harder for students than addition, especially when re-grouping (or borrowing) is involved. Just like with learning double-digit addition, we first learned so basic strategies to understand the idea of going backwards. Students worked on hopping back tens and ones on a hundred chart, hopping back tens and ones on an open number line, and counting back tens and ones mentally. We then moved on to the traditional method of subtracting with borrowing (re-grouping). Many students have a hard time not just subtracting right away. For instance, if a student sees 52 - 38, they automatically just want to say that 2-8=6. I then ask students if you have 2, can you take away 6? Or I have them draw it out. Students were introduced to some poems to try to help them remember when they need to borrow and when they can just subtract straight away: "More on top? No need to stop!" Students can just subtract straight away, as they like. "More on the floor? Go next door to get 10 more." I also pretend to knock on the tens place value like it's an apartment next door and say, "Oh Mr. 10, may I borrow one of you to come over please?" That has helped in some instances. "Numbers the same? 0s the game." Again students know that if they have 3 and we're taking away 3, they have 0. This helped many students, but some were still struggling so we used connecting blocks to build place value blocks of tens and ones. Then students could physically see they didn't have enough and have to take one of the tens and break it apart into 10 ones to see that now they have 1 less ten and 10 more ones. Majority of the students have it now, but this will have to be something we continue as with break coming up, it will be easy to forget if they weren't strong in it yet.
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We had been working on place value for the last few weeks. Students worked on understanding the value of each number in a place value. For instance, in 325 the 2 means 20 or 2 tens. They also continued learning about standard form, expanded form, word form, and drawing out the place value blocks. We also used place value to help us count patterns. We counted by 10s and 100s from any number: 67, 77, 87, 97, 107....
We are now using what we learned about place value to add double-digit numbers. The way that we have practiced so far is using the partial-sums way. In that way, students take what they learned about place value to help them add the numbers without assistance from their number grid. Partial-sums is basically the breaking apart numbers method we learned. It does a great job of having students understand place value and exactly what they are doing when they regroup and carry the 1. We had them start with the ones place since that is what they will do when they learn the algorithm way (traditional method). Partial-Sums: 45 +37 12 ---> First you add the ones 5 + 7 = 12 +70 --->Then you add the tens: 4 tens (40) + 3 tens (30) = 7 tens, which is 70. 82 ---> Finally you add the tens and ones together. This shows the students what exactly each number means when they are adding. We moved on from learning the partial-sums method of adding double-digit numbers to adding using the traditional algorithm of regrouping. There are quite a few students who are forgetting to add the 1 that we've carried over to the tens place. We've been working on this by writing the answer to the ones place on the side of the ones place (so if it's 36 + 27 then we add 6 +7 and write a 13 on the side) and drawing an arrow from the 1 to the top of the tens place and another arrow from the 3 to the ones place. Then we add the tens together. The more we practice, the better it's getting but it's still a work in progress. We started out the year with Topic 1. Topic 1 is all about fluently adding and subtracting within 20. Lesson one was Addition Fact Strategies. Students learned about turn around facts and how the addends can be added in any order and they will get the same sum.
Example: 3+4=7, 4+3=7 Lesson two was Doubles and Near Doubles. Students learned that if they know the doubles fact they can quickly figure out the newer doubles fact. Example: 5+5=10 so 5+6=11. 6 is one more than 5 so the sum is one more. 6+6=12 so 6+8=14. 8 is two more than 6 so the sum is two more. The remaining lessons for the topic were all to aid students in adding and subtracting basic facts quickly: Make a 10 to Add, Addition Fact Patterns, Count on and Count back to Subtract, Think Addition to Subtract, Make a 10 to Subtract, Practice Addition and Subtraction Facts, and Solve Addition and Subtraction Word Problems, The math homework card games are a fun way to help student fluently add and subtract and get those math facts memorized. We then moved on to Place Value, Topic 9. Students worked on understanding the value of each number in a place value. For instance, in 325 the 2 means 20 or 2 tens. They also continued learning about standard form, expanded form, word form, and drawing out the place value blocks. We also used place value to help us count patterns. We counted by 10s and 100s from any number: 67, 77, 87, 97, 107.... We will finish up our place value unit this week and then will move on to our next unit which is Double-Digit Addition in Topics 3 & 4. We will use what we learned about place value to add double-digit numbers. Students will start off learning some different methods to help them understand that when adding double-digit numbers they are just adding tens and ones and that place value matters when adding. Once they understand what you are actually doing (what carrying over to the tens place means) when you're adding double-digit numbers, they will learn the traditional way of adding. These other lessons (that might seem confusing to you) are actually great stepping stones to help them understand the relationship between place value and addition. To start off the year students learn math games to use with a deck of cards. They learn a game one day and practice it. Then they'd practice it the next day again before learning a new game. Students have learned the games Fishing for Ten, Battle, Odd or Even, Slap, and Salute. These games, along with many others, are what students will do for their math homework once a week. You will be getting direction cards to all the games students can choose from. It's a fun way to practice math skills and to get together as a family instead of worksheets.
Students also started their math warm-ups, Daily Math Boxes, which we are starting out the year doing together. These are a great way to continually review math skills we've practiced and to even get a preview and beginning practice of skills we will be learning during the year. We will do them all together for the first couple of weeks as students get to understanding them and how to do them and then students will do them on their own and we will go over them so they can check their answers and fix whatever they need to fix before math time ends. This week we are also starting our math curriculum Envision. Our first math topic is Topic 1: Fluently Add and Subtract within 20. In this topic students learn different math strategies to help them learn to do their math facts quickly. |
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