Show How To Make A Ten To Find 12 4

Making a ten

Alignments to Content Standards: 3.OA.D.ix

Task

Below is a table showing all the means to add the numbers from i to ix.

1. Each sum which is larger than 10 can be found past commencement making a 10. For example, to find 8 + 5, we tin write

   \begin{marshal} 8+five &= 8 + (2+3) \\ &= (8+2) + iii \\ &= ten + 3 \\ &= 13. \end{align}

   Explain why this reasoning works and utilize this method to discover 7 + eight. How can you visualize these equations using the table?
2. Adding 9 to another unmarried digit number can also be washed by offset making a 10. For case

   \begin{align} 3+9 &= 3 + (10-1) \\ &= (3+10) - 1 \\ &= xiii - 1 \\ &= 12. \terminate{align}

   Explicate why this reasoning works and apply this method to find 7+9. How can you visualize these equations using the table?

IM Commentary

Students are expected to be fluent with add-on and subtraction within xx in second grade (come across 2.OA.2). This job builds on that knowledge past request them to report more advisedly the make-a-ten strategy that they should already know and employ intuitively. In this strategy, knowledge of which sums brand a ten, together with some of the properties of addition and subtraction, are used to evaluate sums which are larger than 10. The 10's in the table are shaded because they are essential to the technique. The second part of the job focuses on adding ix'due south which can as well exist accomplished past adding a ten and then subtracting 1. The teacher may wish to indicated to students for function (b) that showing how to add 9 by first making a ten with the addition table requires an extra column on the tabular array. Alternatively, students tin merely add one box, with the number 17, to show the sum 7+x. This job is intended for pedagogy purposes as it takes time to identify the patterns involved and understand the steps in the procedures.

The Standards for Mathematical Practice focus on the nature of the learning experiences by attending to the thinking processes and habits of listen that students need to develop in lodge to attain a deep and flexible understanding of mathematics. Certain tasks lend themselves to the sit-in of specific practices by students. The practices that are observable during exploration of a task depend on how didactics unfolds in the classroom. While information technology is possible that tasks may be continued to several practices, just 1 practice connection will be discussed in depth. Possible secondary practice connections may exist discussed but non in the same degree of detail.Â

This job helps illustrate Mathematical Practice 7, Look for and make use of structure. During this activity, 3rd graders are actively connecting the strategy of brand-a-ten along with properties of addition and subtraction to solve sums greater than 10.  During this process they are looking at the structure of the base ten arrangement, and composing and decomposing numbers based on this structure.  Students will have the opportunity to retrieve virtually the meaning and usefulness of composing tens without struggling with the computations which for a third grader will not be challenging.  They are asked to visualize this make-a-ten strategy using the add-on table and explain why this reasoning works (MP.3). Through this in-depth exploration of the make-a-10 strategy, students are immersed in pattern-recognition and pattern-generalizing which not only develops a ameliorate understanding of our base 10 structure simply allows them to apply this understanding to solve other problems.

Â

Solution

1. The showtime equation comes from writing 5 as 2+iii. The reason for this is that in the next step nosotros will group the 2 together with the 8 to make a 10. This second step uses the associative property of improver. In the third step, nosotros add ten + 3 to observe the reply of 13.

   In terms of the addition tabular array, nosotros tin can visualize adding 5 to 8 by starting at the 8 in the cavalcade of addends and moving over 5 spaces to the right. Detect that afterward two steps, nosotros achieve x. Then three more steps puts us at 13. This is shown in the picture below:

   

   Applying this method to summate vii+viii we discover

   \begin{marshal} 7+eight &= seven + (3+v) \\ &= (7+3) + 5 \\ &= 10 + 5 \\ &= fifteen. \stop{align}

2. This method is similar to the making a ten method in part (b). In this instance, however, a 10 is made past rewriting 9 every bit 10 - one. And then the three and 10 are grouped together first before performing the subtraction in the final pace. This is shown in the picture below:

   

   Applying this method to find 7+9 gives

   \brainstorm{align} 7+nine &= seven + (10-i) \\ &= (7+x) - 1 \\ &= 17 - 1 \\ &= xvi. \end{align}

Making a x

Below is a table showing all the ways to add the numbers from ane to 9.

1. Each sum which is larger than x can be found past beginning making a x. For example, to detect viii + 5, we tin can write

   \begin{align} eight+five &= 8 + (2+3) \\ &= (viii+2) + 3 \\ &= 10 + 3 \\ &= 13. \cease{align}

   Explain why this reasoning works and apply this method to find 7 + 8. How can you visualize these equations using the table?
2. Calculation 9 to another single digit number can also be done by first making a x. For example

   \begin{align} 3+9 &= 3 + (10-1) \\ &= (iii+ten) - 1 \\ &= thirteen - 1 \\ &= 12. \end{align}

   Explain why this reasoning works and use this method to find 7+9. How tin can you visualize these equations using the table?

Source: https://tasks.illustrativemathematics.org/content-standards/tasks/955

Share this post