Using “Fact Sheets” for Next Year’s Math Planning

In the Smarter Balanced section of our website, each grade level (3-HS) has a link to the “Concept and Procedure (Claim 1) Fact Sheets”.  These fact sheets were designed to help you in your classroom planning around the skills students need to acquire to be considered proficient in the standards.  These Fact Sheets were designed by taking the Smarter Balanced Item Specifications released in September 2015 and summarizing the key information.

When you print out all the Smarter Balanced math item specifications for all grades, it will take about 1,500 sheets of paper!  What teacher has time to look through those?!  Our SMc Curriculum team took these 1,500 pages of information and created the “Fact Sheets” for you to use to inform your scope and sequence as you think about what you covered this year and what you will change for the 2016-17 school year.

Each “Fact Sheet” (see this Grade 8 example) includes the following information:

  • The Target’s (cluster) priority level – either be “Priority” or “Supporting”.  Priority targets make up 75% or more of the Claim 1 items on the CAT Smarter Balanced assessment.  These priority targets are the topics that should be addressed in our classrooms for conceptual understanding, procedural fluency and application.  In most cases, these priority targets should make up 75-80% of our scope and sequence for a school year!
  • The standards included in the Target – the actual Common Core State Standards the Target on Smarter Balanced refers to
  • The Achievement Level Descriptors (ALD) – the most important part!  The ALDs go from Level 1 to Level 4 with Level 3 considered a “proficient” or meeting level on Smarter Balanced.  Unlike a rubric, a Level 1 on a target’s ALD does not mean a student knows nothing about a standard. Instead it describes what a student should be able to do at the entry level of this on-grade-level target.  Level 1 descriptors are often a great goal for some students with special needs at the RTI Tier 2 or Tier 3 levels.  Each ALD after Level 1 is building on the previous levels.  Some components of the standards don’t actually appear in the ALDs until Level 4(i.e. mean absolute deviation in Grades 6 and 7).  This information can help you as a teacher not spend too much time on parts of the standards that can be reserved for extensions for certain students (Level 4 ALDs) while making sure you are scaffolding and hitting all the necessary components of the target (Levels 1-3).
  • Construct-Revelant Vocabulary – the vocab words used with students for a specific target.  There are times when you read the standards and you wonder, “Will they actually ask students to ‘decompose’ the number on the test?”  The list of construct-relevant vocabulary helps you answer that for each target by listing out the math vocabulary students may see in assessment items for this target.
  • Allowable Stimulus Materials – the way students will see the items.  This is just another piece to inform your instruction and make sure you are using the models they will be seeing at assessment time.  For example, if I know they might see a “function machine” in Grade 8 for Target E, I will want to make sure I include “function machines” in my instruction on functions.
  • Allowable Tools (for Grades 6-HS only) – is the calculator turned on or not?  The only allowable tool we focused on while creating these Fact Sheets was the calculator.  Other tools might be turned on for individual items, like a protractor for measuring angles, but whether or not a calculator is allowed for certain targets at the secondary grades (it is never turned on in Grades 3-5 in Smarter Balanced) is hugely important for guiding classroom work and assessment.  By examining when a calculator is made available to students in the summative assessment (Smarter Balanced or other large benchmarking assessment), you can have informed conversations with your collaborative teams about whether or not you will allow students to use a calculator in a unit for all, some or none of the work.

The item specifications also include sample items which we have chosen to share with you item slide shows (you can read about those here).  Let us know other thoughts on how to use the Fact Sheets or other information you feel would be helpful in your planning for instructing in a standards-based classroom!

Performance Task = Math Masterpiece

One of the components to the Smarter Balanced Assessment (SBA) is the performance task. Performance tasks allow students to engage in an extended problem solving situation. The rich task gives students an opportunity to show their mathematical and critical thinking knowledge and skills across different standards. Using all of these skills helps students on their path to college and career readiness. However, preparing students for this new component may seem overwhelming for some teachers.

The teachers at SMc Curriculum met at the beginning of the school year to determine how best to help teachers practice the performance task. We quickly found that doing a Google search for “performance tasks” would mostly either: 1) lead us to the practice tasks on the SBA website or; 2) lead us to really problem-solving tasks but not performance tasks when comparing to Smarter Balanced item specifications for a performance task. A good performance task that will allow students to practice the skills required by the Smarter Balanced Assessment must have questions that reach up to a Depth of Knowledge Level 4. Unfortunately, a majority of the resources we found online did not quite reach that far. So, we adapted! We took the tasks that were really good and appropriate for the grade level and extended the questions to include DOK levels 3 and 4 if they did not already exist. You can see our final products under the Performance Task tab.

Once you have a good performance task, then what? How can you instruct students in the skills of perseverance and attention to precision that is necessary for success on a performance task? One idea is to create a Math Masterpiece.

Supplies needed per partner or group:

  • a piece of construction paper (11 x 17 is preferable);
  • a glue stick;
  • a performance task cut into strips so that there are only 1 – 2 questions per strip.

How to run the activity:

  1. Students work in pairs on their first strip and bring it up to the teacher to get checked once they think they have completed the questions accurately. Consider asking students to have the writer on each strip rotate between the partners to ensure participation by all.
  2. The teacher will put a tick mark in the corner of the strip to indicate the partners have come up to get the task strip checked. If the answer is correct and the work sufficient, the tick mark is circled and the partners are given back that strip of paper along with the next strip of the performance task. If the answer is incorrect or the work is insufficient, the strip is handed back and a hint is given.
  3. Each time the teacher sees a strip, a new tick mark is added and scaffolded hints are given.  The tick marks help you as a teacher keep track of how students are doing on each part of the task.
  4. Strips of paper with tick marks circled are glued onto the construction paper to begin their Math Masterpiece. This process continues until all partner sets have all the strips of paper glued onto their construction paper.

A Math Masterpiece gives students the chance to practice skills they need for the performance task. By keeping their strips of paper and gluing them onto the construction paper students are able to see how their answers from the first part of a problem solving task will affect the rest of the problem. For teachers, once the Masterpieces are complete and hung around the room or collected, you will be able to look at the strips of paper to see trends. Did most of your students get only one tick mark circled on the first strip? That most likely means that students understand the content from that question. But what if the fourth strip took almost every groups 2 or 3 times of trying (indicated by the tick marks) before they got the correct answer? Perhaps the skill practiced by that part of the task could stand to be retaught in class the next day. By working together and breaking the larger performance task into smaller, more manageable pieces students tend to more easily persevere through the large task.

Hopefully the different performance tasks we have collected will prove helpful in your classroom. What other ways have you been able to help prepare students for the performance task?

Building Academic Math Vocabulary

Academic vocabulary in mathematics is often one of the largest barriers for students.  They understand the mathematics when asked to perform it in a specific way, but when asked using vocabulary they are not comfortable with, they may respond like they have never seen the content before!  Students must also be able to “attend to precision” (Math Practice 6) and understand that many terms in mathematics have similarities but yet the differences between the terms makes them not interchangeable.  For example, a third grader who does not know the difference between an expression and an equation may lose half-credit on a Smarter Balanced item if they type in an equation when asked for an expression.

In the Item Specifications for Smarter Balanced, the “construct relevant” vocabulary is listed for each Claim 1 (Concepts and Procedures) target.  We at SMc Curriculum have taken these vocabulary words and formatted them on individual cards to be used in the classroom to introduce or reinforce the vocabulary.

One way to use the vocabulary cards would be through a small group activity called Math Password.  In this activity, students (3-4 per group) are given a set of the vocabulary cards which they place upside-down in the center of their group.  One player draws a card and, without looking, holds it to his or her forehead for others to see.  The others in their group give him/her mathematical  clues on what their word until the person whose turn it is guesses the word or gives up.  Words that the clue-givers don’t know can be put into a separate pile.  At the end of the activity, each group is responsible for looking up the words they did not know from this pile and sharing one learning with the class.

You can find your grade-level vocabulary cards by selecting your grade-level in the Smarter Balanced section of this website and then clicking on the top button (purple) that reads “Concepts and Procedures (Claim 1) Fact Sheets and Vocabulary”.  The vocabulary cards will be the top link on this next page.  A sample of these cards (Grade 7) can be viewed here.

Smarter Balanced Item Slide Shows

In our Smarter Balanced resources here at CCSS Math Activities, we have taken the sample items Smarter Balanced Assessment Consortium has released in the Item Specifications (Version 3.0 September 28, 2015) and created slide shows for a variety of uses for teachers.  Some possible uses of these slide shows include:

  1. For Planning:  Prior to an upcoming unit of instruction, previewing sample items that corresponding to targets within the unit.  By previewing the way the questions are asked as well as the models and vocabulary used allows you to plan your unit to match the rigor, terminology and create flexibility in the way students are asked questions.
  2. For Instruction: The items can be used in a variety of activities in the classroom, both with topics that align to a current unit or as a method of spiral review.  An activity could be created where the slide shows are printed full page as “station” cards and students visit a variety of stations and complete the items at these stations.  Teachers can gather information about how the students have performed on different items to guide future activities and instruction.  Teachers can also choose one or two items that correlate to a certain lesson and insert these slides into their instruction.
  3. For Assessment:  The items in the slide shows can be used for both formative and summative assessment items.  One or two items on a current topic could be projected (or printed) and given to students as an exit card at the end of class period to gauge student understanding on a topic.  The items can also be duplicated (with or without numbers changed) on a unit assessment to measure student proficiency.
  4. For Smarter Balanced Review:  As the Smarter Balanced assessment approaches, it is helpful for students to see a variety of items that are not just from the current unit.  You can pick items for a variety of slide shows and paste them into one presentation.  Students could complete the problems on individual white boards or as a team competition.

These are just a few ideas for implementing this tool in the classroom.  Feel free to comment if you have had success using these slide shows in the mentioned ways or other ways!