Author Archives: ctspedmathdude

Elapsed Time Part 2 – IEP Objective

I previously posted a scaffolded handout for identifying elapsed time between times on a pair of presented clocks (see image below of a page from the handout.)

A parent asked for a possible IEP objective. Here is one, along with some explanation.

Let’s start with a real life scenario many of our students may face. A municipal bus stops at a location a 7:04am. The individual is supposed to be at work at 7:30am. How much time does he have to walk to work from the drop off location? We can use this real life scenario to inform an IEP objective.

Here is a possible objective:

Given two times in a real life situation, presented with visuals and written or verbal context, Billy will identify the elapsed time. (For example: The bus drops you off at 7:23am and you have walk to work by 7:45am. How much time do you have to walk?). He will do so 9 out of 10 times correctly over 2 consecutive assessments. This would be aligned with the Common Core State Standard 3.MD.A.1.

The student can start with problems presented like what is shown in the handout I shared in the previous post as a step towards mastering the objective.

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Elapsed Time – Scaffolded Handout

Several elementary teachers shared that elapsed time was the hardest topic to teach. Here is a scaffolded handout to help compute elapsed time. The elapsed time setting is presented with two clocks, starting and stopping time. Below is an image for one of the more advanced pages of the handout. Here is how the strategy works.

  • The time is divided into minutes and hours.
  • The students identify how may minutes are needed in the first clock to get to the next hour.
  • Then they identify how many minutes are present in the second clock.
  • Finally, students determine the change in the hours.
  • I did not include a spot to place the total elapsed time as the focus is to identify how to break up the problem into parts.

The handout starts with a focus on identifying the minutes leading up to the the next whole hours and the minutes after the last whole hour. The task demand is increased incrementally with whole hours only, then only one or the other clock having minutes then both clocks having minutes.

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Rounding to Nearest 10 with Scaffolding Faded

The first page has maximum scaffolding with the student focusing only on which tens to round to. In turn, an a different element is the focus (e.g., writing the 0s then rounding) and then the scaffolding is increasingly faded.

Here is a link to a WORD document so you can change numbers AND add digits in the hundreds. Here it is in PDF for easier access.

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Introduction to Key Characteristics of Graphs Using a Rollercoaster

I introduce key characteristics with parabolas and use the analogy of a rollercoaster. Riding once (and never a again) the Superman rollercoaster at Six Flags New England got me thinking about this. At one point the rollercaster hits ground level (a zero) and then goes underground (negative y values).

Here is a handout I use for the introduction. Here are images showing how I use the handouts. The table helps students visualize the x-values and y-values when looking at the graph. The rollercoaster provides extra context for the various characteristics, e.g., increasing means the rollercoaster is going up. Note the scaffolding by adding context clues for each characteristics.

I start with max height of the rollercoaster. I highlight the actual graph first, then the y-values in the table. Then point out we are looking for the x-values for what we highlighted.

The issue of highlighting the vertex for the increasing and decreasing values would be addressed when writing the interval. The idea of the rollercoaster at the tip top provides context to develop the concept.

Similarly, I start with the zeroes. Again, highlight the graph, then the y-values, then the x-values.

The issue of highlighting the zeroes for the positive and negative values would be addressed when writing the interval. The idea of the rollercoaster at the ground level provides context to develop the concept.

I has been effective to have students highlight the parts of the respective axis when discussing the domain and range (not discussed yet). A common challenge is understanding that the x-values continue to the right or left when it appears they simply go down. To address this, I use a very wide parabola to show more lateral movement.

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Intro to Linear Functions and Proportionality Equations Using Context, Tables, and Graphs.

Here is a link to the handout. This approach uses the other representations to lead into the symbol representations – the equations. You can follow up by asking them the total for 0. This allows you to highlight the intercept.

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Introduction to Intercepts – Mini-lesson with Scaffolded Section for Computing

Here is a link to the document, with images showing the notes. This is a mini-lesson with the following components.

  • A fill in the blank for writing the lesson objective.
  • A Do now which serves as an initiation to the lesson. The y-intercept can be discussed in the context of buying 0 slices of pizza and paying $1.
  • A notes section on what an intercept is.
  • Practice session on identifying intercepts in graphs and tables.
  • A scaffolded steps section on computing the ordered pair of the intercepts.
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Introduction to Volume – Manipulatives (starting with perimeter and area)

Here is a Jamboard to introduce volume and units of volume. (See photo at very bottom for making a copy to edit.)

The students start with building an animal pen and shading in the space inside. The hands on approach and connection to prior knowledge of a fenced in area for animals sets the stage for actual measurement units in subsequent slides.

The photos below show how students will count out meters and square meters, adding a formal layer to the fence they built previously.

The following slide provides an entry point to understanding volume and units for volume. The students count out cubes, building on the counting of meters and square meters. The cubes were created using WORD Paint 3D. Here is an article I used to create these. For the grid that is tilted, I used functions on WORD – see this document. (I could have used Paint again.) I then show them the prism that is created but I am not discussing shapes yet to keep the focus on the concept of volume.

I then have students recreate the volume using NCTM’s Illuminations activity called Cubes.

Finally, I show examples of volume and move from cubic units to liters (litres – as I was initially teaching this lesson to a 5th grade class in India).

Make a copy and you can edit it.

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Graphing a Quadratic Function in Vertex Form – Scaffolded Handout

Here is a scaffolded handout. The first problem has additional scaffolding to convert from addition to subtraction and vise versa. The first problem does not require the transformation of the operations but the second one does.

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Completing the Square – Scaffolded Handout

Here is a link to a scaffolded handout with all the steps, including the step to convert the lead coefficient to 1. The scaffolding is complex because the math topic is complex. There is an example showing how to use the document.

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1 Step Word Problems Addition and Subtraction – Scaffolded

The Jamboard incorporates scaffolded handouts. The compare problems has two separate scaffolded sections. The first is to unpack the concepts of difference and compare, followed by writing a math sentence.

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